Activity Reports ofMaterials Design through Computics:
Complex Correlation andNon-equilibrium Dynamics
July, 2015

Scientific Research on Innovative Areas by MEXT
during July 2010 and March 2015

PREFACE

This booklet is a report of a research project ``Materials Design through Computics: Complex
Correlation and Non-equilibrium Dynamics” conducted as a ``Scientific Research on Innovative
Areas” supported by Ministry of Education, Culture, Sports, Science and Technology (MEXT),
Japan. The project started in July of 2010 and successfully ended in March of 2015. The research
project was conducted by 45 research groups including 135 researchers in total.
Computational approach to science was started around 1960s. An approximation called HartreeFock approximation in describing the electron-electron interaction was developed and applied to avariety of molecules in 60s with the aid of computers.1 Density-functional theory (DFT) innovatedby Walter Kohn, Pierre Hohenberg and Lu Sham in 1964 had been developed in 60s and 70s andprovided a firm theoretical framework and actual prescriptions to calculate electron states of not
only molecules but also condensed matters. 2 Today, computational science is recognized as thethird approach which complements the previous two approaches, experimental and theoretical, andallows us to access new aspects of phenomena in nature.
One of the typical stances of people in the field of computational science has been solving the basic
equations with the aid of computers. Computers themselves have been black boxes for scientists inphysics and chemistry. Collaboration between physical/chemical science and computer science orinformation technology has been very rare.
Current dramatic change in computer architecture is awakening scientists with this happy and oldstance. The performance of a single CPU or a compute core is already saturated, corresponding to
the limitation of Moore’s scaling law on the device integration. Then the only way to make asupercomputer is gathering a huge number of compute cores and nodes and connecting them withhigh speed networks. The K computer at Kobe, Japan, for instance, which shows the peak
performance of 10.62 PetaFLOPS is composed of 640 thousands compute cores connected by the
6-dimensional Tofu (Torus Fusion) networks. In the coming supercomputers, in addition to suchmany-core massively parallel architecture, some hardware accelerators should be introduced. 3
Owing to this complexity in the current and next computer architecture, it is almost impossible toexploit potential power of the supercomputers, unless we tune our application codes progressively.
The tuning in this context means not only improvements of the existing application codes but also
1

The ``super”-computer in those days has the performance of only 1 MFLOPS (Mega FLoating-point
Operations Per Second) [CDC 6600, (1964)], being much slower than the current personal computers.
2 A systematic calculations for the structural characteristics and energy bands for simple metals are
performed and documented in 1978 (V. L. Moruzzi, J. F. Janak, and A. R. Williams, CalculatedElectronic Properties of Metals, Pergamon Press)
3 Top500 supercomputing sites: http://www.top500.org/
idevelopments of new algorithms suitable to the parallel architecture. The algorithms to solve theissues rely on mathematical methods. Hence the tuning includes innovation of new mathematicalmethodology to tackle most important scientific issues and then its implementation on the newcomputer architecture. This requires an effort to analyze basic equations describing phenomena innature and innovate new algorithms. These efforts we call compuics. Mathematics has contributed
a lot to progress in science since Principia by Isaac Newton. Computics in this century may be a
new approach to clarify underlying principles in nature.
This project focuses complex correlation and non-equilibrium dynamics in phenomena in materials.
Properties of materials are determined by competition of various physical and chemicalinteractions: Covalency, ionicity and metallicity are typical ingredients to determine properties ofmaterials. Electron Correlation is also an important factor. In nano-materials and structures,nanoscale shape decisively affects the relevant wave-functions and then induces new properties
hidden in bulk structures. We call this complex correlation. Femtosecond laser irradiation onmaterials, for instance, causes electron excitation and then ionic motions. It occasionally induces
structural transformation. This is a new way of materials design by utilizing non-equilibrium
dynamics.
In order to reveal complex correlation and non-equilibrium dynamics, developments ofcomputational schemes along three axes are required. First, in the nanometer scale objects,
quantum effects are important. On the other hand, 10-cube-nanometer objects are composed of 100
thousands atoms. Quantum mechanical electronic structure calculations for 100-thousands atoms
are certainly unprecedented. This is a challenge along the space axis. Second, the electron
excitation followed by the ionic motions is a multi-scale phenomena: Electron excitation takes
place in femtosecond timescale and ionic motions are in picoseconds; structural transformation
requires nano-, micro, or even mili-seconds. We are challenged along the time axis. Thirdly,
materials are composed of many electrons and nuclei. In describing their electronic properties,
materials are regarded as interacting electron systems. Accurate calculations based on quantum
mechanical many-body theory are indispensable. This is a challenge along the accuracy axis. In
our projects, many efforts have been done on these lines.
This report consists of three parts. In Part I, activities in ``Architecture and Algorithms of High
Performance Computing” are reported. They are mainly in the field of computer science and/or
applied mathematics. But the collaborations between this field and the field of computational
materials physics are also reported. Principal investigators in this Part are Mary Inaba (Universityof Tokyo), Daisuke Takahashi (University of Tsukuba) and S.-L. Zhang (Nagoya University).
Activities of other two research groups performed during 2013-2014 are also reported in Part I.
Part II is devoted to the activities in ``New Development in Density-Functional Theory”. Densityii

functional theory (DFT) has been contributing tremendously to reveal materials properties in these
decades. The exchange-correlation functional which describes many-body effects is still improved
and widens a set of the target materials which are described by DFT. Efforts along the space axis
and time axis are also documented in Part II. Principal investigators in this Part are Atsushi
Oshiyama (University of Tokyo), Shinji Tsuneyuki (University of Tokyo), Satoshi Watanabe(University of Tokyo), Hiroshi Nakanishi (Osaka University) and Takahisa Yamato (Nagoya
University). Activities of other nine research groups including experimental works performed
during 2013-2014 are also reported in Part II.
In Part III, activities in `` Beyond Density-Functional Theory” are reported. Current DFT has
certainly limitation. In particular, materials with strong electron correlation are difficult to betreated by the current DFT. Theory and computational schemes which are beyond DFT are certainly
important. In our project, several efforts based on the perturbation theory, a new down-folding
approach and so forth have been done. Principal investigators in this Part are Masatoshi Imada(University of Tokyo), Yasutami Takada (University of Tokyo) and Kazunori Sato (Osaka
University). Activities of other seven research groups including experimental works performed
during 2013-2014 are also reported in Part III.
Research activities achieved by other ten research groups during the period of 2011 – 2012 are notincluded in this booklet due to the limitation of the pages. The activities are accessible on thecomputics web page, http://computics-material.jp/index-e.html. The researchers in the ten projects
include I. Hamada (NIMS), M. Hase (University of Tsukuba), H. Hirayama (Tokyo Institute ofTechnology), H. Ono (Kyushu University), F. Shimojo (Kumamoto University), M. Kitajima(National Defense Academy), M. Saito (Kanazawa University), H. Tanaka (Osaka University), Y.
K. Zhou (Osaka University) and T. Kotani (Tottori University).
The online version of this report is available thorough http://computics-material.jp/index-e.html. I
wish this booklet contributes to the progress in a new growing field, computics.
Tokyo, July 2015

Atsushi Oshiyama
LeaderMaterials Design through Computics:
Complex Correlation and Non-equilibrium Dynamics

iii

CONTENTS

Part I

Architecture and Algorithms of High Performance Computing

High-Speed Ultra-Low-Power Simulation Methodology for Material Science
M. Inaba, H. Imai, R. Suda, K. Hiraki····························································································· 1
Numerical Computation Algorithms for Large-Scale Parallel Environment
D. Takahashi, T. Imamura, H. Tadano ··························································································· 11
Fast Solution for Ultra-Large Scale Systems as a Basis of Computational Materials Science
S.-L. Zhang, T. Sogabe, I. Imahori, T. Miyata, Y. Yamamoto························································· 22
Development of High Performance Parallel Eigensolvers for the Needs in Computational Quantum
Science
T. Sakurai ······································································································································ 33
Hybrid Mathematical Principles for Ultra-Large-Scale Massively Parallel Electronic Structure
Calculations
T. Hoshi ········································································································································· 37

Pat IINew Development in Density-Functional Theory

Density-Functional Approach to Atomic and Electronic Structures and their Dynamics in NanoStructures
A. Oshiyama, J.-I. Iwata, T. Ozaki, T. Miyazaki, E. Tsuchida ······················································· 45
Studies on Structure Sampling and Non-Equilibrium Dynamics Using Ab-Initio Molecular
Dynamics Methods
S. Tsuneyuki, Y. Yoshimoto, J. Yamauchi, M. Otani ···················································· 59
Nanoscale Non-Equilibrium Electric Transport Dynamics Based on Density Functional Theory
S. Watanabe, K. Watanabe, S. Souma, T. Ono ··············································································· 71
New Properties of Materials Probed by Proton and Muon, and their Quantum Dynamics
H. Nakanishi, H. Goto, M. Geshi, M. Wilde, W. Dino,
H. Kasai, K. Fukutani, H. Kikuji ································································································· 85

iv

Reaction Analysis and Conformational Sampling for Multidimensional Large Scale Systems
T. Yamato, A. Mitsutake ················································································································· 99
Developments of First-Principles Multiscale Simulation for Coupled Dynamics of Light-Wave andElectrons in Dielectrics
K. Yabana ····································································································································· 111
Hybrid-Density-Functional Theory for Magnetic Materials
Y. Gohda ······································································································································· 117
Dynamics of Electron, Spin and Heat Transport through Single Atomic and Molecular Junctions
M. Kiguchi ··································································································································· 121
Electron-Phonon Coupling Dynamics and High-Sensitive Detection of Nano-Scale Phonon
Wavepackets in Carbon-Based Materials
J. Takeda .................................................................................................................................... 125
First-principle molecular dynamics analyses on nonlinear optical properties change of Si nano-dot
Y. Shigeta, K. Shiraishi, M. Nakano ···························································································· 129
De novo design of the functional transition metal proteins using a coiled-coil scaffold
Y. Takano ····································································································································· 134
Construction of Material Design System on Next-Generation Density Functional Theory
Y. Imamura ·································································································································· 141
First Principles Simulation of Nonequilibrim Transport at Nano-contact and Design of Functional
Materials
H. Nakamura ······························································································································· 145
Reactions Analysis of Plasma with Self-Assembled Monolayer
M. Shinohara ······························································································································· 152

Part III

Beyond Density-Functional Theory

Frontiers of Ab-Initio Effective Models and Correlation Science
M. Imada, T. Miyake, K. Nakamura, T. Oguchi, R. Arita, S. Ishibashi,
A. Fujimori, S. Shin ····················································································································· 156v

Many-Body Theory from First Principles
Y. Takada, K. Shirai, R. Maezono, H. Maebashi, M. Sakurai······················································ 170
Computational Design and Realization of Spintronics Materials
K. Sato, T. Oda T. Nozaki, M. Ogura··························································································· 182
MBE Growth and Magnetic Properties of Diluted Magnetic Semiconductors Based on II-VI and
IV-VI Compounds
K. Zhang, S. Ishitsuka, T. Domon, R. Sakurai, R. Akiyama,
K. Kanazawa, S. Kuroda ············································································································· 194
Surface Plasmons and Magneto-Optics in Metal/Magnetic Quantum Wells
H. Matsui ····································································································································· 198
Development of Nonequilibrium Dynamical Mean-Feld Theory and its Application to LowDimensional Strongly Correlated Systems
N. Tsuji ········································································································································ 202
Effect of Electron-Phonon Couplings on Electronic Structures and Material Design
T. Koretsune, S. Saito ·················································································································· 206
Development of Computational Code of Electron Excitation Dynamics in Green’s Function
MethodK. Ohno, S. Ono, R. Kuwahara ··································································································· 210
Large Scale First-Principles Calculations on Transition Metal Oxide Superlattices
F. Ishii, M. Saito ·························································································································· 214
Development of Quantum Multi-Component Molecular Theory and its Application to Material
DesignM. Tachikawa ······························································································································ 217

vi

Part I
Architecture and Algorithms ofHigh Performance Computing

High-speed ultra-low-power simulation methodology
for material science
Mary Inaba1,2, Hiroshi Imai1,2, Reiji Suda1,2, Kei Hiraki1,3
The University of Tokyo1
Co-Investigator(Kenkyu-Buntansha)2
Co-Investigator(Renkei Kenkyusha)3

1. Outline	  2011 - 2014 Research Project
We performed studies on High-speed ultra-low-power simulation methodology formaterial science. The main goal of the study is to establish technologies forhigh-speed computation, high-speed network and high-speed memory systems toaccelerate simulations in material science area. Our focus is the use of FPGA (field
programmable gate array) for accelerating computation, network operation andmemory access acceleration.
During 2010 – 2014 periods, we have constructed two computation accelerator, two
network accelerator and several other FPGA board to perform network and memory
emulation.

As results of these studies, we have established basic architecture for

the FPGA based platform for simulation in wide application area including materialscience.
Another important contribution of this project is establishing a new educational
unit, “Computing Science Educational Course” as a joint activity between thedepartment of computer science, graduate school of information science andtechnology and the department of physics, graduate school of science at the
University of Tokyo. This educational course is a result of collaboration in thisproject.

2.

Research topics in 2010 – building basic structure for the study.

2010 was the starting year of this project. We compiled the R&D team, then we

1

performed

study

on

measurementsofprocessor

architecture

and

power

consumption, constructing FPGA based computation accelerator, high-efficiency
data-transfer on long distance high-speed internet, high-speed high-productivity
language HPC Ruby and fast GPGPU-host data-transfer mechanisms.
Figure 1 shows results of GPGPU-host data-transfer optimization, where parallel
data-transfer is scheduled to minimized waiting time of the PCIE bus connecting
GPGPUs and a host. Evaluation is performed using 8192×256 matrix multiply
with Nvidia GPGPU.

Fig 1. Optimization of GPGPU-host data-transfer
3. Research topics in 2011 – FPGA based accelerator and HPC Ruby
We developed a computation accelerator that use very large FPGA that have both a
PCIE interface and a 40Gbps Ethernet interface (Figure 2). Very high-speed
Ethernet connection (40Gbps) gives very short connection latency between
computation accelerators (less than 1 μsecond) compared to a large latency using
PCIE (about 10 μsecond including host drivers). Short latency connections are
essential to realize scientific applications that have strong-scaling computation
behavior.
In 2011 we also develop HPC ruby system that consists of static HPC rubycompiler, type inference system and runtime systems. Since Ruby is a dynamic
weakly typed language with very-high productivity, the only shortcoming of Ruby
was its very slow execution speed. The reason why original Ruby is so slow is that
Ruby is a weakly typed dynamic language that require runtime analysis of data
type and variable bindings. Figure 3 shows speed-up ratio of HPC-Ruby vs. Ruby
1.8 on various numerical application programs. This figure shows clear advantage
of static analysis in dynamic language for numerical computations.

2Fig 2. Block diagram of Computation

Fig 3.

Accelerator

Speedup ratio of HPC Ruby fromoriginal Ruby 1.8

4,Research topics in 2012 – Research on deficiency of compilers and processors
We investigate requirements for future HPC processor that aims EXA flops bymeasuring power performance of SPARC64 XIfx, Intel IvyBridge, IBM Power7 and
IBM BlueGene/Q processor. The results show large difference of absoluteperformance and power efficiency. In order to investigate the performancedifference in detail, we compared performance of programs using several different
compilers (Intel C compiler, GCC and Fujitsu C compiler).
Figure 4 shows performance difference in SPEC CPU2006flt performance of
SPARC64 IXfx with FCC and Intel IvyBridge Xeon with Intel compiler. Due to thelimitation of the space we omit results from other benchmarks and othercombination of processors and compilers, these results shows large performancedifference even if they are normalized by CPU clock.
The largest reason of performance difference is integer and memory performanceof processors. As shown in figure 5, even in floating point heavy applications, more
integer and memory instructions than floating point arithmetic instructions are
executed in many applications. As a result, integer and memory performance ismore important than floating point performance especially in simulations inmaterial science where the problems are less regular than commonly used CFD or
FEM execution.
We further investigate the cause of integer and memory performance. We foundthat part of integer/memory performance is caused by the difference in optimizationof compiled codes.

3Figure 4. Performance comparison of SPARC64 IXfs with Fujitsu C compiler andIntel Xeon E5-2687 with Intel C compiler . Benchmark programs are SPEC
CFP2006.

size=S	
 
ua
mg
is

Int

ep

Fp

bt
0%

Figure 5.

20%

40%

60%

80%

100%

Percentage of integer and memory instructions executed in NASPAR

benchmarks with Intel C compiler.
We compared the performance and object codes of (1) GCC 4.5.3, (2) Intel Composer XE
2013 and Fujitsu C compiler V1.2.1.
For example, we compiled the source code as:
Proc_3 (Rec_Pointer *Ptr_Ref_Par){ if (Ptr_Glob != Null)*Ptr_Ref_Par = Ptr_Glob->Ptr_Comp;4

Proc_7 (10, Int_Glob, &Ptr_Glob->variant.var_1.Int_Comp);}
FCC outputs 22 instructions, GCC outputs 15 instructions. The main performance andcode size difference between these two are-

Unnecessary save/restore-

Partial use of available addressing modes of instructions-

Address calculation is performed by combination of general-purpose instructions-

FCC does not use brz branch instruction. Instead it use a combination of cmp and be

These absence of basic optimization cancelled many complicated optimization include in
FCC.
Consequently, INT performance / power consumption becomes worse than expected.

Figure 6.

Yearly progress in INT/memory processing speed/W
Red line shows that of SPARC64 IXfx (FX10)

Figure 6 shows yearly progress in INT/memory processing speed /W by executing
Dhrystone benchmarks for various processors. This figure shows about 8 times
MIPS/W improvement is necessary to catch up latest efficient processors, and morethan 16 times is necessary to construct Exa Flops system only with general purpose
processors.
５．Research topics in 2013 – FPGA base network accelerator prototype
In 2015, we developed 2nd

FPGA based network accelerator that use large-scale

FPGA with ARM processor cores (Figure 7). Interconnections between FPGA boards

5are realized by 24-port SATA 6Gbps connections that can be dynamicallyre-configured. This FPGA based network emulator have been used to evaluatevarious design parameters of an interconnection network in a parallel system andnetwork on chip (NoC) for many-core processor systems.
Figure 8 shows an example of resource evaluation for various network topologies.
As shown in Figure 8, mesh, ring, torus and shuffle-exchange network have almost
the same amount of FPGA hardware resource because major part of the resource isused to make router buffers.

Figure 7.

FPGA based network accelerator and its block diagram

Figure 8 FPGA hardware budgets of different network topologies
6. Research topics in 2014 -- Optimization of hardware resource for networks
During 2014, we conducted studies on (1) Network performance optimization using
Genetic Algorithm, (2) FPGA based network accelerator/emulator (continued from2012,2013), (3) reduction of power consumption of networks by dynamic routing
function,(4) FPGA based computation accelerator for machine learning by neural6

networks and (5) Software DSM to access PGAS with LRC protocol.

Fig 9. Optimized to random traffic

Fig 10. Optimized to transpose

Figure 11. Torus network optimized for various traffic
Due to space limitation, we showed results of Network performance optimization
using Genetic Algorithm.
Almost all the interconnection network, especially network on chip(NoC) has been
designed manually without optimization of the width of network links and capacityof routing nodes. As a result, performance and power consumption of networks are
not fit to their major applications.
We adopt genetic algorithm (GA) to optimize heterogeneous networks thatmaximize performance and power efficiency. In this study, all the links can beselected from fast links and slow links where the bandwidth is 2 times different.
Also, all the routers can be selected from large (buffer) routers and small routers.
We applied GA to find the most optimized configuration of the network to transfer acertain defined traffic patterns such as random, transpose, all to all etc. We perform
two optimization with GA, where the one assumes X and Y symmetric property ofthe target traffic,, and the one without this assumption.
The target topology of the network is either 2-D mesh or 2D-torus. Figures 8 and 9is the result for 2-D mesh and Figure 10 is for 3-D torus.	
  These results show that
equally distributed mesh or torus is far worse from optimized configuration. Thismeans, commonly used mesh network or torus network of7

many core processors

are not optimal and gives worse power consumption.
We are now performing more detailed evaluation using real network traffic ofmajor application programs.
Selected Publications 2010 -- 2015[1] Hisanobu Tomari, Mary Inaba, Kei Hiraki, “Compressing Floating-Point
Number Stream for Numerical Applications”, The First International Conference on
Networking and Computing, Hiroshima, 2010.
[2] Seongsoo Moon, Mary Inaba, “Modeling and simulation for EMS”, 3rdInternational

Conferenceon

Wireless

Information

Networks&

Business

Information System (WINBIS'11), pp.94-100, Kathmandu Nepal, 2011.
[3] T. Tanuma, H. Imai and S. Moriyama, “Revisiting Hyperbolic Voronoi Diagramsfrom Theoretical, Applied and Generalized Viewpoints”, 2010 International
Symposium on Voronoi Diagrams in Science and Engineering (ISVD '10), pp.23-32,
Quebec, 2010.
[4] Kamil Rocki, Reiji Suda, “MPI-GPU Monte Carlo Tree Search”, IEEE 2011
International Conference on Information and Computer Applications(ICICA), Dubai,
UAE, 2011.
[5] Kamil Rocki and Reiji Suda, “Massively Parallel Monte Carlo Tree Search”,
Proceedings of VECPAR 2010, 9th International Meeting High Performance
Computing for Computational Science, 2010.
[6] Yasuo Ishii, Mary Inaba, Kei Hiraki, “Access Map Pattern Matching for High
Performance Data Cache Prefetch”, The Journal of Instruction Level Parallelism,
Vol.13, (ISSN 1942-9525), pp.1-24, 2011.
[7] R. Suda, K. Naono, K. Teranishi and J. Cavazos, “Software Automatic Tuning:
Concepts and State-of-the-Art Results”, Chapter 1 of “Software Automatic Tuning:
From Concepts to the State-of-the-Art Results”, Springer, Sep. 2010. pp.3-18.
[8] R. Suda, “A Bayesian Method of Online Automatic Tuning”, Chapter 16 of“Software Automatic Tuning: From Concepts to the State-of-the-Art Results”,
Springer, Sep. 2010.
[9] Junichiro Makino, Hiroshi Daisaka, Toshiyuki Fukushige, Yutaka Sugawara,
Mary Inaba, Kei Hiraki, “The performance of GRAPE-DR for dense matrix
operations”, the International Conference on Computational Science, ICCS 2011,
Nanyang, Singapore, 2011.
[10] Yasuo Ishii, Keisuke Kuroyanagi, Takeo Sawada, Mary Inaba, Kei Hiraki,“Revisiting Local History for Improving Fused Two-Level Branch Predictor”, 2nd

8

JILP Workshop on Computer Architecture Competitions (JWAC-2): Championship
Branch Prediction, San Jose, USA, Jun4, 2011.
[11] Tomohiro Sonobe, Mary Inaba, Ayumu Nagai, “Counter Implication Restart”,
Pragmatics of SAT 2011,

Ann Arbor, USA, Jun.18, 2011[12] Tomohiro Sonobe, Mary Inaba, “Counter Implication Restart for Parallel SAT
Solvers”, Learning and Intelligent Optimization Conference (LION6), Paris, France,
2012[13] Yasuo Ishii, Kouhei Hosokawa, Mary Inaba, and Kei Hiraki,“High Performance
MemoryAccessSchedulingusing

Compute-Phase

Prediction

andWriteback-Refresh Overlap”, 3rd JILP Workshop on Computer Architecture
Competitions (JWAC-3): Memory Scheduling Championship (MSC), 2012.
[14] Tomohiro Sonobe and Mary Inaba,“Division and Alternation of Decision
Variables”, Pragmatics of SAT 2012, 2012.
[15] Yasuo Ishii, Mary Inaba, Kei Hiraki,“Unified Memory Optimizing Architecture:
Memory Subsystem Control with a Unified Pedictor”, 26th International
Conference on Supercomputing, 2012.
[16] Tomohiro Sonobe and Mary Inaba,“Portfolio with Block Branching for Parallel
SAT Solvers”, Learning and Intelligent OptimizatioN conference (LION7), 2012.
[17] Toru Motoya and Reiji Suda, “Conjugate Gradient Methods Relieved for Inner
Product Communication Latencies”, International workshop on HPC, Krylov
Subspace method and its applications, 2012.
[18]

Reiji

Suda,“Toward

TunableMulti-Scheme

Parallelization”,

SIAM

Computational Science and Engineering, 2013.
[19] V. Suppakitpaisarn, M. Edahiro, and H. Imai,“Fastest Multi-Scalar
Multiplication Based on Optimal Double-Base Chains”, World Congress on Internet
Security (WorldCIS-2012), 2012.
[20] N. Fu, A. Hashikura and H. Imai,“Geometrical treatment of periodic graphswith coordinate system using axis-fiber and an application to a motion planning”,
The 9th Int. Symposium on Voronoi Diagrams in Science and Engineering, 2012.
[21] C.Chuengsatiansup, H.Imai, and V.Suppakitpaisarn,“Evaluating Optimized
Computation in Double-Base Chain for Efficient Elliptic Curve Cryptography”, 15th
Japan-Korea Joint Workshop on Algorithms and Computation, 2012.
[22] V. Suppakitpaisarn, M. Edahiro, and H. Imai,“Fast Elliptic Curve
Cryptography Using Optimal Double-Base Chains”, the International Conferenceon Informatics & Application (ICIA2012), 227, pp190-204, 2012.
[23] V. Suppakitpaisarn, M. Edahiro, and H. Imai,“Optimal Elliptic Curve Scalar

9Multiplication Using Double-Base Chains”, International Journal of Digital
Information and Wireless Communications (IJDIWC), Vol. 2, pp115-134, 2012.
[24] T. Satoh, F. Le Gall, and H. Imai,“Quantum network coding for quantum
repeaters”, Phys. Rev. A 86, 032331, 2012.
[25] Norie Fu, Akihiro Hashikura, and Hiroshi Imai,“Proximity and Motion
Planning on 1-Rigid Planar Periodic Graphs”, Transactions on Computational
Science, Vol.XX (LNCS Vol.8110), pp.72–91, 2013.
[26] Reiji Suda, Luo Cheng, Takahiro Katagiri,“A Mathematical Method for Online
Autotuning of Power andEnergy Consumption with Corrected Temperature
Effects”Procedia Computer Science, Vol 18, pp 1302-1311, ISSN 1877-0509, 2013.
[27] Kei Hiraki, Mary Inaba, Akira Kato, “Efficient utilization of 40/100 Gbps
long-distance network by a single TCP stream”, TERENA NETWORKINGCONFERENCE (TNC2013), 2013.
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Keigo Nitadori, Steven Rieder, Cees de Laat, Stephen McMillan, Kei Hiraki, Stefan
Harfst,“The Cosmogrid Simulation: Statistical Properties of Small Dark Matter
Halos” The Astrophysical Journal, DOI: 10.1088/0004-637X/767/2/146.
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ICS 2014: 171, 2014[35] Tomohiro Sonobe, Shuya Kondoh, Mary Inaba, “Community Branching for
Parallel Portfolio SAT Solvers,”

SAT 2014: 188-196, 201410

Numerical Computation Algorithms for Large-scale Parallel Environment
Daisuke Takahashi1, Toshiyuki Imamura2, Hiroto Tadano1
University of Tsukuba1, RIKEN, Advanced Institute for Computational Science2
Research was conducted on the use of large-scale parallel environments, whose
performance exceeded 10 petaflops, for numerical computation algorithms. These
included the fast Fourier transform (FFT), quadruple- and octuple-precision basic linear
algebra subprograms (BLAS) on graphics processing units (GPUs), triple- andquadruple-precision floating point operations on GPUs, sparse matrix-vector
multiplication on GPUs, and a real symmetric eigenvalue solver operating in a CPU +GPU environment. An evaluation was also carried out of the performance of a newly
developed eigenvalue solver and an existing solver in a GPU environment, ahigh-performance eigenvalue solver employing third-generation NVIDIA GPUs, solution
acceleration of simultaneous linear algebraic equations using the Block Krylov algorithm,
accuracy improvement of Block Krylov partial space iterative methods, andperformance-tuning methods.

1. Introduction
As of March 2015, five supercomputer systems (one of which incorporate GPUs) haveappeared with performances exceeding 10 petaflops. Future mainstream supercomputers are
expected to incorporate multi-core CPUs as well as accelerators such as GPUs as computation
nodes, of which there will be several thousand or several tens of thousands.
However, supercomputers whose configurations incorporate multi-core CPUs (and multipleGPUs) are beginning to experience difficulty in gaining high execution efficiency as aconsequence of the increased processor core count and deficient memory bandwidth per
operational performance unit. Therefore, the parallel numerical computing algorithms andperformance-tuning methods proposed until now will be insufficient to meet futurecomputational science challenges.
The following research topics have therefore been selected in the present study, andperformance-tuning methods were also investigated:- Parallel three-dimensional Fast Fourier transform (FFT) algorithm for next-generation
supercomputers- Performance evaluation of quadruple- and octuple-precision BLAS implementation on
GPUs- Acceleration of sparse matrix-vector multiplication by automatic storage format selection
with GPU- Performance evaluation of parallel two-dimensional FFT using Intel AVX instructions- Study of triple- and quadruple-precision floating point operations with GPU- Optimization and performance tuning technique for a numerical software on Multi-{core,socket, GPU} computing environments- Development of efficient Block Krylov subspace methods for linear systems with multiple
right-hand sides and their applications
These parallel numerical computing algorithms and performance-tuning methods are11expected to allow computation on a scale previously considered impossible when they areapplied to actual programs used in computational material science.

2. Parallel three-dimensional FFT algorithm for next-generation supercomputers
A typical decomposition for performing a parallel three-dimensional FFT is slab-wise. In thiscase, a three-dimensional array x(Nx, Ny, Nz) is distributed along the third dimension Nz.
However, Nz must be greater than or equal to the number of MPI processes. This becomes anissue with very large node counts for clusters.
To solve this problem, a scalable framework for three-dimensional FFTs on Blue Gene/L
supercomputer and a three-dimensional FFT on the six-dimensional network torus QCDOC
parallel supercomputer have been proposed. The parallel three-dimensional FFT algorithms use
the three-dimensional decomposition for the three-dimensional FFT. These schemes require
three all-to-all communications.
We have proposed a two-dimensional decomposition for the parallel three-dimensional FFT.
This requires only two all-to-all communications.
In addition to reducing the communication time through two-dimensional decomposition,
overlapping operations and communications further improved the performance compared toprevious implementations.
The parallel three-dimensional FFT performance for the T2K-Tsukaba is shown in Fig. 1.
Performance improvement through overlapping of operations and communications is evident.

Fig. 1. Parallel three-dimensional FFT performance for T2K-Tsukuba(64 nodes, 256 MPI processes × 4 threads)

2. Performance evaluation of quadruple- and octuple-precision BLAS implementation on GPUs
BLAS functions supporting quadruple- and octuple-precision operations were implemented
on GPUs and evaluated. For quadruple- and octuple-precision operations, 2 double-type
double-precision numbers were linked to represent quadruple-precision numbers indouble-double (DD) type quadruple precision operations, and 4 double-type double-precision
numbers were linked to express octuple-precision numbers in quad-double (QD) type octuple
precision operations.
Performance evaluation with an NVIDIA Tesla C2050 revealed that quadruple-precision
AXPY was accelerated approximately 9.5 times and octuple-precision AXPY was accelerated

12

approximately 19 times compared to an Intel Core i7 920 for the same operations. In addition,
quadruple-precision general matrix multiplication (GEMM) was accelerated approximately 29
times compared to the CPU, and octuple-precision GEMM was accelerated approximately 24
times. The quadruple-precision AXPY for the Tesla C2050 was only 2.1 times the
double-precision operations, and the increased computing times for double-precision operations
with the GEMV and GEMM were also greatly reduced in comparison to the CPU case.
When PCI-Express (PCIe) data transfer times were considered, double-precision GEMM
showed a tendency to be rate-limited by the PCIe data transfer rate, but quadruple- andoctuple-precision GEMM essentially eliminated this limit.

3. Acceleration of sparse matrix-vector multiplication by automatic storage format selection
with GPU
Sparse matrices are frequently the target of simultaneous linear algebraic equations inscientific and engineering computations. Solutions are derived in this case through iterative
methods, and thus acceleration of sparse vector-matrix multiplication is desired. Various storage
formats for sparse matrices have been proposed. Depending on the target sparse matrix,
performance differences emerge for sparse matrix-vector multiplication. Since sparse
matrix-vector multiplication involves more memory access than computation operations,
optimum storage format selection is important for enhancing GPU performance.
This research focused on automatic selection of the storage format for sparse matrices inorder to enable acceleration of sparse matrix-vector multiplication. As a preliminary assessment,
sparse matrix-vector multiplication was implemented with four types of storage formats for
performance evaluation. Consequently, performance differences were evaluated based on
variances in non-zero elements and percentages of non-zero elements. Based on the results, analgorithm was implemented for the automatic selection of the optimum storage format, andsolutions of simultaneous linear algebraic equations employing iterative methods were used forevaluation.
According to the performance evaluation results with an NVIDIA Tesla C2050, optimum
storage format selection occurred for many of the sparse matrices employed, and enabled speedsthat were comparable to or higher than that achieved using CUSPARE directly with the CRS
format. In addition, the proposed automatic selection was found to be effective even for very
low numbers of iterations.

4. Performance evaluation of parallel two-dimensional FFT using Intel AVX instructions
Recent processors such as the Intel Xeon SSE, SSE2, SSE3, SSSE3, SSE4, and AVX; theMotorola PowerPC AltiVec; and the Fujitsu SPARC64 Viiifx HPC-ACE often incorporate Short
Vector SIMD commands to accelerate processing of floating point operations.
The data supply performance of recent processors, however, relies on cached memory. Even
if Short Vector SIMD commands are used, memory access optimization needs to be conducted.
The FFT library FFTE was implemented to improve the performance of the FFT kernel portion
by employing AVX commands, and by using a six-step FFT block algorithm, the highperformance of FFTE was maintained even when the data could not fit within the cachedmemory.
The parallel two-dimensional FFT performance is shown in Fig. 2 for the Intel Xeon E5-2670(Sandy Bridge 2.6 GHz, 20MB L3 cache, 2 CPUs, 16 cores, 128 GB DDR3-SDRAM). It can beseen that the performance of FFTE is higher than that of FFTW.

13

Fig. 2. Parallel two-dimensional FFT performance with Intel Xeon E5-2670(Sandy Bridge-EP 2.6 GHz, 20 MB L3 cache, 2 CPUs, 16 cores)

5. Study of triple- and quadruple-precision floating point operations with GPU
In recent years, memory and network bandwidth shortages have become an issue as processor
performance improves. When precision was insufficient in floating point operations withdouble-precision operations, the employment of quadruple-precision operations had beenstudied previously, but cases are believed to exist where triple-precision operations with lessdata-access volume can be valid. In the present study, triple-precision numbers were treated as a
combination of double and single numbers, which were stored separately (D+S type).
Performance was evaluated by implementation of a triple-precision BLAS routine on a Tesla
M2090 GPU. D+S-type operations implemented a method in which some operations were
performed as single-precision operations for the double-double type quadruple-precision
operation (DD-type operation) algorithm. Type conversion between double-precision numbers
and single-precision numbers occurred frequently, however, and D+S-type operations became
higher in cost than DD-type operations. Consequently, a system in which BLAS I/O wasconducted with the D+S type, and computing using DD-type operations was implemented.
During performance evaluation on the Tesla M2090, triple- and quadruple-precision AXPY and
GEMV became memory rate-limited, and their execution times were shown to be respectively 3
and 4 times more strongly proportional to data size than single-precision routines, and 1.5 and 2
times more strongly proportional than double precision routines.
Although GPUs have a high floating-point operation performance, PCI Express and network
bandwidths are far lower than that for global memory, and can frequently become performancebottlenecks in a GPU cluster environment. The memory space on a GPU is limited, and thislimitation can cause communications with the host via PCI Express. In such environments,
cases are believed to exist where triple precision with smaller data sizes than quadruple
precision is valid.

146. Optimization and performance tuning technique for a numerical software on Multi-{core, socket,
GPU} computing environments
6.1. Introduction
In this study, we focused on the potential of GPGPU, which have been widely spread over not
only HPC but general purpose computing, for running a highly advanced material science programcode. The essence of the study is to accelerate an eigenvalue solver on a desktop class computer
system in order to contribute to this research program shortly. We mainly studied two topics in thisprogram. First, we accelerated the performance of CUDA BLAS library by introducing a novel
CUDA GPU algorithm. Second, we developed a new GPU-based eigenvalue solver by taking
advantage of newly developing CUDA-BLAS functions. This report briefly summarizes theirresults.

Fig. 3. High-end GPU card
(nVIDIA Tesla K20c, peak performance 1.17TFLOPS/Double Precision)
6.2. New Atomic-operation-based SYMV algorithm on a CUDA GPU
In literatures [8,9,18], we studied a new SYMV (symmetric matrix vector multiplication routine)
implementation by taking advantage of utilizing the atomic operations. In the study, ahigh-performance SYMV kernel was implemented on several GPU generation cores using an
atomic-operation based algorithm. The algorithm is effective for the memory bandwidth and reduced
memory usage. In fact, the latest implementation demonstrates sustained double-precision andsingle-precision performances of approximately 67 GFLOPS and 130 GFLOPS, respectively, on a
Tesla K20c GPU card [18]. This is also nearly peak performance of the memory bandwidth, and thealgorithm outperforms major CUDA BLAS kernels; CUBLAS, KBLAS, MAGMABLAS, and
CULA-BLAS. By this novel algorithm, we can expect extreme performance improvement on a GPU
computer system since eigenvalue computations in most of material simulation code bounds bymemory bottleneck. It has a significant impact to the simulation code on which the SYMV kernel isplugged into.

15

Fig. 4. Performance evaluation of the DSYMV kernels (for lower triangular format) in the latest
CUDA-BLAS libraries (ASPEN.K2 (‘+’ marker) is our development).
6.3. GPU-based eigenvalue solver
In literatures [14,3,19], we studied a GPU-based eigenvalue solver by taking advantage of newly
developed SYMV kernel presented in the previous topic. We developed Eigen-G, which is a
GPU-based eigenvalue solver for real-symmetric matrices. We confirmed that Eigen-G outperforms
state-of-the-art GPU-based eigensolvers such as magma dsyevd and magma dsyevd 2stage
implemented in the MAGMA version 1.4.0, when we select appropriate CUDA kernels called in
the solver. In fact, we apply the best-performing CUDA BLAS libraries and the GPU-CPU hybrid
DGEMM technologies (see Fig. 5) into the Eigen-G, the Eigen-G solver yields an even better
performance improvement. In the latest report of Eigen-G [19] reveals good performance
improvement (2x to 3x) compared with the CPU-based eigenvalue solver. We believe that thisperformance improvement must give a big impact to the material science simulation code.

Fig. 5. Two Typical GPU offload model studied in Eigen-G16

7. Development of efficient Block Krylov subspace methods for linear systems with multiple
right-hand sides and their applications
Linear systems with multiple right-hand sides:

appear in many scientific applications such as lattice quantum chromodynamics (QCD)
calculation, an eigensolver based on contour integral, and so on. As numerical solvers forsolving these linear systems, Block Krylov subspace methods have been proposed. However,
the relative residual norm of Block Krylov subspace methods may not converge due to the
influence of numerical instability when the number L of right-hand sides is large. In this project,
we improve the convergence behavior and accuracy of approximate solutions of Block Krylov
subspace methods.
7.1. Improvement of the convergence behavior of the Block BiCGSTAB method
As one of Block Krylov subspace methods, the Block BiCGSTAB method has been proposed.
The number of iterations of the Block BiCGSTAB method may smaller than that of the
BiCGSTAB method. However, if column vectors of n×L matrices of the Block BiCGSTAB
method are numerically linearly dependent, the method becomes unstable. We improve theconvergence behavior of the Block BiCGSTAB method by performing orthonormalization ofcolumn vectors.
Fig. 6 shows the relative residual history of the Block BiCGSTAB method and the Block
BiCGSTAB method with orthonormalization. Test problem is a linear system derived fromlattice quantum chromodynamics calculation. The size n of the coefficient matrix is 1,572,864,
and the number L of the right-hand sides is 8. From Fig. 6, the relative residual norm of theBlock BiCGSTAB method diverged. On the other hand, that of the Block BiCGSTAB methodwith orthonormalization converged.

Fig. 6. Relative residual history of the Block BiCGSTAB method and the Block BiCGSTAB
method with orthonormalization. ■: Block BiCGSTAB method，■: Block BiCGSTAB methodwith orthonormalization.
7.2. Accuracy improvement of approximate solutions of the Block BiCR method
The Block BiCR method is a natural extension of the BiCR method for linear system withsingle right-hand side. This method often shows smooth convergence behavior compared with
the Block BiCG method. However, approximate solutions generated by the Block BiCR method17may deteriorate due to an error matrix arise from the matrix multiplication. We modify thealgorithm of the Block BiCR method to improve accuracy of approximate solutions.
The test problem is Si5H12 from The University of Florida Sparse Matrix Collection. The
size n of the matrix is 19,896, and the number L of the right-hand sides is 32. Fig. 7 shows thetrue relative residual history of the Block BiCG method, the Block BiCR method, and themodified Block BiCR method. In this numerical experiment, residual orthonormalization isapplied to improve numerical stability. The true relative residual norm is used for evaluating
accuracy of the obtained approximate solution. If the true relative residual norm is sufficiently
small, accuracy of the obtained approximate solution is good. From Fig. 7, the true relative
residual norm of the Block BiCR method stagnates around 3.0×10-11. On the other hand, that ofmodified Block BiCR method decreases to 4.3×10-13.

Fig. 7. True relative residual history of the Block Krylov subspace methods. ■: Block BiCG
method，■: Block BiCR method，■: Modified Block BiCR method.
7.3. Speed-up of the eigensolver based on contour integral by using Block Krylov subspacemethods
The eigensolver based on contour integral (SS method: Sakurai-Sugiura method) has been
proposed. The SS method can compute eigenvalues in a specified region on the complex plane
and their corresponding eigenvectors. In this method, linear systems with multiple right-handsides need to be solved. The solution of these linear systems is the most time-consuming part of
the SS method. We consider solving these linear systems by Block Krylov subspace methods tospeed up the SS method.
We solve the generalized eigenvalue problem derived from molecular orbital calculation of
dimerization of epidermal growth factor receptor by the SS method. The size n of the matrix is
96,234. The number L of right-hand sides of linear systems that appear in the SS method is 32.
In this calculation, 16 linear systems are solved. These linear systems are solved in parallelbecause these systems are mutually independent. As solvers for solving linear systems, the
COCG method and the Block COCG method with residual orthonormalization (Block
COCGrQ) are used. Numerical experiments are carried out on eight nodes of T2K-Tsukuba.
Each node consists of four quad-core AMD Opteron 8356 2.3GHz. Two sockets are assigned tosolve a linear system.
Fig. 8 shows the computation time of the SS method. The left graph shows the computation
time of the SS method when the COCG method is used. From Fig. 8 (a), we can see that thecomputation time for solving each linear system is very different. In this case, it takes about
7,300 seconds for computing eigenpairs. On the other hand, Fig. 8 (b) shows that the18

computation time for solving each linear system is almost the same when the Block COCGrQ
method is used. In this case, it takes about 900 seconds for computing eigenpairs. By using theBlock Krylov subspace methods, the computation time of the SS method can be reduced.

(a) COCG method.

(b) Block COCGrQ method

Fig. 8. Computation time of the SS method. ■: Matrix distribution, ■: Preconditioning, ■:Solving linear systems, ■: Extracting eigenpairs.

8. Conclusion
The following topics were investigated in the present study for the purposes of performancetuning.
- Parallel three-dimensional FFT algorithm for next-generation supercomputers- Performance evaluation of quadruple- and octuple-precision BLAS implementation on
GPUs- Acceleration of sparse matrix-vector multiplication by automatic storage format selection
with GPU- Performance evaluation of parallel two-dimensional FFT using Intel AVX instructions- Study of triple- and quadruple-precision floating point operations with GPU- Optimization and performance tuning technique for a numerical software on Multi-{core,socket, GPU} computing environments- Development of efficient Block Krylov subspace methods for linear systems with multiple
right-hand sides and their applications
Further research will be carried out into these topics in the future, in collaboration withcomputational material science researchers, in order to accelerate actual applications.

9. Publications
1)

2)

Y. Kubota and D. Takahashi, “Optimization of Sparse Matrix-Vector Multiplication by Auto
Selecting Storage Schemes on GPU”, Proc. 11th International Conference on Computational
Science and Its Applications (ICCSA 2011), Part II, Lecture Notes in Computer Science, No.
6783, pp. 547–561, Springer-Verlag, 2011.
T. Nakayama and D. Takahashi, “Implementation of Multiple-Precision Floating-Point

19

3)
4)

5)

Arithmetic Library for GPU Computing”, Proc. 23rd IASTED International Conference on
Parallel and Distributed Computing and Systems (PDCS 2011), pp. 343–349, 2011.
T. Otaki, K. Fujiyama, T. Imamura, S. Yamada and M. Machida, “Performance evaluation of
Eigen_sg+ASPEN.K2”, In the proceedings of HPCS2012, poster presentation, 2012.
D. Mukunoki and D. Takahashi, “Performance Comparison of Double, Triple and Quadruple
Precision Real and Complex BLAS Subroutines on GPUs”, Proc. ATIP/A*CRC Workshop
on Accelerator Technologies for High-Performance Computing: Does Asia Lead the Way?
(ATIP/A*CRC Workshop '12), pp. 788-790, 2012.
D. Takahashi, “An Implementation of Parallel 2-D FFT Using Intel AVX Instructions on
Multi-Core Processors”, Proc. 12th International Conference on Algorithms andArchitectures for Parallel Processing (ICA3PP 2012), Part II, Lecture Notes in Computer
Science, No. 7440, pp. 197-205, Springer-Verlag, 2012.

6)

Y. Nakamura, K.-I. Ishikawa, Y. Kuramashi, T. Sakurai, and H. Tadano, “Modified Block
BiCGSTAB for Lattice QCD”, Comput. Phys. Comm., Vol. 183, pp. 34—37, 2012.

7)

M. Naito, H. Tadano, and T. Sakurai, “A modified Block IDR(s) method for computing highaccuracy solutions”, JSIAM Letters, Vol. 4, pp. 25—28, 2012.
T. Imamura, S. Yamada, and M. Machida, “A High Performance SYMV Kernel on a
Fermi-core GPU”, High Performance Computing for Computational Science - VECPAR
2012, Lecture Note in Computer Science (LNCS) 7851, pp.59-71, 2013.
T. Imamura, T. Utsumi, X. Lin，S. Yamamda, and M. Machida, “Performance tuning for
SYMV kernels on multi-generation GPU’s, Fermi and Kepler”，IPSJ SIG-HPC，Vol.
2013-HPC-138(7), pp.1-7, 2013. (in Japanese)8)9)10) I. Yamazaki, H. Tadano, T. Sakurai, and T. Ikegami, “Performance comparison of parallel
eigensolver based on a contour integral method and a Lanczos method”, Parallel Computing,Vol. 39, Iss. 6—7, pp. 280—290, 2013.
11) T. Sakurai, Y. Futamura, and H. Tadano, “Efficient parameter estimation and implementationof a contour integral-based eigensolver”, J. Alg. Comput. Tech., Vol. 7, No. 3, pp. 249—269,
2013.
12) I. Yamazaki, A. Imakura, H. Tadano, and T. Sakurai, “A parameter estimation for thepreconditioning using space direct solvers for Krylov subspace methods based on theminimal residual approach”, Transactions of the Japan Society for Industrial and Applied
Mathematics, Vol. 23, No. 3, pp. 381—404, 2013 (in Japanese).
13) D. Takahashi, “Implementation of Parallel 1-D FFT on GPU Clusters”, Proc. 2013 IEEE 16th
International Conference on Computational Science and Engineering (CSE 2013), pp.
174—180, 2013.
14) T. Imamura, S. Yamada and M. Machida, "Eigen-G: GPU-based eigenvalue solver for
real-symmetric dense matrices", 10th International Conference on Parallel Processing andApplied Mathematics (PPAM2013), Lecture Note in Computer Science (LNCS) 8384, pp.
673--682, 2014.
15) A. Imakura, L. Du, and H. Tadano, “A weighted Block GMRES method for solving linear
systems with multiple right hand sides”, JSIAM Letters, Vol. 6, pp. 65-68, 2014.
16) S. Saito, H. Tadano, and A. Imakura, “Development of the Block BiCGSTAB(l) method forsolving linear systems with multiple right hand sides”, JSIAM Letters, Vol. 6, pp. 65—68,
2014.
17) H. Tadano, Y. Ishikawa, and A. Imakura, “Improvement of the accuracy of the approximate
solution of the Block BiCR method”, JSIAM Letters, Vol. 6, pp. 61—64, 2014.
18) T. Imamura, D. Mukunoki, S. Yamada, and M. Machida, “Implementation and evaluation of
CUDA-xSYMV”, IPSJ-SIHPC, Vol. 2014-HPC-146(14), pp.1-12, 2014. (in Japanese)19) T. Imamura, D. Mukunoki, S. Yamada and M. Machida, “Performance evaluation of the20

fastest GPU-based eigensolver by selecting CUDA-BLAS parameters”, IPSJ-SIGHPC, Vol.
2015-HPC-148(5), pp.1-9, 2015. (in Japanese)21

A01-3: Fast solution for ultra-large scale systems as a basisof computational materials science
S.-L. Zhang1, T. Sogabe2, I. Imahori1, T. Miyata1, Y. Yamamoto3
Nagoya University, 2Aichi Prefectural University,
3
The University of Electro-Communications

1

Finding novel complex correlation phenomena and clarifying the non-equilibrium
dynamics are of prime importance in the field of materials design. This researchgroup tackles the challenging problems from the viewpoints of numerical linear
algebra, optimization and high-performance computing.
The major purpose of the researches is to develop robust and efficient numericalalgorithms for solving large linear systems and eigenvalue problems in order toshed light on a breakthrough toward the challenging problems. For achieving the
purpose, the research group is organized by sophisticated experts as follows:
Professor Shao-Liang Zhang as the principal investigator; Professor Yusaku
Yamamoto as a project member in the field of high-performance computing forlarge eigenvalue problems; Associate professor Shinji Imahori as a project
member in the field of optimization; Associate professor Tomohiro Sogabe as aproject member in the field of numerical linear algebra for large linear systems;
Assistant professor Takafumi Miyata as a project member in the field of
numerical linear algebra for large eigenvalue problems.

1. Introduction
Computational science is now widely known to be a third mode of science for understanding
and predicting the behavior of artificial and natural systems with multiple degrees of freedom,
and it goes without saying that recent development of computational science highly depends oninnovation and breakthrough in the field of numerical linear algebra such as numericalalgorithms for linear systems and eigenvalue problems. In fact, millions of systems frequently
arise in the field of materials design through computics, and obtaining numerical solutions are
known to be one of the most time-consuming parts in the whole computation. Innovation andbreakthrough in terms of numerical linear algebra, therefore, will play an crucial role in further
development of materials design.
The primary purpose of the research is to develop high-performance numerical algorithms inorder to support disclosing hidden nature of the systems with multiple degrees of freedom. To
be more specific, the faster the better; the more accurate the better; and enhancing numericalmathematics for turning difficult problems into much simpler ones.

2. Novel high-performance numerical algorithms
In this section, the results on linear solvers, eigenvalue solvers and optimization solvers arereported.

22

2.1
2.1.1

Results on solvers for large linear systems
Subspace methods“Krylov subspace methods” is known as a Top10 algorithm of the 20th century [SIAM News,
Volume 33, Number 4], which is a iterative method for solving large and sparse linear systems.
The BiCG (Bi-Conjugate Gradient)-type method and the GMRES (Generalized Mimimal
REsidual) method are well known Krylov subspace methods for solving nonsymmetric linear
systems.
First, the result based on the GMRES method is described. As mentioned above, the GMRES
method is a representative Krylov solver. The method is proved to be optimal in terms of thenumber of iteration steps until convergence. It, however, is not practical in use due to growing
memory requirement and computational costs. Thus, restarted variant is widely used in practice.
Here, the restart means that after reaching at a prescribed iteration number m, the GMRES
method is restarted by setting the initial guess as the approximate solution at m iteration steps.
The restarted GMRES method, known as GMRES(m), is indeed useful in practice but there is a
disadvantage over the GMRES method in that the required number of iterations tends to glow
and at worst it may suffer from stagnation. In order to overcome the disadvantage, we focusedon the initial guess at every restart. The conventional GMRES(m) method uses the initial guess
to be the approximate solution obtained at the restart. We developed this part, i.e., we proposed
to set the initial guess to be the sum of the approximate solution and a modified vector. It is easy
to see that this approach includes the conventional one. Since there is a freedom in choosing themodified vector, we further investigated this effect in terms of matrix polynomials, and thenobtained how to choose the modified vector. As a result, we succeeded in obtaining themodified Look-Back GMRES(m) method. For some applications, the method outperformed the
GMRES(m) method.
Second, the result based on the BiCG method is described. The BiCG method is also a
representative Krylov solver and it is a cost-efficient algorithm in that the computational costs ateach iteration step is relatively small. The algorithm, unlike the GMRES(m) method, shows
irregular convergence behavior. To remedy the behavior, one of the most successful classes is
product-type Krylov subspace methods such as the BiCGStab (BiCG Stabilized) method andthe GPBiCG (Generalized Product-type BiCG) method. The key idea of the class is applying asuitable matrix polynomials to the BiCG residual vectors. The BiCGStab method uses a matrix
polynomial of degree 1 such that the resulting residual norm is locally minimized, and the
GPBiCG method uses a matrix polynomial of degree 2 for further stabilizing the BiCGStab
method. Recently, Sonneveld and van Gijzen proposed the Induced Dimension Reduction
method, so called IDR(s). The IDR(s) method finds approximate solution over Sonneveld
subspaces that include the subspace used by the BiCGStab method. In many applications the
IDR(s) method is known to be attractive. Recently, for further analyzing the property of theIDR(s) method, Sleijpen used a BiCG polynomial that is close to the IDR polynomial forclarifying the relation between the IDR(s) method and the BiCGStab method. Based on
Sleijpen’s analysis, we developed a product type Krylov subspace methods based on the BiCG
polynomial close to the IDR one, and then we obtained a modified BiCGStab method and amodified GPBiCG method. After the modification, in order to obtain father stabilization, we
proposed a Quasi-Minimal Residual variant of the IDRstab method. In fact, the variant often
gives smoother convergence behavior than the conventional one. In addition, we proposed amodified IDRstab method in order to reduce the number of DAXPY operations: addition of ascalar multiple of a real or complex vector to another real or complex vector using double

23

precision arithmetic.

2.1.2

Preconditioning techniquePreconditioning techniques are commonly used for boosting the speed of convergence of
Krylov subspace methods. The standard preconditioning techniques are transforming theoriginal system into another suitable one by means of multiplying the original systems by apreconditioning matrix. The resulting algorithm has a specific operation that corresponds tosolving the extra linear system with the preconditioning matrix at each iteration step. Since thepreconditioning matrix can be changed at each iteration step, there are some flexible
preconditioned Krylov solvers such as the FGMRES method, the GMRESR method, and the
GCR method with a variable preconditioning using the SOR (Successive Over-Relaxation)
method. When one uses the SOR method for the variable preconditioning, one cannot use theconventional SOR method for the case where the coefficient matrix has zero diagonal entries. In
order to remedy the difficulty, we modified a way of splitting the coefficient matrix andconstructed a variant of the generalized SOR method. From numerical experiments, we showed
the effectiveness of the variable preconditioning based on the variant of the generalized SOR
method. Furthermore, since solving the extra linear system is one of the most time-consuming
parts, we proposed a stopping criterion for solving the extra linear system from the viewpointsof the accuracy of the dot products arising in computing the coefficients of residual
polynomials.

2.1.3

Subspace methods for solving generalized shifted linear systems

Shifted linear systems with complex symmetric matrices arise in condensed matter physics
and the coefficient matrices are available in program package of ELSES (Extra Large Scale
Electronic Structure Calculation) led by Prof. Fujiwara at the university of Tokyo. The shifted
COCG method [1] is known as an efficient solver for the shifted linear systems.
We developed subspace methods for solving a generalized shifted linear system with complex
symmetric, which also arises in condensed matter physic. The key idea of the method is asfollows: first, transforming the generalized shifted linear systems into the standard shifted linear
systems; second applying the shifted COCG method with a bilinear form to the transformed
linear systems. The key idea made it possible to use the theory constructed in [1] for solving thegeneralized shifted ones.
For a numerical example, we use a matrix Au864 from large scale electronic structure
calculation, where the size of the coefficient matrix is 7776. The generalized shifted linear
systems to be solved is as follows(σ k S − H)x (k) = e 1 , k = 1,2,…,mwhere，σ k = −0.4+(k−1+i)/1000, m=1001, and H comes from Au864 and S is a given overlap
matrix. The result of comparison among the COCG method and our algorithms is shown in
Table.1.
Table1: Comparison among the COCG method and proposed methods ([2]).
CPU Time [s]SolverSeed system

Shifted system

Total

GSCOCG

486.2050.10

536.30

GSQMR

324.2261.61

385.83

GSQMRB

298.1649.28

347.44------

16867.8

COCG

24

We see from Table 1 that our algorithms outperform the COCG method in terms of the CPU
time. In fact, our algorithms are at least 30 times faster than the COCG method.

References:[1] T. Sogabe, T. Hoshi, S.-L. Zhang and T. Fujiwara, On a weighted quasi-residual minimization
strategy for solving complex symmetric shifted linear systems, Elec. Trans. Numer. Anal., 31(2008), pp. 126-140.
[2] T. Sogabe, T. Hoshi, S.-L. Zhang, and T. Fujiwara, Solution of generalized shifted linear systems
with complex symmetric matrices , J. Comput. Phys., 231 (2012), pp. 5669-5684.

2.1.4 On an improvement of Ye’s hybrid method for solving sphere constrained
quadratic opitimization
The sphere constrained quadratic optimization problem:

has a basic and important problem in optimization. Ye’s hybrid method [1] is one of the mostwell-known solvers. Ye’s hybrid method requires to solve the following shifted linear systemsof the form:

where Q is a symmetric positive definite matrix and the parameters are real. The fast solution of
the shifted linear systems is a bottleneck in the whole computation.
We proposed the implicit evaluation method for solving the above linear systems by using
shift-invariance property of Krylov subspaces. Let Q be a matrix bcsstk09 obtained from Matrix
Market (url: http://math.nist.gov/MatrixMarket/). Then the numerical result is given in Fig.1.

Fig.1. Comparison of explicit and implicit evaluations.
Step i (i=1,2,…,9) in Fig.1 means the computational costs for solving ith linear system to besolved. We see from Fig. 1 that total CPU time for the implicit evaluation method is almost thesame as the CPU time of step 1, which means 8 kinds of linear systems are efficiently solved.

25

Reference:[1] Y. Ye, A new complexity result on minimization of a quadratic function with a sphere constraint,
in C. Floudas and P. Pardalos eds., Recent Advances in Global Optimization, Princeton
University Press, NJ, 1992.

2.2

Subspace methods and high performance computing for eigenvalue problems
with applications

Eigenvalue problems as well as linear systems arise in rich variety of applications anddeveloping the efficient algorithms plays a crucial role in not only reducing the execution timeof the whole simulation but also deeper understanding physical phenomena. This section
describes the results of efficient algorithms suitable for computing specific eigenvalues and highperformance algorithm for all eigenvalues.

2.2.1

A fast solver for eigenvalue problems arising in photonic crystals

Photonic crystals have recently been intensively studied and the integrated circuits using
photons, instead of electrons, have received much attention. In the field of designing thenext-generation integrated circuits, computing eigenvalues located on the unit circle in thecomplex plane is required [1]. This requirement is much different from others. For example,
electromagneto dynamics and large scale electronic structure calculations require several
eigenvalues on the neighboring area of the targeted point in the complex plane, and some
important applications require extremal eigenvalues. Thus, algorithms for this purpose havebeen developed [2]. When it comes to the requirement in photonic crystals, it is a challenging
problem because all eigenvalues on the unit circle are required.
We focused on Sakurai-Sugiura (SS) method [3] as one of the most promising methods formeeting the requirement. The SS method finds all the eigenvalues inside the given region.
Based on this property, we extend the SS method to computing all the eigenvalues on the unit
circle. The key idea is to extend the SS method to computing all the eigenvalues on multiply
connected region. Then we set the multiply connected region to be double circles (inner andouter circles). By setting the two circles so that the unit circle is located between the two circles,
we can obtain all the eigenvalues on the region of the disc with hole. See Fig. 2 for details.
For numerical experiments, we used the eigenvalue problems from photonic crystals given by
Prof. Lu at Hong Kong University of Science and Technology, and showed that all eigenvalues
on the unit circles were obtained.
References:[1] Y. Huang, Y. Y. Lu, and S. Li, Analyzing photonic crystal waveguides by Dirichlet-to-Neumannmaps, J. Opt. Soc. Am. B, 24 (2007), pp. 2860-2867.
[2] Z. Bai, J. Demmel, J. Dongarra, A. Ruhe and H. van der Vorst, eds., Templates for the solution of
Algebraic Eigenvalue Problems: A Practical Guide, SIAM, Philadelphia, 2000.
[3] T. Sakurai and H. Sugiura, A projection method for generalized eigenvalue problems using
numerical integration, J. Comput. Appl. Math., 159 (2003), pp. 119-128.

26

Fig. 2. Spectrum in the complex place. (Red circle: required eigenvalues.)

2.2.2

The Arnoldi (M,W,G) method for large eigenvalue problems

Large scale electronic structure calculations require solving large and sparse generalized
eigenvalue problems. For symmetric eigenvalue problems, the Lanczos method is widely known
and for nonsymmetric ones, the Arnoldi method is useful, which is an extension of the Lancos
methodWe succeeded in extending the Arnoldi method to solving generalized eigenvalue problems.
The resulting method is referred to as the Arnoldi(M, W, G) method. The relation among the theArnoldi(M, W, G) method, the Arnoldi method and the Lanczos method is as follows: Let thegeneralized eigenvalue problems be Ax=λBx. Then the Arnoldi(B, B*B, B) method corresponds
to the Arnoldi method and the Arnoldi(B, B, I) method corresponds to the Lanczos method.
From numerical experiments, we found the Arnoldi(I, I, I) method to be a method of choice fora problems arising in large scale electronic structure calculations

2.2.3

Eigenvalue problems arising in large scale electronic structure calculations

Recently, there is a strong need to compute the kth smallest eigenvalue for symmetriceigenvalue problems that arise in large scale electronic structure calculations.
One of the standard methods may be the Lancos method. In fact, the Lanczos method cancompute the smallest eigenvalue and neighboring eigenvalues. It is, however, difficult to tell
how many eigenvalues there are smaller than the obtained eigenvalue. This motivated us todesign an algorithm for avoiding the difficulty.
The key idea of the work is to use Sylvester's law of inertia together with a bisection search.
For a mall test problem, we successfully obtained the the kth smallest eigenvalue [1]．
Reference:[1] D. Lee, T. Miyata. T. Sogabe, T. Hoshi and S.-L. Zhang, Eigenvalue computation for a specificneed arising from electronic structure calculation, The 8th East Asia SIAM Conference, Taipei,
Taiwan, June 25-27, 2012.

27

2.2.4

Study on massively parallel algorithms for small scale symmetric eigenvalue
problemEigenvalue problem of a real symmetric matrix, Ax = λx, is an important problem thatfrequently arises in quantum chemistry and electronic structure calculations. We consider the
problem of computing all the eigenvalues and eigenvectors of a relatively small matrix (n ~10,000) on a massively parallel computer with thousands of computing nodes. The standard
algorithm for the symmetric eigenvalue problem is based on tri-diagonalization of the input
matrix, followed by the solution of the tridiagonal eigenvalue problem and back-transformationof the eigenvectors. While this approach is the best one among known algorithms in terms ofcomputational work, it is not efficient in our situation. This is because the tri-diagonalization
step is fine-grained and incurs many inter-processor communications. As a result, for relatively
small problems, the cost of inter-processor communication or synchronization becomesdominant and the speedup saturates around only a few hundred processors.
As an alternative to the tri-diagonalization based methods, we focus on the block-Jacobi
algorithm, which is a generalization of the well-known Jacobi algorithm for the symmetriceigenvalue problem. It works on a matrix partitioned into small blocks and tries to diagonalize
the matrix by eliminating the off-diagonal blocks by orthogonal transformations. Although thisalgorithm requires much more work than the tri-diagonalziation based algorithms, it has simpler
computational patterns and larger parallel granularity. Thanks to these features, the algorithm iseasier to optimize on modern high performance processors. Moreover, it is expected to attainbetter scalability for medium-size problems because the overhead of inter-processor
communication and synchronization is smaller. An additional feature of the block-Jacobi
algorithm is that most of the computation is done using the level-3 BLAS, or matrix-matrix
multiplication, which is a cache-friendly operation.
We implemented the block Jacobi method on the K computer and did some optimizations
such as hiding the inter-processor communications and tuning the solver of a 2 by 2 small
eigenproblem, which is the most time consuming part of the algorithm. According to ournumerical experiments, the resulting program shows good scalability on the K computer andoutperforms ScaLAPACK when solving an eigenvalue problem of size 10,000 using up to
10,000 computing nodes.
Another advantage of the block-Jacobi algorithm is that the convergence becomes faster
when the input matrix is nearly diagonal. In a certain type of first-principles molecular
dynamics method, the Hamiltonian matrix needs to be diagonalized at each time step. In thatcase, if we transform the Hamiltonian matrix at a time step with the (unitary) eigenvector matrix
at the preceding step, the resulting matrix becomes nearly diagonal. Hence, the convergence ofthe block-Jacobi method can be accelerated. We are planning to investigate this effect in moredetail and exploit it to speed up first-principles molecular dynamics methods.

2.2.5

Maximum Eigenvalue Problem and Local Search for Escher-Like Tilings

Maurits Cornelis Escher (1898-1972) is a Dutch graphic artist who is famous for impossible
structures, transformation prints and regular division of the plane. Inspired by his art works,
Kaplan and Salesin [1] introduced an optimization problem to design Escher-like tilings.
Koizumi and Sugihara [2] gave a new formulation of the problem and proposed an effective
algorithm for the problem; their method computes the maximum eigenvalue and corresponding
eigenvector to find an Escher-like tiling. A shortcoming of their method is sensitivity; for an
input line figure, different sets of points can approximate it, but they may output entirely28different tilings. In [2], good sets of points are generated manually through trial and error.
In this study [3], we propose two local search techniques to design good tilings automatically.
In the first method, a good set of points are automatically generated for an input line figure. For
the purpose, the features of the input figure are extracted and some fixed points are put on theboundary to keep the features. We then search good positions of remaining points forEscher-like tilings by local search technique. In the second method, constraint conditions arereconsidered. Koizumi and Sugihara uniquely determined a matrix to represent constraint
conditions for a tiling type. (It is known that there are 93 different tiling types for isohedraltilings.) Our method generates multiple matrices (i.e., many possibilities of shapes for tilings)
for each tiling type. By using these ideas, we design efficient algorithm for high-quality
Escher-like tilings.

Figure 1: Tiling of “Golden Dolphin”
We evaluate the proposed algorithm via computational experiments. In Figure 1 we show aresult of our method: (a) represents initial positions of points on the boundary of “Golden
Dolphin”, (b) is an optimal shape for (a) computed by the method in [2]. When our method
reached a local optimal solution, shape (c) that tiles the plane was output. Figure 1(d) is thetiling generated by this shape. From these figures, our method seems to work well for complex
input figures.
References:[1] C. S. Kaplan and D. H. Salesin, Escherization. Proceedings of SIGGRAPH, pp. 499-510 (2000).
[2] H. Koizumi and K. Sugihara, Maximum Eigenvalue Problem for Escherization. Graphs andCombinatorics, 27 (2011), pp. 431-439.
[3] S. Imahori and S. Sakai, A Local-Search Based Algorithm for the Escherization Problem. The
IEEE International Conference on Industrial Engineering and Engineering Management, (2012),
pp. 151-155.

3. Major publications
1)

M. E. A. El-Mikkawy and T. Sogabe, Notes on particular symmetric polynomials withapplications, Appl. Math. Comput., 215 (2010), pp. 3311-3317.

2)

M. E. A. El-Mikkawy and T. Sogabe, A new family of k-Fibonacci numbers, Appl. Math.
Comput., 215 (2010), pp. 4456-4461.

3)

T. Miyata, Y. Yamamoto and S.-L. Zhang, Performance Modeling of Multishift QR Algorithms
for the Parallel Solution of Symmetric Tridiagonal Eigenvalue Problems, (Proceeding) Lecture
Notes in Computer Science, 6082 (2010), pp. 401-412.

29

4)

Y. Mizuno, K. Ohi, T. Sogabe, Y. Yamamoto and Y. Kaneda, Four-point correlation functionof a passive scalar field in rapidly fluctuating turbulence: Numerical analysis of an exact
closure equation, Phys. Rev. E 82, 036316 (2010), pp. 1-9.

5)

A. Fukuda, Y. Yamamoto, M. Iwasaki, E. Ishiwata and Y. Nakamura, A Bäcklund t
ransformation between two integrable discrete hungry systems, Physics Letters A, 3753 (2011),
pp. 303-308.

6)

Y. Hirota, Y. Yamamoto and S.-L. Zhang, Cache optimization of a non-orthogonal joint
diagonalization method, JSIAM Letters, 3 (2011), pp. 9-12.
7) T. Miyata, Y. Yamamoto, T. Uneyama, Y. Nakamura and S.-L. Zhang, Optimization of theMultishift QR Algorithm with Coprocessors for Non-Hermitian Eigenvalue Problems, East
Asian Journal on Applied Mathematics, 1 (2011), pp. 187-196.
8) T. Sogabe and S.-L. Zhang, An extension of the COCR method to solving shifted linear
systems with complex symmetric matrices, East Asia J. on Appl. Math., 1 (2011), pp. 97-107.
9) Y. Tanaka, S. Imahori, M. Yagiura, Lagrangian-Based Column Generation for the Node
Capacitated In-Tree Packing Problem, Journal of the Operations Research Society of Japan, 54(2011), pp. 219-236.
10) H. Teng, T. Fujiwara, T. Hoshi, T. Sogabe, S.-L. Zhang and S. Yamamoto, Efficient andaccurate linear algebraic methods for large-scale electronic structure calculations with
non-orthogonal atomic orbitals, Phys. Rev. B 83, 165103 (2011), pp. 1-12.
11) Y. Yamamoto and Y. Hirota, A parallel algorithm for incremental orthogonalization based on
the compact WY representation, JSIAM Letters, 3 (2011), pp. 89-92.
12) A. Fukuda, Y. Yamamoto, M. Iwasaki, E. Ishiwata and Y. Nakamura, Error analysis for matrix
eigenvalue algorithm based on the discrete hungry Toda equation, Numerical Algorithms, 61(2012), pp. 243-260.
13) Y. Hama, A. Fukuda, Y. Yamamoto, M. Iwasaki, E. Ishiwata and Y. Nakamura, On Some
Properties of Discrete Integrable System Derived from Hungry Lotka-Volterra System ofMultiplicative Type, Journal of Math-for-Industry, 4(A) (2012), pp. 5-15.
14) T. Hoshi, S. Yamamoto, T. Fujiwara, T. Sogabe and S.-L. Zhang, J. Phys., An order-n electronic
structure theory with generalized eigenvalue equations and its application to a ten-million-atomsystem, J. Phys.: Condens. Matter, 24 (2012), pp. 1-5.
15) S. Imahori, Y. Miyamoto, H. Hashimoto, Y. Kobayashi, M. Sasaki and M. Yagiura, The
Complexity of the Node Capacitated In-Tree Packing Problem, Networks, 59 (2012), pp. 13-21.
16) S. Imahori and S. Sakai, A Local-Search Based Algorithm for the Escherization Problem, The
IEEE International Conference on Industrial Engineering and Engineering Management, (2012),
pp. 151-155.
17) A. Imakura, T. Sogabe and S.-L. Zhang, An Efficient Variant of the GMRES(m) Method Basedon the Error Equations, East Asian Journal on Applied Mathematics, 2 (2012), pp. 19-32.
18) D. Mori, Y. Yamamoto and S.-L. Zhang, Backward error analysis of the AllReduce algorithm
for householder QR decomposition, Japan Journal of Industrial and Applied Mathematics, 29(2012), pp. 111-130.
19) T. Sogabe, T. Hoshi, S.-L. Zhang and T. Fujiwara, Solution of generalized shifted linear systems
with complex symmetric matrices, Journal of Computational Physics, 231 (2012), pp.
5669-5684.
20) Y. Tanaka, S. Imahori, M. Sasaki and M. Yagiura, An LP-Based Heuristic Algorithm for theNode Capacitated In-Tree Packing Problem, Computers & Operations Research, 39 (2012),

30

pp. 637-646.
21) A. Fukuda, Y. Yamamoto, M. Iwasaki, E. Ishiwata and Y. Nakamura, On a shifted LR
transformation derived from the discrete hungry Toda equation, Monatshefte für Mathematik,
170 (2013), pp. 11-26.
22) A. Fukuda, E. Ishiwata, Y. Yamamoto, M. Iwasaki and Y. Nakamura, Integrable Discrete
Hungry Systems and Their Related Matrix Eigenvalues, Annali di Matematica Pura ed
Applicata, 192 (2013), pp. 423-445.
23) A. Fukuda, E. Ishiwata, Y. Yamamoto, M. Iwasaki and Y. Nakamura, Integrable discrete
hungry systems and their related matrix eigenvalues, Ann. Mat. Pura Appl., 192 (2013), pp423-445.
24) Y. Hu, H. Hashimoto, S. Imahori and M. Yagiura, Efficient construction heuristic algorithms forthe rectilinear block packing problem, Proceedings of the International Symposium on
Scheduling 2013, (2013), pp. 80-85.
25) A Imakura, T Sogabe and S.-L. Zhang, An Efficient Variant of the Restarted Shifted GMRES
Method for Solving Shifted Linear Systems, Journal of Mathematical Research with
Applications, 33 (2013), pp. 127-141.
26) J. Jia, T. Sogabe, and M.E.A. El-Mikkawy, Inversion of k-tridiagonal matrices with Toeplitz
structure, Comput. Math. Appl., 65 (2013), pp. 116-125.
27) D. Lee, T. Miyata, T. Sogabe, T. Hoshi and S.-L. Zhang, An interior eigenvalue problem fromelectronic structure calculations, Japan Journal of Industrial and Applied Mathematics, 30(2013), pp. 625- 633.
28) T. Miyata, S. Honda, R. Naito and S.-L. Zhang, A numerical approach to surface Green's
functions via generalized eigenvalue problems, Japan Journal of Industrial and Applied
Mathematics, 30 (2013), pp. 653- 660.
29) S. Imahori, Y. Chien, Y. Tanaka and M. Yagiura, Enumerating bottom-left stable positions forrectangle placements with qverlap, Journal of the Operations Research Society of Japan 57(2014), pp. 45-61.
30) Y. Yamamoto, Z. Lan and S. Kudo: Convergence analysis of the parallel classical block Jacobi
method for the symmetric eigenvalue problem, JSIAM Letters, 6 (2014), pp. 57-60.

5. Major invited talks
1)

S.-L. Zhang, A. Imakura and T. Sogabe, GMRES(m) Method with Look-Back-type Restart for
Solving Nonsymmetric Linear Systems, 7th International Conference on Scientific Computing
and Applications, Dalian, China, Jun. 13-15, 2010.

2)

S.-L. Zhang, T. Miyata, L. Du, T. Sogabe and Y. Yamamoto, A Projection Approach Based on
the Residue Theorem for Eigenvalues within a Multiply Connected Domain, The 2010 NIMS
Conference & The Third China-Japan-Korea Joint Conference on Numerical Mathematics,
Gangneung, Korea, Aug. 19-23, 2010.

3)

S.-L. Zhang and T. Miyata, A Numerical Method for Solving the Eigenvalues in a Multiple
Connected Domain, 2011 LHD Workshop, Beijing, China, Jan. 15, 2011.

4)

S.-L. Zhang and T. Miyata, A Projection Approach Based on the Residue Theorem for
Generalized Eigenproblems within a Multiply Connected Domain, Center of Mathematical31

Modeling and Scientific Computing, Chiao Tung University, Taiwan, Sep. 15, 2011.
5)

S.-L. Zhang and T. Sogabe, Iterative Solutions of Large Nonsymmetric Linear Systems ---Two
Attempts to Improve Bi-CG ---, Taida Institute for Mathematical Sciences National, National
Taiwan University, Taipei, Sep. 16, 2011.

6)

S.-L. Zhang, A. Imakura and T. Sogabe, Look-Back GMRES(m) for Solving NonsymmetricLinear Systems, Department of Mathematics, National Taiwan University, Taipei, Sep. 19, 2011.

7)

S.-L. Zhang,T. Miyata,T. Sogabe and T. Yamashita, An Arnoldi(M,W,G) Approach for
Generalized Eigenvalue Problems, National Center of Theoretical Science & Department ofMathematics, National Cheng Kung University, Tainan, Sep 20, 2011.

8)

S.-L. Zhang, A. Imakura and T. Sogabe, Look-Back GMRES(m) for Solving NonsymmetricLinear Systems, Department of Mathematics, National Sun Yat-sen University, Gaoxuong, Sep.
21, 2011.

9)

S.-L. Zhang,T. Miyata,T. Sogabe and T. Yamashita, An Arnoldi-like Approach for Generalized
Eigenvalue Problem, The 8th International Conference on NTmerical Optimization andNumerical Linear Algebra, Xiamen, China, Nov. 7-11, 2011.

10) S.-L. Zhang,T. Miyata and T. Sogabe, A Numerical Method for Eigenvalue Computations in a
Multiply Connected Domain, School of Mathematical Sciences, South China Normal University,
GuangZhou, China, Dec. 8, 2011.
11) S.-L. Zhang, A. Imakura and T. Sogabe, GMRES(m) method with Look-Back Restart for
Solving Nonsymmetric Linear Systems, the 2011 Workshop on Scientific Computing, Macau,
December 10-12, 2011.
12) S.-L. Zhang, A. Imakura and T. Sogabe, Look-Back GMRES(m) for Solving Large
Nonsymmetric Linear System, Numerical Linear Algebra ---Algorithms, Applications, andTraining, an NOW-JSPS joint seminar, Delft, Apr. 10-13, 2012.
13) T. Sogabe, T. Hoshi, S.-L. Zhang and T. Fujiwara, Numerical Methods for Generalized Shifted
Linear Systems with Complex Symmetric Matrices, 4th China-Japan-Korea Conference on
Numerical Mathematics, Otsu City, Shiga Prefecture, Japan, Aug. 25-28, 2012.
14) S.-L. Zhang, D. Lee, T. Miyata and T. Sogabe, An Intermediate Eigenvalue Problem inElectronic Structure Calculation, The 4th Workshop on Numerical Algebra and High
Performance Computation, Macau, Dec. 8-10, 2012.
15) Y. Yamamoto: A Nonlinear Eigenvalue Problem Arising in Theoretical Fluid Dynamics and Its
Solution Using Signed Singular Values, 2013 NCTS Workshop on Numerical Linear Algebraand High Performance Computing (2013 NLA-HPC), National Tsinghua University, Hsinchu,
Taiwan, Dec. 9-12, 2013.

32

Development of High Performance Parallel Eigensolvers
for the Needs in Computational Quantum Science

Tetsuya Sakurai
Department of Computer Science, University of Tsukuba, Tsukuba 305-8573
CREST, Japan Science and Technology Agency (JST), Kawaguchi 332-0012

1. Introduction
The large-scale eigenvalue problem is one of the common problems in computational design
and analysis of materials. High speed and high accuracy algorithms and their high performance
software are the fundamental technologies necessary to solve this problem efficiently. We haveinvestigated the complex moment-based eigensolver named the Sakurai-Sugiura method (the SS
method), which can selectively compute the eigenvalues in a certain region and thecorresponding eigenvectors based on a contour integral. Since the SS method has hierarchicalparallelism, it suits well for recent hierarchical architectures.
In order to efficiently apply the SS method to some applications in computational quantum
science on recent supercomputers, we specifically proceeded with 1) improving the algorithmand developing a highly parallel software implementation, and 2) developing interfaces andcomputational kernels specialized for each application.
Our Fortran-based software "z-Pares" supports the Reverse Communication Interface(RCI). Since RCI is independent of the particular distributed data structures of applications, RCI
makes it possible to provide a seamless connection in several applications. Our C Languagebased software is listed in the Scalable Library for Eigenvalue Problem Computation (SLEPc)
ver.3.4 as "CISS". In this research project, we also developed implementations using GPU for
speed-up of the software.

2. Achievements
The SS method selectively computes the eigenvalues in a certain region and the corresponding
eigenvectors. It constructs an invariant subspace associated with the target eigenvectors basedon a contour integral. The Arnoldi/Lanczos method, which is one of the most widely usedeigensolvers, constructs the subspace by sequential computation; on the other hand, the SS
method can construct the subspace by independent computation based on the contour integral.
Therefore, the SS method is expected to achieve higher parallel efficiency than traditional
eigensolvers.
The most time-consuming part of the SS method is to solve linear systems with multiple
right-hand sides on quadrature nodes. The SS method has the following three layers ofhierarchical parallelism; see Fig. 1.
Layer 1: Contour paths can be run independently.
Layer 2: Each linear system can be solved independently.
Layer 3: The linear systems can be solved in parallel.
A software implementation of this algorithmic hierarchy enables users to exploit theperformance of recent hierarchically structured architectures.
Based on cross-disciplinary cooperation with researchers in computational quantum
science, we have specifically proceeded as follows:33

Fig. 1: Hierarchical algorithm for solving sparse eigenproblems

Fig. 2: Parallel performance of an application of z-Pares to a matrix derived fromorder-N DFT.
(i) Improvement of the SS method and development of high performance software;(ii) Application to DFT code;(iii) Implementations using GPU for speed-up of the software.

2.1 Improvement of the SS method and development of high performance software
From research on applications in this application area, we fixed a specification of highperformance software z-Pares based on the SS method, and then developed z-Pares. z-Pares is
implemented in Fortran, which is widely used in computational physics, and used Message
Passing Interface (MPI) for implementations of distributed parallel processing. z-Pares supports
the Reverse Communication interface (RCI), which makes it possible to provide a seamlessconnection to several applications. z-Pares is available from http://zpares.cs.tsukuba.ac.jp/.

2.2 Application to DFT codes
2.2.1 Application to CONQUEST
We applied z-Pares to the order-N DFT code named CONQUEST. The test system is a SiGe hut
cluster system of 200,000 atoms. Single zeta basis is used as the basis set. Matrix size is34

778,292 and 223 eigenpairs around HOMO-LUMO are computed. We have executed theperformance evaluation on the supercomputer COMA at the University of Tsukuba. The total
number of nodes of COMA is 392. From these, we used up to 256 nodes during the application.
MUMPS is used as a linear solver. The parallel performance is shown in Fig. 2. The solid line
indicates parallel performance of z-Pares and the dotted line indicates an ideal scaling. From 4
nodes to 64 nodes, we used parallelism of quadrature points. In addition, from 64 nodes to 256,
we used parallelism of linear solver. We observe that up to 64 nodes parallel performance scales
almost linearly, whereas it degrades from 64 to 256 nodes. The linear scaling is caused by the
independence of computations of quadrature points. Parallel performance from 64 nodes isalmost equivalent to that of MUMPS. We observe that the parallel performance of the linear
solver is the key factor of highly parallel computational environment.

2.2.2 Application to RSDFTFor efficient parameter setting of the SS method, information of eigenvalue distribution (like theelectronic density-of-states) is needed. We have computed eigenvalue density of eigenproblems
derived from RSDFT code with contour integral based approach. To reduce the computational
cost of the approach, we proposed a variant of a method that efficiently computes block bilinear
form [10]. We have tested our approach on eigenproblems of SiNW with 9,924 atoms and107,292 atoms.

2.3 Implementations using GPU for speed-up of the software
Many of recent supercomputers listed in TOP500 have accelerators like GPU. In order tobenefit from this situation, we developed software for using GPU that is mainly based on zPares. The developed software for GPU uses the linear computational library Matrix Algebra on
GPU and Multicore Architectures (MAGMA) for some computation kernels of the SS method.
Fig. 3 shows the computational results of the developed software for computing 10%
eigenpairs of a 10,000 dimensional real symmetric generalized eigenvalue problem with random
dense matrices. We have executed the performance evaluation on the supercomputer HA-PACS
at University of Tsukuba. We used up to 16 GPUs of HA-PACS.
The most-time consuming part of the SS method is to solve independent linear systems: the"solve" and "fact" routines. Since these computations have trivial parallelism, total execution
time shows linear scaling specifically for the case of a small number of GPU.

Fig. 3: Calculation time of GPU implementation.

35

3.

Collaborators

Hiroto Tadano (University of Tsukuba) and Akira Imakura (University of Tsukuba)

4.

List of achievements

Paper[1] Akira Imakura, Lei DU, Tetsuya Sakurai, Error bounds of Rayleigh-Ritz type contour
integral-based eigensolver for solving generalized eigenvalue problems, Numerical
Algorithms, (accepted)[2] Lijiong Su, Akira Imakura, Hiroto Tadano and Tetsuya Sakurai, Improving theconvergence behaviour of the BiCGSTAB method by applying D-norm minimization,
JSIAM Letters, (accepted)[3] Shusaku Saito, Hiroto Tadano, Akira Imakura, Development of the Block BiCGSTAB(ell)method for solving linear systems with multiple right hand sides, JSIAM Letters, Vol. 6,
2014, pp. 65-68[4] Akira Imakura, Lei Du, Tetsuya Sakurai, A block Arnoldi-type contour integral spectral
projection method for solving generalized eigenvalue problems, Applied Mathematics
Letters, Vol. 32, 2014, pp.22-27[5] Hiroto Tadano, Youichi Ishikawa, Akira Imakura, Improvement of the accuracy of theapproximate solution of the Block BiCR method, JSIAM Letters, Vol. 6, 2014, pp. 61-64[6] Ikuro Yamazaki, Akira Imakura, Hiroto Tadano, Tetsuya Sakurai, A parameter estimation
for the preconditioning using sparse direct solvers for Krylov subspace methods based on
the minimal residual approach, Transactions of JSIAM, Vol. 23, 2013, pp.381-404 (inJapanese)[7] Akira Imakura, Tomohiro Sogabe and Shao-Liang Zhang, An efficient variant of therestarted shifted GMRES method for solving shifted linear systems, Journal of
Mathematical Research with Applications, Vol. 33, 2013, pp.127-141[8] Yuki Nagai, Yasushi Shinohara, Yasunori Futamura, Yukihiro Ota and Tetsuya Sakurai,
Numerical construction of a low-energy effective Hamiltonian in a self-consistent
Bogoliubov-de Gennes approach of superconductivity, J. Phys. Soc. Jpn., Vol. 82, 2013,
094701[9] T. Yano, Y. Futamura, T. Sakurai, Multi-GPU scalable implementation of a contourintegral-based eigensolver for real symmetric dense generalized eigenvalue problems,Proceedings of 8th International Conference on P2P, Parallel, Grid, Cloud and Internet
Computing (3PGCIC-2013), 2013, pp.121-127[10] Lei Du, Yasunori Futamura, Tetsuya Sakurai, Block conjugate gradient type methods forthe approximation of bilinear form, Computers & Mathematics with Applications, Vol. 66(12), 2014, pp.2446-2455
Award[11] Best paper award of 8th International Conference on P2P, Parallel, Grid, Cloud andInternet Computing (3PGCIC-2013), T. Yano, Y. Futamura, T. Sakurai, 201336

Hybrid mathematical principles
for ultra-large-scale massively parallel electronic structure calculations
Takeo Hoshi,

Tottori University

Abstract
Hybrid mathematical principles were introduced to large-scale electronic structure theories andrealized one-hundred-million atom (100-nm-scale) calculations on the K computer. Novellinear-algebraic theories were constructed as Krylov-subspace solvers for generalized shifted
linear equations ((zS-H)x=b) and were implemented in our order-N calculation code ‘ELSES’(http://www.elses.jp/) with modeled (tight-binding-form) systems. A high parallel efficiency
was obtained with up to the full core calculations on the K computer. The linear-algebraic
theory is general and, recently, was applied to ab initio quantum transport calculations on thereal space grid formalism. Moreover, hybrid mathematical priciples are constructed on iInternal
eigen-pair calculation with Sylvester's theorem of inertia and hybrid direct solver for
generalized eigen-value problem. Several application studies were carried out: The nano domainof sp2-sp3 nano-composite carbon solid was calculated for the nano-polycrystalline diamond, aultrahard material and typical domain shapes and boundary structures were obtained. An ionicliquid (N-Methyl-N-propylpiperidinium bis trifluoromethanesulfonyl imide), a battery-relatedmaterial, was calculated and the diffusion mechanism was revealed. Several amourphous-likestructures and bundles of conjugated polymers were calculated and characteristic localized πstates were obtained. The present work was carried out, with several members of Computics
Project: T. Sogabe, S.-L. Zhang, and T. Miyata (Nagoya U), T. Ono (Tsukuba U), asinter-disciplinary collaborations among physics, mathematics and the high-performancecomputation field or ‘Application-Algorithm-Architecture co-design'.

Fig. 1 (a) Concept of Application-Algorithm-Architecture co-design. (b) The
schematic workflow of the order-N algorithm based on the shifted Krylov subspace
theory.
1. Introduction
The current or next generation (exa-scale) computational physics requires‘Application-Algorithm-Architecture co-design', or inter-disciplinary collaborations among
physics, mathematics and the high-performance computation field. Figure 1(a) illustrates
our basic strategy for large-scale calculations with the co-design. The essential concept is tocombine new ideas among the three fields for a breakthrough. A schematic workflow is37

shown in Fig. 1(b). The mathematical solvers are general and can be shared, as middlewaresor ‘simulation kernels’, among applications not only in electronic structure calculations but
also in other computational science fields.

	  	 Fig. 2 (a) Benchmark for the order-N scaling. [7] The calculated system is an amorphous-likeconjugated polymer (aCP), poly-(9,9 dioctyl fluorene). (b) Benchmark for the parallel efficiency
or the strong scaling, on the K computer with one hundred million atoms. [1,2] The calculated
systems are aCP and an sp2-sp3 nano-composite carbon solid (NCCS).

2. Shifted Krylov subspace theory
One of our fundamental mathematical theories is novel linear algebraic algorithms
with Krylov subspace. The research was carried out with T. Sogabe and S.-L. Zhang(Nagoya U) within Computics Project. As shown in Fig. 1(b), the generalized shifted linear
equations ((zS-H)x=b) are solved instead of conventional generalized eigen-value problems.
A Krylov subspace is defined as the linear (Hilbert) space of Kn(A;b) ≡ span{ b, Ab,
A2b, ...., An-1b } with a given integer n, a square matrix A and a vector b. Krylov subspace isa general mathematical concept and gives the foundation of various iterative
linear-algebraic solvers, such as the conjugate gradient method.
Two ‘families’ of the solvers were constructed for the generalized shifted linear
equations. One is the solvers based on the collinear residual theorem (*1) and the other isthose based on the Galerkin principle. The solvers of the former family are the generalized
shifted Conjugate-Orthogonal Conjugate-Gradient method and the generalized shifted
Quasi-Residual Minimization method [6, 9]. The solvers of the latter family are thegeneralized Lanczos method, [9] the generalized Arnoldi method [9], the Arnoldi (M,W,G)
method [8] and the multiple Arnoldi method [7]. These solvers are compared in Ref. [7]. In
conclusion, the efficiency of the solvers depends on the system and purpose and themultiple Arnoldi method was adopted in the molecular dynamics simulations [7].
Figure 2 shows the benchmarks of the multiple Arnoldi method. The order-N scaling isshown in Fig. 2(a), in which the computational time is order-N or proportional to thenumber of atoms N. [7] Figure 2(b) shows the parallel efficiency on the K computer with
one hundred million atoms. [1,2] Since a system with one hundred million atoms is a
(126nm)3 region of silicon crystal, we call the calculations 100-nm-scale calculations. The
MPI/OpenMP hybrid parallelism is used. The results are shown for the nano-composite
carbon solid (NCCS) system (See Sec. 5) with N = 103, 219, 200 [2] and anamourphous-like conjugated polmer system, poly-(9,9 dioctyl fluorine) (See Sec.7), with N= 102,238,848 [1].

38The high parallel efficiency stems not only from the fundamental mathematical theory
but also from several programing techniques that do not affect the numerical results but
affects the computational time. In particular, programing techniques for saving memory andcommunication costs [7] are crucial for the massively parallel computations. Moreover, theparallel file I/O technique is sometimes important [1,7]. The K computer contains a parallel
file I/O function, called 'rank directory function' and was used in the present benchmark
with split input files [1,7].
The fundamental mathematical theory is general and, recently, was applied to the abinitio quantum transport calculation with real space grid, (*2) because the shifted linear
equaions appears on the conductor part of the systems. The research was carried out in thecollaboration with T. Ono (Tsukuba U) and his coworkers within Computics Project. As amethodological point, the shifted Conjugate-Orthogonal Conjugate-Gradient method is usedin the three-term recurrence formalism (*3), instead of the original two-term recurrence
formalism (*4) (*5). The three-term recurrence formalism is mathematically equivalent to
the two-term recurrence formalism but can save the memory consumption, when one uses
the seed switching technique, a techniques for optimal calculation among various situations.
(*1) W. A. Frommer, ‘BiCGStab(l) for Families of Shifted Linear Systems.’ Computing 70,
87 (2003).
(*2) S. Iwase, T. Hoshi, T. Ono, submitted.
(*3) S. Yamamoto, T. Sogabe, T. Hoshi, S.-L. Zhang and T. Fujiwara, 'Shifted
conjugate-orthogonal conjugate-gradient method and its application to double orbital
extended hubbard model', J. Phys. Soc. Jpn. 77,114713, 8pp, (2008).
(*4) R. Takayama, T. Hoshi, T. Sogabe, S.-L. Zhang, and T. Fujiwara, 'Linear algebraic
calculation of the Green's function for large-scale electronic structure theory', Phys. Rev. B
73, 165108, pp.1-9 (2006)(*5) The two-term and three-term recurrence formalisms are compared in several
mathematical papers from the viewpoint of numerical rounding error. For example, M. H.
Gutknecht and Z. Strakos, Accuracy of Two Three-term and Three Two-term Recurrencesfor Krylov Space Solvers, SIAM. J. Matrix Anal. & Appl., 22(1), 213–229 (2000).

Fig. 3 Iterative procedure for obtaining an internal eigen-value [3]. The target eigen value is the
HOMO level of an amorphous-like conjugated polymer. The number of the eigen values in the
search range is plotted as the function of iteration number. When the number of the eigen values isreduced to one, the iterative procedure will stop.

3. Internal eigen-pair calculation with Sylvester’s theorem of inertia

39

The theory was also constructed for calculating internal eigen pairs, sets of eigen
values and eigen vectors, with Sylvester’s theorem of inertia [3]. The research was carriedout with S.-L. Zhang, and T. Miyata (Nagoya U) within Computics Project. A popular needamong electronic structure calculations is to calculate specific eigen pairs, such as HOMO,
LUMO levels or levels near the Fermi level. The theory enables us to calculating the target
eigen pair with Sylvester’s theorem of inertia. The range that contains the target eigen value
will be determined in an iterative procedure, as in Fig. 3. After that, the precise eigen value
and the eigen vector is determined in the Arnoldi(M,W,G) method. [8]. The theory wastested with amourphous-like conjugated polymer and a nano metal. [3]Fig. 4 Benchmark of the hybrid direct solver on the K computer. (a) Strong scaling benchmark foran electronic structure problem in the matrix size of M=430,080 with up to 10,000 nodes. (b) The
explanation of the hybrid algorithms A-H used in (a).

4. Hybrid direct solver for generalized eigen-value problem
Optimally hybrid direct solvers were constructed for massively parallel generalized
eigenvalue computations. [10](*6) Though the direct solver consumes a heavy O(M3)operation cost with the matrix size M, it gives all the eigen pair exactly and forms a strong
need among electronic structure calculations. The generalized eigenvalue computation
procedure is decomposed into the two subprocedures of (i) the reducer to the standard
eigenvalue problem (SEP) and (ii) the solver of SEP. A hybrid solver is constructed, when aroutine is chosen for each subprocedure from the three parallel solver libraries of
ScaLAPACK, ELPA (*7) and EigenExa (*8). The strong scaling benchmark was carriedout on the K computer and other supercomputers for electronic structure calculation
problems in the matrix sizes of M = 104 -106. The hybrid solvers with the two newer
libraries, ELPA and EigenExa, give better benchmark results than the conventional
ScaLAPACK library, as shown in Fig. 4. Detailed performance analysis implies that theCholesky decomposition in the reducer can be a bottleneck in the next (post-petascale)computer and gives a guideline for further improvement on the algorithm. The code willappear online as a general middleware in Fig. 1(a).
(*6) H. Imachi and T. Hoshi, submitted.
(*7) A. Marek, et al., ’The ELPA Library - Scalable parallel eigenvalue solutions forelectronic structure theory and computational science’, J. Phys. Condensed Matter 26,

40

213201 (2014); http://elpa.rzg.mpg.de/(*8) T. Imamura, 'The EigenExa Library - High performance & scalable direct eigensolver
for large-scale computational science,’ ISC 2014, Leipzig, Germany (2014).'

Fig. 5 Nano-domain analysis of sp2-sp3 nano-composite carbon solid (NCCS) visualized with the
COHP or πCOHP analysis. [4] The sp2 (graphite-like) and sp3 (diamond-like) domains arevisualized in (a), while only the sp2-like domains are visualized in (b). A closeup of a sp2-sp3
domain boundary is shown in (c). The atoms at a typical domain boundary are shown in (d).

5. Nano-composite carbon solids
The large-scale calculation method was applied to nano-domain analysis of sp2-sp3
nano-composite carbon solids [4] for the formation process of the nano-polycrystalline
diamond (NPD) (*9). The NPD is a novel ultrahard material and is obtained by directconversion sintering process from graphite under high pressure and high temperature andhas characteristic 10-nm-scale lamellar-like structures. The NPD is of industrial importance,
because of its extreme hardness and strength that exceed those of conventional single
crystals. Sumitomo Electric Industries. Ltd. began commercial production from 2012.
Our simulation is motivated by the investigation of possible precursor structures in theformation process of NPD and the structures should be nano-scale composites of sp2(graphite-like) and sp3 (diamond-like) domains. Figures 5 shows such a result of our
finite-temperature simulation with a periodic boundary condition. Here the sp2 domains andthe sp3 domains are distinguished by a novel analysis method called 	  ‘π-crystalline
orbital Hamiltonian population (COHP) method’. The method is an analysis method for
local bond energy based on the Green’s function and is a theoretical extension of theoriginal COHP method. (*10) The πCOHP analysis is used, because sp2 domains can be
distinguished from sp3 domains by the presence of π bonds. Figures 5(a) and (b) are
drawn by the bond visualization by the original COHP and the πCOHP, respectively. In
Fig. 5(a), a bond is drawn for an atom pair according to the COHP analysis, and the sp2 andsp3 domains are visualized. In Fig. 5(b), on the other hand, a bond is drawn for an atom pairaccording to the πCOHP analysis, and only the sp2 domains are visualized. The analysis
concludes that layered domains are sp2 domains and non-layered domains are sp3 domains.
Figure 5(c) is a close-up of a domain boundary between sp2 and sp3 domains, which showsthat a layered domain forms a graphite-like structure and a non layered domain forms a
diamond-like structure, as expected from the πCOHP analysis. A typical domain interface,41

schematically shown in Fig. 5(d), is analyzed for the nature of each bond, so as to clarify
how theπCOHP analysis works. The atom labeled ‘A’ in Fig.5(d) is focused on. The atom
has three bonds and the two of them are located within an sp2 domain and have πbonds,
while the rest one is ‘interface’ bond between sp2 and sp3 domains and does not have a πbond. Such a domain shape or domain boundary structure will play crucial role in thestrength of NPD.
(*9) T. Irifune, A. Kurio, A. Sakamoto, T. Inoue, and H. Sumiya, ‘Ultrahard polycrystalline
diamond from graphite’, Nature 421, 599 (2003).
(*10) R. Dronskowski and P. E. Bloechl, ‘Crystal orbital Hamilton populations (COHP).
energy-resolved visualization of chemical bonding in solids based on density-functional
calculations’, J. Phys. Chem. 97 (1993) 8617; http://www.cohp.de/	 Fig. 6 (a)-(c) Snapshots of the finite-temperature dynamics simulation of the ionic liquid
PP13–TFSI at t=(a) 0 ps, (b) 10 ps, (c) 20 ps. (d) The density of states at t=20ps.

6. Ionic liquid
An industry-university collaboration research was carried out for the ionic liquid
N-Methyl-N-propylpiperidinium bis trifluoromethanesulfonyl imide (PP13–TFSI), a
battery-related material [5] (*11). The research is one for long time-scale phenomena, rather
than for large system. A finite-temerature simulation of the ion pairs in the period of 100 ps
at 303 K is shown in Fig. 6 and reveals the characteristic diffusion mechanism, since a
spontaneous dissociation of the ion-pair into the cation and the anion is not observed andthe ions diffuse as the ion-pair.
(*11) A co-auther of Ref. [5] is H. Yamasaki (Toyota Motor Corp.).
7. Conjugated polymer
Figure 7 shows preliminary results of conjugate polymers. [1,7,10] The research ispartially carried out as an industry-university collaboration. (*12) Conjugated polymer is ofgreat industrial importance among (opt)electronics and medical applications. The structures
are not in ideal crystals and the researches for condensed molecules in 100 nano-meter scale
are crucial. The calculated polymers in Fig. 4 are poly-(9,9 dioctyl fluorine) (PFO) andpoly-(para-phenylene vinylene) (PPV). Localized π wavefunctions are obtained from thetwisting (dihedral) angles between the benzene-like rings, such as in Fig.4 (b), and will playa key role for device property.
Now we are developing a transport calculation code based on the wavepacket
dynamics method for conjugated polymers and other organic materials, since the method isapplicable both to ballistic and non-ballistic transport.
.

42

(*12) Several structure data of amourphous-like conjugated polymers were provided by M
Ishida (Sumitomo Chemical Co.,Ltd) [1,7]Fig. 7 Caculattion of conjugated polymers; (a) Polymer structures of poly-(9,9 dioctyl
fluorine) (PFO)(left) and poly-(para-phenylene vinylene) (PPV) (right). (b) Localized
π wavefunction that appears on amourphous-like PFO polymers. [2] The inset
shows a schematic figure of the wave function. (c) Calculated PPV bundle with thelength L≒40 nm. [10]8. Collaborators within the Computics area
Tomohiro Sogabe, Takafumi Miyata, Shao-Liang Zhang (Nagoya U), Tomoya Ono (TsukubaU).

9. List of papers and invited talks
Original papers[1] Takeo Hoshi, Tomohiro Sogabe, Takafumi Miyata, Dongjin Lee, Shao-Liang Zhang, Hiroto
Imachi, Yoshifumi Kawai, Yohei Akiyama, Keita Yamazaki, Seiya Yokoyama, ‘Novel linear
algebraic theory and one-hundred-million-atom quantum material simulations on the K
computer’, PoS 202, 065, 13.pp (2014).
[2] Takeo Hoshi, Keita Yamazaki, Yohei Akiyama, “Novel linear algebraic theory andone-hundred-million-atom electronic structure calculation on the K computer”, JPS Conf. Proc.
1, 016004, 4pp. (2014).
[3] Dongjin Lee, Takafumi Miyata, Tomohiro Sogabe, Takeo Hoshi, Shao-Liang Zhang, “Aninterior eigenvalue problem from electronic structure calculations”, Japan J. Indust. Appl. Math.
30, pp 625-633 (2013).
[4] Takeo Hoshi, Yohei Akiyama, Tatsunori Tanaka and Takahisa Ohno,	  “Ten-million-atomelectronic structure calculations on the K computer with a massively parallel order-N theory”,
J. Phys. Soc. Jpn. 82, 023710, 4pp (2013).
[5] Shinya Nishino, Takeo Fujiwara, Hisatsugu Yamasaki, Susumu Yamamoto, Takeo Hoshi,"Electronic structure calculations and quantum molecular dynamics simulations of the ionicliquid PP13-TFSI ", Solid State Ionics 225, 22–25 (2012)[6] Tomohiro Sogabe, Takeo Hoshi, Shao-Liang Zhang, Takeo Fujiwara, "Solution ofgeneralized shifted linear systems with complex symmetric matrices ", J. Comp. Phys. 231,
5669-5684 (2012)[7] Takeo Hoshi, Susumu Yamamoto, Takeo Fujiwara, Tomohiro Sogabe, Shao-Liang Zhang,"An order-N electronic structure theory with generalized eigenvalue equations and its

43

application to a ten-million-atom system ", J. Phys.: Condens. Matter 24, 165502, 5pp. (2012)[8] Tatsuya Yamashita, Takafumi Miyata, Tomohiro Sogabe, Takeo Fujiwara, Shao-Liang
Zhang, " An Arnoldi (M, W, G) Method for Generalized Eigenvalue Problems", Trans of
JSIAM 21, 241 (2011) [JAPANESE].
[9] Honghui Teng, Takeo Fujiwara, Takeo Hoshi, Tomohiro Sogabe, Shao-Liang Zhang,
Susumu Yamamoto, "Efficient and accurate linear algebraic methods for large-scale electronic
structure calculations with nonorthogonal atomic orbitals ", Phys. Rev. B 83, 165103, 12pp,(2011)

Invited talks on international conference or workshop[10] Takeo. Hoshi and Hiroto Imachi, ‘Krylov subspace theories and one-hundred-million-atomelectronic structure calculations on the K computer’, International Symposium on Computics
Quantum Simulation and Design (ISC-QSD-2014), Koshiba Hall, University of Tokyo1-3, Dec.
(2014).
[11] Takeo Hoshi, Tomohiro Sogabe, Takafumi Miyata, and Shao-Liang Zhang, “Novel linear
algebraic theory and one-hundred-million-atom quantum material simulations on the K
computer”, The First International Workshop on Computational Science and Engineering ,National Taiwan University Taipei, Taiwan, 14-17., Oct., (2013).
[12] Takeo Hoshi, "Krylov subspace theories and ultra-large-scale electronic state calculations
on the K computer ", The 9th East Asia SIAM Conference The 2nd Conference on Industrial
and Applied Mathematics (EASIAM-CIAM 2013) , Institut Teknologi Bandung, Bandung, West
Java, Indonesia, 18-20., June (2013).
[13] Takeo Hoshi, Susumu Yamamoto, Takeo Fujiwara, Tomohiro Sogabe, Shao-Liang Zhang,
Yohei. Akiyama, Takahisa. Ohno, 'Ten-million-atom electronic structure calculations with novel
linear-algebraic algorithm and the K computer, International Symposium on Computics:
Quantum Simulation and Design (ISC-QSD), Osaka University Hall, 11-13. Oct. (2012)[14] Takeo Hoshi, Tomohiro Sogabe, Susumu Yamamoto, Shinya Nishino, Takeo Fujiwara,
Shao-Liang Zhang, "Novel linear-algebraic theories in large-scale electronic structure
calculation and its application to nano-materials ", Dresden-Kobe Joint Workshop on Electronic
Simulations for Nanosystems, Kobe University, 7. Mar. (2012)
Invited talks on domestic conference or workshop：totally 9 talks ( 1 talk in 2011, 2 talks in 2012,
4 talks in 2013, 1 talk in 2014, 1 talk in 2015).

44

Part IINew Development in Density-Functional Theory

Density-Functional Approach to Atomic and Electronic Structures and their
Dynamics in Nano-Structures
Atsushi Oshiyama1, Junichi Iwata1, Taisuke Ozaki2, Tsuyoshi Miyazaki3, and Eiji Tsuchida4
1
Department of Applied Physics, The University of Tokyo
2
Institute for Solid State Physics, The University of Tokyo
3
Computational Materials Science Unit, National Institute for Materials Science
4
Nanomaterials Research Institute, National Institute ofAdvanced Industrial Science and Technology
The main purpose of this project is to develop the density-functional approach which enables us
to perform more accurate and larger scale static and dynamical calculations on massively parallelarchitecture computers, to clarify underlying physics and chemistry in phenomena in nanomaterials and structures, and to predict new phenomena in nano-world. We have adopted a realspace scheme as a principal methodology to solve the Euler equation in the density-functional
theory (DFT). We have also incorporated Krylov subspace method or the density-matrixoptimization method to make the computation cost scaling linearly to the system size N. Thoroughthe computations using these calculation schemes on the K computer at Kobe, Japan and also onother multi-core parallel architecture computers, We have clarified and predicted various
properties in nano-materials and structures. In particular, ACM Gordon Bell Prize in 2011 wasawarded to our real-space DFT calculations for silicon nanowires consisting of more than 100,000
atoms. The obtained results in this project are disseminated as 98 papers in scientific journals andpresented in 31 invited talks of major international conferences. The following is a summary of
those achievements (Ref. number cited below corresponds to the number in the publication list).
1.

Development of Real-Space Density-Functional-Theory (RSDFT) Approach [1,6]
To perform accurate density-functional calculations efficiently on the multi-core massively
parallel architecture computers, we have adopted a real-space (RS) finite-difference scheme in
DFT combined with the first-principles pseudo-potential method. We have developed a highly
efficient computation code named RSDFT. In the real-space scheme, discrete grid points are
introduced in real space, and the Hamiltonian in the Kohn-Sham (KS) equation in the DFT isexpressed as a matrix represented at the grid-point space. Differential operators for kinetic energy
are replaced by finite-difference operators with sufficiently high orders. The Hamiltonian matrix
therefore becomes sparse and Fast-Fourier Transformation (FFT), which is heavy communication
burden among all the compute nodes in the conventional plane-wave basis-set scheme, isunnecessary in the Hamiltonian operation. Hence, the communication becomes essentially local
only among neighboring compute nodes so that the total communication cost is tremendously
reduced in RSDFT.
The basic algorithm to solve Kohn-Sham (KS) equation is almost the same as that used inconventional O(N3) scaling method. The main procedures consist of three parts: ConjugateGradient minimization, Gram-Schmidt ortho-normalization, and subspace diagonalization. The
latter two are the bottlenecks which have O(N3) scaling. Those procedures are basically linear
algebraic calculations. In high performance computing (HPC), it is important to perform thecomputation using the data on the cache, the nearest memory to the compute node, since to fetch
the data from far memories or the hard disk costs a lot of time. Then when a ratio of the numbersof computation operations to the number of data required for the computation is high in an
algebraic calculation, it can be performed using mainly the data on the cache and thus the HPC is
feasible. In the matrix times matrix calculation, this ratio becomes high with increasing the target

45

size, compared with the inner product of vectors and also with the matrix times vector product.
In the Gram-Schmidt ortho-normalization in RSDFT code, eigenvectors, {¥it i.e.}, Kohn-Shamorbitals, are gathered in several groups so that apparent inner products of the vectors are converted
to the matrix-times-matrix calculations. This conversion renders our ortho-normalization to beefficiently done: The computational performance has reached 80 - 90 % of the theoretical peak
performance by using Basic Linear Algebra Subprograms (BLAS) level 3 on the K computer in
Kobe, Japan.
In addition to the ground state properties, we have made RSDFT applicable for Car-Parrinello
molecular dynamics (CPMD) simulation. Several benchmark tests on the K computer show thatthe real-space scheme is also suitable for CPMD implementation. We have further tuned the realspace CPMD code on the K computer. We are now capable of performing CPMD simulations fora few-thousands atom systems with practical CPU cost.
Our nano-meter scale targets consist of tens of thousands of atoms. In studies of such largesize systems, electronic energy-band structures provide important information to understandoptical and electrical characteristics of the systems. However, the calculation of energy bands inthe nano-system often becomes a heavier task than the self-consistent field calculation since many
eigenvalue problems with a large number of k-point parameters need to be solved and thecalculations must be performed in double-complex precision. In collaboration with people in thefield of applied mathematics, we have implemented in RSDFT code the Sakurai-Sugiura (SS)method for eigenvalue problems in which we are capable of obtaining eigenvalues in a specified
energy region. Hence the SS method is applied to the computation of the eigenvalues near the
Fermi level, thus substantially reducing the computational costs. In the SS method, we have tosolve linear equations with multiple shifts many times. We have also introduced an efficientalgorithm to solve the linear equations with multiple shifts.
2.

Application to RSDFT SchemeElectron States and Electric Current Distribution in Si Nanowires (NWs) [6,15]: Current
miniaturization of field effect transistors (FETs) is suffered from the limitation of the performance
inherent to the planar structures. Nanowire structures, i.e., all-surrounding gate structures arepromising in the next-generation FETs [Int. Tech. Roadmap for Semiconductors:
http://www.itrs.net/].
We have performed RSDFT calculations for various cross-sectional shapes such as circles,
ellipsoids and dumbbells with several cross-sectional dimensions and crystallographic wire
directions. The obtained energy bands show benefits of [110]-SiNW with the ellipsoid shape [15].
Combining the obtained energy bands and Koh-Sham orbitals from the RSDFT calculations witha simple transport mode [K. Natori, IEEE Trans.
Electron Devices 55, 2877 (2008)], we have calculateed the electric current density underappropriate bias voltage. Figure 1 shows calculated
current density represented on the wire crosssections. This information is important since thecarrier scattering at the interface of the wire and theoxide insulator may be crucial in designing allsurrounding gate transistor. The RSDFT calculationsfor SiNW were awarded Gordon Bell Prize for its
high performance.
Silicene on Ag Substrates[17,18]: Graphene is a
Fig. 1: Current density distribution on the
hexagonally bonded carbon sheet. Its most intriguingcross section of silicon NW FET as aproperty is the linear energy dispersion near thefunction of gate voltage.

46

Fermi level (EF) at particular symmetry
points (Dirac cone) in the Brilloine zone
(BZ). This gives rise to unique phenomena such as the anomalous quantum
Hall effect and the unexpected magnetic
ordering. Moreover, the very high inplane mobility makes graphene a
promising material utilized for nextgeneration devices. However, fromviewpoints of the technology connectivity, Si, which is located just below C in
the periodic table, is a more attractive
element. There has been a lot ofexperimental efforts to synthesize Si
monolayer (silicene) mainly on Ag
substrates. In this project, we have
performed RSDFT calculations forsilicene on Ag and found that Dirac
Fig. 2: Calculated STM images (right parts) and top
electrons are absent in this system due toviews of atomic structures (left parts) of the silicene on
the mixing between π orbitals of silicene Ag(111) surfaces. The stable [(a), (c) and (e)] and theand Ag orbitals. Instead we have propose metastable [(b), (d) and (f)] structures with the 4 x 4periodicity [(a) and (b)], the 13 x 13 periodicity [(c)that the BN sheets or the hydrogen- and (d)], and the 2 x2 periodicity[(e) and (f)] are3
3
passivated Si (111) surface is a good shown. Each circle of the left parts depicts the position
candidate for the substrate which provide of the Si atom in the silicene layer: The positions of the
topmost Si and the bottommost Si are depicted by the
Dirac electrons.
largest(red) and the smallest (blue) circles; theFigure 2 shows the stable structures ofintermediate-size circles depict the Si atoms between
the monolayer silicene on Ag(111) sur- the top and the bottom. The large gray balls depict theface. Experimentally several structures positions of the substrate Ag atoms. The lateral unit cellswith super- periodicity are identified. Our
calculations reproduce all the experimenttally observed structures and also predict
new atomic structures. The total energiesof those structures are close to each otherwith the energy difference of a few tens ofmeV, awaiting the experimental confirmation. Calculated STM images are in excellent agreement with the experiments whenavailable (Fig. 2).
Fig. 3: Calculated energy bands (a) of the silicene on
Our calculations show that in the freestanding silicene there are Dirac cones at EF the hydrogen-covered Si(111) surface [inset of (a)]and contour plots of the mixed π+ (π+*) states (b)though the silicene plane is substantially [absolute values]. Enlarged energy bands near EF = 0
buckled (a half Å). On the contrary, we have are shown in another inset and the distributions of thefound that Dirac cones are absent in any mixed π+ (π+*) states at K point marked by thestable structure of the silicne on Ag. The square are shown on the plane perpendicular to thesurface. The blue and pink balls in the inset depict Sibuckling itself mixes σ and π orbitals but
and H atoms, respectively.
keeps the Dirac cone near EF. The mixing ofSi π plus σ orbiatls and Ag orbitals, however, produces bonding and antibonding states between
Si and Ag orbitals, thus removing linear-dispersion states from EF.

47

As an alternative for the Ag substrates, we consider hexagonal BN sheet and hydrogenterminates Si (111) surface. Figure 3 shows calculated energy bands for the stable silicene on Hterminated Si (111) surface. The calculations show that the distance between the silicene layer
and the substrate hydrogen is 2.44 Å and the binding energy is 140 meV per Si atom. The energy
bands unequivocally shows the existence of Dirac cone at EF. The character of the states isobviously Si π orbitals. Those calculations clarify that soft-landing substrates are good candidates
for preparing silicene with Dirac cone.
Moiré-Induced Electron Localization in Twisted Bilayer Graphene[25]: Bilayer graphene
is synthesized by either the exfoliation or
by heat treatments of SiC surfaces,
introducing a new degree of freedom,
i.e., the way of stacking of C atomic
layers. When each hexagonal sheet isstacked identically, i.e., an atom of eachlayer is on top of a partner atom of theadjacent layer, it is called AA stacking. In
graphite, each layer is rotated in the basal
plane from the adjacent layer by 60o. Fig. 4: Side and top views of geometry optimized TBLG
This is called AB stacking or Bernal with the twist angles θ of (a) 29.4o and (b) 8.26o. In (b),stacking. In bilayer graphene (BLG), two the corrugation ∆ is visible with the far and the near
distances, dfar and dnear.
layers may be stacked with a twist angle
θ being 0o < θ < 60o (θ=0o and θ = 60o correspond to the AA and AB stackings, respectively).
Twisted bilayer graphene (TBLG) is indeed observed experimentally. The layers with a tiny twist
angle θ generate a Moiré pattern with its period L = 3d / [2sin(θ / 2)] , where d is the C-C bondlength. Interlayer interaction in BLG is smaller than the intralayer interaction by an order ofmagnitude. Hence one may consider that the difference in the stacking plays only minor role inatomic and electronic structures of BLG. However, it is not true for twisted bilayer graphene(TBLG) with small twist angle θ, as is shown below.
We have performed RSDFT calculations for 59 TBLGs with various twisted
angles including the smallest θ=0.76o(22,708 atoms in a unit cell) using the
local-density approximation (LDA). We
have examined the validity of LDA byrepeating some of the calculations using
van der Waals (vdW)-DFT functional. The
results obtained are found to be essentially
identical to those by LDA. Figure 4 showsgeometry optimized TBLGs for two
representative twist angles θ. For θ=29.4o,
Fig. 5: Fermi velocity normalized to that of monolayer
graphene vF0, as a function of θ: the velocities in thethe two layers are almost flat [Fig. 4(a)]optimized
structures (vF); those for the flat structureswith the interlayer distance of 3.42 Å.
with the interlayer distances of 3.61 Å (vFfar) and 3.34 Å
When θ becomes small, we find Moiré (v near). Circles are experimental data [Luican et al.,Fpatterns in which the AA and AB stacking PRL, 106, 126802 (2011)]. The vertical dashed lines
regions as well as other stacking regions depict the position of the critical angle θe.
constitute a patchwork as in Fig. 4(b). The
period L of the patchwork pattern and the size of each of the AA and AB stacking regions increase48

as θ becomes close to 0o (or 60o). For small θ, the two layers are corrugated. The interlayer
distance is large (dfar) in the AA stacking region and small (dnear) in the AB stacking region.
The variation of the Fermi velocity vF as a function of θ is shown in Fig. 5. We have foundthat vF is almost the same as that in monolayer graphene for θ > 10o, and that it is dramaticallyreduced toward zero when θ < θe. When we adopt the twist angle at which the Fermi velocity
becomes half of the velocity in monolayer graphene, θe is about 3o. Although the value of θe has
ambiguity in a sense that the half-maximum setting is not uniquely adopted, the existence of thiscritical angle is evident. Analyses of the Kohn-Sham orbitals clarify that the reason for the
reduction of vF and then the emergence of the flat bands is ascribed to the electron localization
due to the Moiré pattern. For larger twist angle, the Kohn-Sham orbitals at EF are characterizedby π orbitals extending over the whole carbon sheet. However, when θ becomes as small as 1o,
the Moiré pattern becomes prominent and the Kohn-Sham orbitals at EF are localized in the AA
stacking region. The Moiré pattern which becomes prominent for small θ induces inhomogeneity.
The electron wave senses the inhomogeneity, and finally the Kohn-Sham orbitals are localized.
Moreover, the reduction in vF is not monotonic. As shown in the inset of Fig. 5, vF vanishes at θM=1.08o and then slightly increases for the smaller θ. There is a magic angle θM at which vF vanishes.
Magnetic Ordering with Non-Magnetic Elements on SiC Nanofacet[23]: Nanometer-scale
structures are now accessible through cutting-edge fabrication technique or a gift of selforganization phenomena. Common expectation that such nanostructures break through limitationsof current technology may rely on a fact that nano-scale shapes affect wave-functions of relevant
electron states. However, a way of designing nano-shapes which decisively affect the electronstates and therefore are intriguing in science and useful in technology is lacking. Our RSDFT
calculations here show that peculiar electron states which are localized near but extended along
step edges of the nano-facets of SiC exhibit either ferromagnetic (FM) or anti-ferromagnetic(AFM) spin polarization. Considering that SiC is an emerging material in the next-generation
environmental-friendly power electronics and that spin current is the new non-dissipative carrier
for the information in future, this finding based on our RSDFT scheme has great impact.

Fig. 6: Side view of the(11-2n) (n=12) nanofacet
on the 4H-SiC(0001) vicinal surface, which wehave found is most stable.
Green, yellow and purple
balls indicate the Si, C
and H atoms, respectively.

Figure 6 shows the obtained stable structure of the nano-facet on SiC (0001) surface. The
shape of the nano-facet is characterized by the magic facet angle ( ϕ = 15.3o ) and facet height withthe unit-cell dimension, being in excellent agreement with the nano-facet experimentally observed.
The energy bands of this nano-facet is shown in Figure 7. Near EF, we observe many states whichhave characters of dangling bonds (DBs) of surface Si atoms on the long terrace. The energy
bands more than 1.5 eV below EF is mainly ascribed to the valence bands of the bulk SiC, whereas
the bands at about 1 eV above EF are from the bulk conduction bands. Apart from those states, wehave found four distinct states in the energy gap, labeled as SE1, SE2, SE3 and SE4 in Fig. 7(a).

49

From the analyses of the Kohn-Sham (KS) orbitals of these states [Figs. 7(b)-(e)], we have foundthat they originate from the step-edge states: The KS orbitals of the SE1 and SE2 states are
localized near the step edges where the upper terraces have cubic symmetry, whereas the orbitalsof SE3 and SE4 states are near the step edges where the upper terraces have the hexagonal
symmetry They are localized near but extended along the step edges, exhibiting dispersion-freeflat bands.

Fig. 7: Energy bands along the ΓX parallel to the step edge of the stable (11-2n) nanofacet on 4HSiC (0001) surface obtained by our LDA calculations. The Fermi level is set to be zero. The SE1 andSE2, and also the SE3 and SE4 are almost degenerate. The Kohn-Sham orbitals of the SE1, SE2, SE3
and SE4 states at the Γ point are shown in (b), (c), (d), and (e), respectively, as isovalue surfaces. The
red and blue colors depict positive and negative values, respectively, of the Kohn-Sham orbitals.

This flat-band nature is indicative of the magnetic ordering if EF shifts downwards to SE states.
We have found that this is realized by the hydrogen passivation. Our detailed DFT calculations
have clarified that H passivation/adsorption on Si surface atoms and further edge Si atoms areenergetically favorable. Without hydrogen, the Si DBs are either doubly occupied or unoccupied.
The H adsorption annihilates this DB states and generates the low-energy lying Si-H bonding
states which are doubly occupied. Then the H adsorption shifts EF, depending on which sites are
H passivated. Our RSDFT calculations have indeed clarified that the H passivation is capable ofcontrolling the filling of the SE states and induce either FM or AFM chains along the step edgesof SiC nano-facets which are organized spontaneously.
3.

Development of Numerically Exact Low-Order Scaling Method
Many scientific problems can be cast to an eigenvalue problem, and it is known that thecomputational cost of solving the eigenvalue problem scales as O(N3), where N is the dimensionof the problem. The density functional theory (DFT) for molecules and solids is also cast to an
eigenvalue problem within semi-local approximations such as local density and generalized
gradient approximations, and thereby the computational cost must be O(N3). Thus, it is interesting
to question whether the computational cost of the DFT calculation can be reduced from O(N3) toa low-order scaling without introducing approximations. We have addressed the problem andfound that such a method can be actually developed by utilizing of locality of basis functions [3].
Our method directly computes selected elements of the density matrix by a contour integration ofGreen's function [T. Ozaki, PRB 75, 035123 (2007)], which allows us to evaluate only O(N)density matrix elements due to the locality of basis functions. The Green's function is evaluatedwith a nested dissection approach for sparse matrices as shown in Fig. 8. It turns out that thecomputational effort of the method scales as O(N(log2N)2), O(N2), O(N7/3) for one-, two-, and50

three-dimensional systems, respectively. Unlike O(N)methods developed so far the approach is a numericallyexact alternative to conventional O(N3) diagonalization
schemes in spite of the low-order scaling, and can beapplicable to not only insulating but also metallic systems
in a single framework. It is also noted that the well
separated data structure is suitable for the massively
parallel computation. We expect that the direction will befurthermore explored in the near future to extend theapplicability of DFT calculations for large-scale systems
without sacrificing the accuracy.
4.

Development of massively parallel O(N) method
One of ways to extend applicability of the density
functional theory (DFT) calculations towards large-scale
scale systems is to employ O(N) methods of which
computational cost is proportional to the number of atoms.
We have been developing such an O(N) method based on
Fig. 8: (a)-(c) Nested dissection of athe divide and conquer method and Krylov subspace sparse matrix, (d) binary tree
method [T. Ozaki, PRB 74, 245102 (2006)], and proven by structure for the interaction in (c).
applying the method to a wide variety of systems
that the O(N) method can be applied to not only
insulators but also metals. In the method, a largescale system is divided into a set of small clusters,
where each cluster centers on each atom, and thecalculation of each cluster is performed nearly
independently. After performing the calculations of
all the clusters, the Green’s function associated withall the central atoms are collected as a patch work,
which enables us to calculate density matrix
elements which are required in the calculation of
charge density. Thanks to the algorithm, the O(N)method is intrinsically suitable to parallelFig. 9: Atomic decomposition by acalculation. However, it is not so obvious how themodified bisection and inertial tensor
clusters should be distributed to MPI processes in methods.
the parallel calculation to minimize communication
volume and memory usage. It is important for increase of parallel efficiency to localize data thateach process accesses and to minimize the volume and the number of MPI communication
involved. We have addressed the issue and developed a spatial decomposition method based on amodified recursive bisection method and inertia tensor [29]. The method consists of three steps:(1) for a given number of MPI processes a binary tree structure is constructed by using a modified
recursive bisection method, (2) a principal axis for a set of atoms is determined by diagonalizing
an inertia tensor with load balancing weights, and these atoms are projected onto the principal
axis, (3) these atoms are grouped on the principal axis based on the binary tree structure generated
in the step (1). As shown in Fig. 9, performing the steps (2) and (3) according to the binary tree
structure generated in the step (1) allows us to spatially decompose atoms while keeping
localization of atoms. The dynamic load balancing is also possible by taking account of elapsed
time in previous molecular dynamics or geometry optimization step in constructing the inertial51tensor. As an example, how a supercell of diamond is decomposed is shown in Fig. 10, where thesupercell contains 16384 carbon atoms, 19 MPI processes are used, and atoms colored by thesame color are allocated to the same MPI process. It is found that the spatial decomposition isproperly performed even using 19 MPI processes being a prime number. We have implemented
the decomposition method in OpenMX, and measured the parallel efficiency of the O(N) methodon the K-computer. The parallel efficiency reaches at 68 % using 131072 cores on the K-computer,
where the benchmark system is the diamond superlattice consisting of 131072 carbon atoms. We
have been applying the newly developed methods to electrode-electrolyte interfaces [13, 28],
metal-insulator interfaces [20], and grain boundaries in permanent magnets.

Fig. 10: Atomic decomposition of adiamond superlattice where 19 MPI
processes are used.

5.

Application of Open-MX Code to Two-Dimensional Si Structures
Although it is believedthat two-dimensional honeyExpt.
Calculated(b)comb structures consisting ofsilicon atoms do not exist
experimentallydue
torelative instability of its
hybridized sp2 orbitals, a
recent experiment clearly
demonstrates that silicene,honeycomb structure ofsilicon atoms, can be
fabricated on ZrB2 (0001)
thin films [12]. We have
performed detailed studies Fig.11: omparison between angle-resolved photoemisisonon geometrical and electron- spectroscopy (ARPES) data and the theoretical band structure
ic structures of silicene on calculated by the unfolding method of silicene on ZrB2 (0001).
ZrB2 and a related two-dimensional structure by means of electronic structure calculations based on density functional
theories (DFT), guided by close collaboration with experiments. Theoretical chemical shift of Si2p states [12] and band structure calculations [26], as shown in Fig.11, strongly support theformation of silicene having a planar-like structure. The stability of the planar-like structure over
the regularly buckled structure can be understood by interaction between states of the silicene andsurface states consisting of the d-orbital of the top Zr atoms [19]. We have also proposed a possible
mechanism for the formation of the domain structure of silicene on ZrB2 [12, 27]. It is inferredthat the domain structure is induced by an instability of a phonon having a nearly zero frequency,
and is formed in such a way that the k-points having the zero frequency can be removed from thefirst Brillouin zone. The mechanism is verified by performing large-scale total energy calculations
as shown in Fig. 12. We have further explored a possible structure of multi-layer silicene, andfind that the MoS2 structure consisting of silicon atoms is stabilized with atoms in the inner layer
having a sixfold coordination, which results in cigar-shaped nematic orbitals originating from the52Si-sp2 orbitals [Gimbert et al., PRB 90, 165423 (2014)].

Fig. 12: Total energy ofsilicene on ZrB2 (0001) withthe domain structure.

6. Development of Order(N) Density-Matrix Optimization (CONQUEST) Approach
First-principles technique based on the density functional theory (DFT) is a powerful method
widely used to elucidate the physical properties of various materials at the atomic scale. However,the size of the systems modeled with the conventional first-principles methods is limited because
the computational cost increases as the cube of the number of atoms N in the simulation cell. To
overcome this problem, we have been developing a linear-scaling DFT code CONQUEST, whose
memory requirements and CPU time are both only proportional to N (O(N) method). The code ispowerful and efficient on massively parallel supercomputers like K computer in Kobe. We havedemonstrated that DFT calculations on million-atom systems are now possible using K computer.
(Fig. 13)
Fig. 13: Wall-clock time of O(N) DFT
simulations of silicon systems using the K
computer (1 CPU = 8 cores). The horizontal
axis shows the number of atoms, indicatingthat DFT simulations of million-atomsystems are possible. We can see that we cancalculate systems containing twice thenumber of atoms in the same time bydoubling the number of CPUs, meaning thatthe computational cost is O(N) and theklill l ffi i
f hdDevelopment of the efficient and accurate local orbitals used in CONQUEST: We haveintroduced multi-site local orbitals (support functions) into CONQUEST in order to reduce thenumber of support functions to the minimal basis while maintaining as much accuracy as possible.
The multi-site support functions are constructed by taking linear combinations of the Pseudo
Atomic Orbitals (PAOs) on both the target atom and its neighbor atoms within a cutoff. Since thecomputational cost is proportional to the cube of the number of support functions both in O(N)and conventional diagonalization methods, we can significantly reduce the computational timeby using the scheme of multi-site support functions.
To determine the linear-combination coefficients, we have used the local filter diagonalization(LFD) method proposed by Rayson et al. (Phys. Rev. B 80, 205104(2009)) and the optimizationof the coefficients to minimize the total energy. The multi-site support functions with large cutoffs

53

provide energies and forces with comparable accuracy with the original (primitive) PAO results.
When the coefficients are determined only with the LFD method, the multi-site support functions
with small cutoffs provide large deviations from the original results. However, the optimizationof the coefficients significantly improves the accuracy of the multi-site support functions. The
stability and convergence of the calculations with small cutoffs are also improved by the
optimization. Thus, the coefficient optimization enables us to use small cutoff for multi-site
support functions keeping reasonable accuracy, which will reduce the computational cost
significantly. We have demonstrated the accuracy and efficiency of the method for hydrated DNA
system (Fig. 14 and Table 1).

Fig. 14: Density of states of the hydrated DNA system by primitive and multi-site support
functions. Black, blue and red curves correspond to the results by primitive, multi-site (LFD) andmulti-site (LFD + opt) support functions, respectively. rLD is set to be equal to rMS. Deviations
from the DOS by the primitive support functions are shown for the occupied region.
Table 1: Computational times [sec.] for matrix construction, diagonalization and gradientcalculation with respect to the coefficients for the hydrated DNA system by multi-site support
functions (rLD-rMS) and primitive support functions.

(8.0-8.0)(11.0-11.0)(16.0-16.0)
Primitive
DZP

Matrix
Gradient
Diagonalization
construction
calculation
34.5
627.7
4.3
54.4
583.4
8.6
484.8
566.3
25.7
28.0

12317.4–

Stable and Efficient Linear-scaling First-principles Molecular Dynamics (FPMD): The
recent progress of linear-scaling or O(N) methods in the density functional theory (DFT) isremarkable. We expect that first-principles molecular dynamics (FPMD) simulations based on
DFT could treat more realistic and complex systems using the O(N) technique. However, very
few examples of O(N) FPMD simulations exist to date, and information on the accuracy andreliability of the simulations is very limited. We have shown that efficient and robust O(N) FPMD
simulations are now possible by the combination of the extended Lagrangian Born−Oppenheimer
molecular dynamics method, which was recently proposed by Niklasson (Phys. Rev. Lett. 2008,54

100, 123004), and the density matrix minimization method as an O(N) technique. Using ourlinear-scaling DFT code CONQUEST, we have investigated the reliable calculation conditions
for accurate O(N) FPMD simulations and have demonstrated that we are now able to do practicaland reliable self-consistent FPMD simulations of a very large silicon system containing 32768
atoms, using 512 CPUs of FX10 or 1024 CPUs of K computer.
7.

Application of CONQUEST to a Semiconductor Hetero-Structure
Using the ability of CONQUEST, we worked on the growth mechanism of Ge threedimensional (3D) islands, called hut cluster, which are formed when Ge is deposited on the Si(001) surface. The 3D islands are made of four {105} facets and they grow under some conditions
by increasing the length of thelonger side while keeping thewidth constant. To control themorphology of the nanostructured system, understanding
the mechanism of the growth isvery important, but we need totreat the systems containing at
Fig. 15: Adsorption sites (left) and energy map (right) of single
least a few tens of thousands of
Ge dimers adsorbed on large and small facets of Ge hut cluster.
atoms to model these systems.
We have performed DFT studyof adsorption of Ge dimers on the{105} facets of a Ge hut cluster inorder to identify stable nucleationsites. By using a linear scaling
technique, we were able toperform robust and efficient
structure optimization of large
systems (20,000 – 200,000 atoms).
We calculated the energy map ofsingle Ge dimers adsorbed on two
different facets of an elongated hut
cluster (Fig. 15). Our results show
Fig. 16: Energy change during facets completion: red & greythat ridges and edges between two circles – completion of a small facet starting from the basefacets are stable and that the upper and apex, respectively, and blue rectangles – completion of
positions are generally more stable a large facet starting from apex.
than
lower
positionsbyapproximately 0.2eV/atom. We have also investigated that the completion of {105} facets by
calculating the stability of ”imperfect” facets (Fig. 16). The results together with the energy mapof single Ge dimers on the facets suggest that a new facet layer grows from the apex to the bottom.
8.

New Algorithms in Static and Dynamical Density-Functional Calculations
An algorithm for increasing the stability limit of ab initio molecular dynamics
simulations[32]: The computational cost of ab initio molecular dynamics (AIMD) is still aserious obstacle, even on a supercomputer. If, however, the goal of the simulation is to obtainlow-energy conformations through simulated annealing, or to equilibrate the system prior to the
production run, the computational cost is minimized by using the largest possible time step. When
the Verlet method is used to integrate the equations of motion, the maximum size of the time step55

is given by hmax = T/π, where T is the period of the fastest oscillation in the system. In practice,
however, AIMD simulations often break down at ~ hmax /2 due to the strong anharmonicity of
the interatomic forces. We have recently shown that the stability limit of the Verlet method may
be significantly increased by setting an upper bound on the kinetic energy of each atom with onlya small loss of accuracy. The validity of our approach was demonstrated for molten LiF.
Accelerating electronic structure calculations with mixed precision algorithms: Matrix
diagonalization is often the computational bottleneck in large-scale electronic structure
calculations. We have recently demonstrated that a careful use of 32-bit floating point operations
in matrix diagonalization allows us to accelerate the electronic structure calculations by more than
30% on Intel/AMD CPUs, while keeping 64-bit accuracy. Moreover, most of the computationallyexpensive operations are performed by level-3 BLAS/LAPACK routines in our implementations,thus providing optimal performance on many platforms. This approach may also be extended tosimilar cases, e.g. density-functional perturbation theory and/or time-dependent density
functional theory. It will also be interesting to utilize the mixed precision arithmetic in conjunction
with Graphics Processing Units (GPUs). [Tsuchida & Coe, Comp. Phys. Commun. 183, 980 (2012)]
Accelerating ab initio molecular dynamics using generalized masses[10]: Mass tensor
molecular dynamics method was originally introduced by Bennett four decades ago for enhanced
sampling of the phase. The generalized Hamiltonian is given by
H (q, p) =1
∑ pi M ij−1 (q) p j + U (q)2 i, jwhere M is a positive definite, symmetric matrix of dimension 3Natom. If M is chosen carefully,
the efficiency of ab intio molecular dynamics can be significantly improved without changing
the results. Test calculations on liquid water consisting of 64 molecules showed a threefold
reduction in computational effort without making the fixed geometry approximation. We alsopresented a simple algorithm for estimating the optimal atomic masses using only the first
derivatives of the potential energy. This approach will be particularly useful for calculating
ensemble averages, e.g. radial distribution functions and free energies, in finite temperature
simulations. It would also be interesting to combine this approach with rare event methods, suchas hyperdynamics and metadynamics.
Collaborators
Kazuyuki Uchida (Kyoto Sangyo University), Zhi-Xin Guo (Xiangtan University), Keisuke
Sawada (Riken), Mauro Boero (Strasbourg University), Ken-ichi Koizumi (Institute for
Molecular Science), Shinnosuke Furuya (ARGO GRAPHICS Inc.), Yasuteru Shigeta (Universityof Tsukuba), S. Arapan (NIMS), A. Nakata (NIMS), D. R. Bowler (UCL), Yu-ichiro Matsushita(The University of Tokyo), Sukmin Jeong (Chonbuk University), Shinya Kyogoku (Toshiba
Corporation).
Publications and Invited Talks
Selected List of Publications (the number of papers published in the period of this project =98)
1.

2.
3.
4.

J.-I. Iwata, D. Takahashi, A. Oshiyama, B. Boku, K. Shiraishi, S. Okada and K. Yabana, ``A massivelyparallel electronic-structure calculations based on real-space density functional theory" J. Comp. Phys.
229, 2339 (2010).
Y. Gohda and A. Oshiyama, ``Stabilization mechanism of vacancies in group-III nitrides: Exchange
splitting and electron transfer" J. Phys. Soc. Jpn. 79, 083705 (2010).
T. Ozaki, “Efficient low-order scaling method for large-scale electronic structure calculations withlocalized basis functions”, Phys. Rev. B 82, 075131 (17 pages) (2010).
Y. Matsushita, K. Nakamura adn A. Oshiyama, ``Comparative study of hybrid functionals applied tostructural and electronic properties of semiconductors and insulators" Phys. Rev. B 84, 075205 (2011).

56

5.
6.

7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.

23.
24.
25.
26.

27.

28.
29.
30.
31.

S. Jeong and A. Oshiyama, ``Selective Alignment of Carbon Nanotubes on Supphire Surfaces: Bond
Formation between Nanotubes and Substrates" Phys. Rev. Lett. 107, 065501 (2011).
Y. Hasegawa, J.-I. Iwata, M. Tsuji, D. Takahashi, A. Oshiyama, K. Minami, T. Boku, F. Shoji, A. Uno,
M. Kurokawa, H. Inoue, I. Miyoshi, M. Yokokawa, ``First-principles calculations of electron states ofa silicon nanowire with 100,000 atoms on the K computer”, Proceedings of 2011 International
Conference for High Performance Computing, Networking, Storage and Analysis (SC2011)
M. Toyoda and T. Ozaki, “Exchange functional by a range-separated exchange hole”, Phys. Rev. A 83,
032515 (2011).
T. Ozaki and M. Toyoda, “Accurate finite element method for atomic calculations based on density
functional theory and Hartree-Fock method”, Comp. Phys. Comm. 182, 1245-1252 (2011).
M. P. Sena, T. Miyazaki and D. R. Bowler, “Linear Scaling Constrained Density Functional Theory in
CONQUEST”, Journal of Chemical Theory and Computation, vol. 7, p884-889 (2011)
E. Tsuchida, ``Ab initio mass tensor molecular dynamics”, J. Chem. Phys. 134，044112 (2011).
Y. Matsushita, S. Furuya and A. Oshiyama, ``Floating Electron States in Covalent Semiconductors"
Phys. Rev. Lett. 108, 246404 (2012).
A. Fleurence, R. Friedlein, T. Ozaki, H. Kawai, Y. Wang, and Y. Yamada-Takamura, "Experimental
evidence for epitaxial silicene on diboride thin films", Phys. Rev. Lett. 108, 245501 (5 pages) (2012).
T. Ohwaki, M. Otani, T. Ikeshoji, and T. Ozaki, "Large-scale first-principles molecular dynamics forelectrochemical systems with O(N) methods", J. Chem. Phys. 136, 134101 (9 pages) (2012).
D. R. Bowler and T. Miyazaki, “O(N) methods in electronic structure calculations” , Report on
Progress in Physics, vol. 75, 036503 (2012).
S. Kyogoku, J.-I. Iwata and A. Oshiyama, ``Relation between nanomorphology and energy bands of
Si nanowires" Phys. Rev. B 87, 165418 (2013).
K. Koizumi, M. Boero, Y. Shigeta, and A. Oshiyama, ``Atom-Scale Reaction Pathways and FreeEnergy Landscapes in Oxygen Plasma Etching of Graphene" J. Phys. Chem. Letters 4, 1592 (2013).
Z.-X. Guo, S. Furuya, J.-I. Iwata and A. Oshiyama, ``Absence of Dirac Electrons in Silicene on
Ag(111) Surfaces" J. Phys. Soc. Jpn. Letters 82, 063714 (2013).
Z.-X. Guo, S. Furuya, J.-I. Iwata and A. Oshiyama, ``Absence and Presence of Dirac Electrons in
Silicene on Substrates" Phys. Rev. B 87, 235435 (2013).
C.-C. Lee, A. Fleurence, R. Friedlein, Y. Yamada-Takamura, and T. Ozaki, "First-principles study oncompeting phases of silicene: Effect of substrate and strain", Phys. Rev. B 88, 165404 (2013).
H. Sawada, S. Taniguchi, K. Kawakami, and T. Ozaki, ``First-principles study of interface structureand energy of Fe/NbC", Modelling Simul. Mater. Sci. Eng. 21, 045012 (2013).
T. Otsuka and T. Miyazaki, ”A quantum chemistry study of Ds-Pa unnatural DNA base pair”, Int. J.
Quantum Chem. Vol. 113, p504-509 (2013).
T. Ohkubo, E. Tsuchida, M. Gobet, V. Sarou-Kanian, C. Bessada, Y. Iwadate, ``First-Principles
Molecular Dynamics Simulation and Conductivity Measurements of a Molten xLi2O-(1-x)B2O3
System， J. Phys. Chem. B 117，pp.5668-5674 (2013).
K. Sawada, J.-I. Iwata adn A. Oshiyama ``Magic Angle and Height Quantization in Nanofacets on
SiC(0001) Surfaces", Appl. Phys. Lett. 104, 051605 (2014).
Y. Matsushita and A. Oshiyama, ``Interstitial Channels that Control Band Gaps and Effective Masses
in Tetrahedrally Bonded Semiconductors", Phys. Rev. Lett. 112, 136403 (2014).
K. Uchida, S. Furuya, J.-I. Iwata and A. Oshiyama, ``Atomic corrugation and electron localization
due to Moiré patterns in twisted bilayer graphenes" Phys. Rev. B 90, 155451 (2014).
C.-C. Lee, A. Fleurence, Y. Yamada-Takamura, T. Ozaki, and R. Friedlein, "Band structure of silicene
on zirconium diboride (0001) thin-film surface: Convergence of experiment and calculations in the
one-Si-atom Brillouin zone", Phys. Rev. B 90, 075422 (2014).
C.-C. Lee, A. Fleurence, R. Friedlein, Y. Yamada-Takamura, and T. Ozaki, "Avoiding critical-point
phonon instabilities in two-dimensional materials: The origin of the stripe formation in epitaxial
silicene", Phys. Rev. B 90, 241402(R) (2014).
T. Ohwaki, M. Otani, and T. Ozaki, "A method of orbital analysis for large-scale first-principles
simulations", J. Chem. Phys. 140, 244105 (10 pages) (2014).
T.V.T. Duy and T. Ozaki, ``A three-dimensional domain decomposition method for large-scale DFT
electronic structure calculations", Comput. Phys. Commun. 185, 777-789 (2014).
A. Nakata, D. R. Bowler and T. Miyazaki, “Efficient Calculations with Multisite Local Orbitals in a
Large-Scale DFT Code CONQUEST”, J. Chem. Theory Comput., Vol. 10, 4813-4822 (2014).
M. Arita, D. R. Bowler and T. Miyazaki, “Stable and Efficient Linear Scaling First-Principles

57

Molecular Dynamics for 10000+ Atoms”, J. Chem. Theory Comput., Vol. 10, 5419-5425 (2014).
32. E. Tsuchida，``Stabilization of ab initio molecular dynamics simulations at large time steps”，JPS
Conference Proceedings 5，011019、2015.
33. A. Nakata, D. R. Bowler and T. Miyazaki, “Optimized multi-site local orbitals in the large-scale DFT
program CONQUEST”, Phys. Chem. Chem. Phys., published online (10.1039/C5CP00934K) (2015).

Selected List of Invited Talks in International Conferences(total number in the period of this project =31)
1.
2.

3.

4.
5.
6.
7.
8.

9.

10.

11.

12.
13.

14.

15.

A. Oshiyama, ``Materials Design through Computics: nanowires and Nanotubes" Inernational Focus
Workshop on Quantum Simulations and Design (September 27, 2011, Dresden, Germany)
T. Ozaki, "Low-order scaling methods for large-scale density functional calculations", Summer school
on Electronic Structure Analysis and Computation, Shanghai Jiao Tong Univ., Shanghai, China, June
6-10, 2011.
A. Oshiyama, ``Materials Design through Computics: Nanostructures of Silicon and Carbon" 10th Int.
Meeting on High Peformance Computing for Computational Science (VECPAR2012), July 17-20,
2012, Kobe, Japan).
A. Oshiyama, ``Real-Space Density-Functional Approach to Electronic Properties of Nanostructures"
Conference on Computaional Physics, (October 14-18, 2012, Kobe, Japan)
J.-I. Iwata, “First-principles electronic structure calculations with K computer”, Theory andApplications of Computational Chemistry (TACC2012), 2-7 Sep, 2012, Pavia, Italy
T. Ozaki, “Massively parallelized O(N) Krylov subspace method for large-scale DFT calculations”,
IUMRS-ISEM 2012, PACIFICO Yokohama, Japan, Sep. 23-28, 2012.
T. Ozaki, “Low-order Scaling Density Functional Methods Based on Quantum Nearsightedness”,
SIAM Conference on Parallel Processing for Scientific Computing, Savanna, USA, Feb. 15-17, 2012.
T. Miyazaki, “Atomic and electronic structures of BEDT-TTF and M(dmit)2 systems at highpressures: A first-principles study of organic molecular solids”, Int. Symp. of the Quantum Beam
Science Directorate, Japan Atomic Energy Agency, (Mito, Ibaraki, Japan), Sep. 23-27, 2012.
A. Oshiyama, ``Materials Design through Computics: Large-Scale Density-Functional Calculations
for Nanomaterials in the Real-Space Scheme" Int. Summer School on HPC Challenges in
Computational Sciences (New York City, USA, June 2013).
A. Oshiyama, ``Large-Scale Density-Functional Calculations in the Real-Space Scheme: Graphene
and Silicene" 7th Conf. Asian Consortium on Comnputational Materaisl Science (ACCMS7) (Nakhon
Ratchasima, Thailand, July 2013).
Z.-X. Guo, J.-I. Iwata and A. Oshiyama ``Large-Scale Calculations in the Real-Space Scheme:
Absence and Presence of Dirac Electrons in Silicene" 22th Int. Materials Research Congress (IMRC)
2013 (Cancun, Mexico, August, 2013)
E. Tsuchida，``Adaptive Finite Element Method for Ab Initio Molecular Dynamics Simulations”，
12th U.S. National Congress on Computational Mechanics，U.S.A., 2013/07/22.
A. Oshiyama, ``Large-Scale Real-Space Density-Functional Calculations: Moir¥'e-Induced Electron
Localization in Graphene and Floating States in SiC" 32nd International Conference on the Physics
of Semiconductors (Austin, Texas, USA, August 2014).
T. Ozaki, “Theoretical and experimental exploration of two-dimensional Si structures”, The 17th
Asian Workshop on First-Principles Electronic Structure Calculations, Yonsei University, Seoul,
Korea, Nov. 2-5, 2014.
T. Miyazaki, “Large-scale DFT simulations on nano structured materials using a linear-scaling
technique”, Collaborative Conference on 3D Research (CC3DMR) 2014, Songdo Convensia (Incheon,
South Korea), Jun. 23-27, 2014.

Prizes1.

2.

Y. Hasegawa, J.-I. Iwata, M. Tsuji, D. Takahashi, A. Oshiyama, K. Minami, T. Boku, F. Shoji, A. Uno,
M. Kurokawa, H. Inoue, I. Miyoshi, and M. Yokokawa, ``First-Principles Calculation of Electronic
States of a Silicon Nanowire with 100,000 Atoms on the K Computer” ACM Gordon Bell Prize (peakperformance) 2011
S. Arapan, ``JSST 2013 Outstanding Presentation Award” at the Int Conf on Simulation Technology,
JSST 201358

Studies on Structure Sampling and Non-Equilibrium Dynamics
Using Ab-Initio Molecular Dynamics Methods
Shinji Tsuneyuki1, Yoshihide Yoshimoto2,3, Jun Yamauchi4 and Minoru Otani5
Department of Physics, The University of Tokyo1,
Department of Applied Mathematics and Physics, Tottori University2,
Department of Information Science, The University of Tokyo3,
Department of Physics, Keio University4,
National Institute for Advanced Industrial Science and Technology5

1. Introduction
This group is mainly dedicated to the first-principles study on thermal physics and nonequilibrium dynamics in condensed matter, such as thermal conduction, solid-liquid phasetransition, electrochemical reactions at the electrode-electrolyte interface and so on. In thesimulation of these physical phenomena, where spaciotemporal fluctuation of the atomic structure
is so large, we need careful modeling and long-time/large-scale simulation of the atomic motion
to get statistically meaningful results. This is a hard requirement for first-principles simulations,firstly because the computational cost of the electronic structure calculation usually scales as N3
with N being the number of electrons, and secondly because it is essentially impossible toparallelize the dynamical simulation due to causality. On the other hand, for the simulation ofelectrochemical reactions, microscopic modeling method for the simulation is in itself
problematic due to applied voltage and non-conserving electron number. Comparison of thesimulation with spectroscopic experiments is also a difficult but indispensable task.
In this project, in order to overcome some of these difficulties, we took the following strategy.
Yoshimoto developed a highly parallelized first-principles electronic structure calculation
program package xTAPP and opened it to the public (Section 2). The program can be a powerfulbasis for the simulation of thermal physics and non-equilibrium dynamics. Tsuneyuki developed
an efficient scheme of modeling anharmonic interaction between atoms from first principles(Section 3). The anharmonic model potentials were then used for highly accurate calculation oflattice thermal conductivity. The program package ALAMODE was developed for all theprocedure and it was also opened to the public. Otani developed new useful methods forelectrochemistry by the extension of the effective screening medium method previously proposedby himself (Section 4), with which he realized simulation of electrochemical reaction underarbitrary and constant bias voltage. Finally, Yamauchi investigated the core-level X-ray
photoelectron spectroscopy from first principles, which enabled us to identify local defectstructures in semiconductors (Section 5).
Development of a plane wave basis first-principles electronic structure calculation package
xTAPP (Y. Yoshimoto)First-principles electronic structure calculation based on density functional theory and its local
density approximation is widely used in various research fields because the ratio of its accuracy
to the computational cost is excellent. The method is further classified by the used basis set.
Among them, the method with plane wave basis set using pseudo-potentials is commonly usedbecause it is good at atomic force filed calculations, can equally treat systems from sparse ones
to dense ones, and can control the computational accuracy due to the basis set easily.
2.

59As an implementation of the method, xTAPP was developed based on TAPP and it was opened
to the public at the following web sites.
http://xtapp.cp.is.s.u-tokyo.ac.jp
http://ma.cms-initiative.jp/ja/listapps/xtapp
The developed features of xTAPP in this project are as follows:












hybrid exchange correlation (XC) potentials with GPGPU computation
pseudo-potential library: all elements from H to Bi, except for radioactive ones (Tc, Pm)
and lanthanoids other than La, Ce, Nd, Gd
integration of maximally localized Wannier function code [1] and its application tospontaneous electronic polarization and projected DOS
surface under an electrostatic field by the effective screening medium method [2]total DOS, projected DOS, integrated charge distribution as a function of energy by using
the tetrahedron method
DFT-D[3] dispersion force
linkage with phonopy [4] : phonon related calculation
support for GRAPE-DR accelerator
TAPP input format is replaced with a modern one
user manual(22 page), reference manual for input files(33 page), tutorial and examples (53page), developers reference (7 page), Reference for formulations (72 page)xTAPP-test : examples of input files (93 patterns) and automated comparison program of
the test results

The package is opened to public under GNU General Public License version 3. This license is
a comfortable one in computer science, and it becomes easy for xTAPP itself to incorporate
foreign codes. The copyright of TAPP codes was cleaned and the code that is not suitable for the
public release was replaced. The consortium that maintains the TAPP code consented to makexTAPP open to the public. The replaced code includes the modernized code for sampled k points
with corresponding symmetry operations and it was utilized when the code to compute maximally
localized Wannier functions was integrated.
xTAPP implemented a fast computation of hybrid exchange correlation (XC) functionals byusing GPGPUs. The hybrid XC functionals (PBE, HSE, LC, and B3LYP etc.) are beyond local
density approximation and involve exact computation of exchange interactions. They improve,for example, description of water molecules. The obstacle for its wide use is the highcomputational cost of the exchange interaction. One solution of the issue is to use economical
computing devices such as GPGPUs.
The biggest issue in the use of GPGPUs is the relatively slow data transfer speed between main
memory and the device memory of a GPGPU.
The analysis of the structure of the computation from the computer science resolves the issue.
The computation is performed on each pairs of orbitals and its result is reduced. Namely, the orderof the arithmetic operations is O(N2) although the data size is O(N), where N is the number oforbitals. This means that the blocking of the computations is the appropriate approach: instead ofstep by step transferring each orbital pair to GPGPU and transferring back the computed potential,
we should transfer Nblk orbitals from each two series of orbitals to the device memory at a time,compute all the potentials for Nblk×Nblk pair block formed by the transferred orbitals and transfer
back the reduced potential. This improves the ratio of arithmetic operations to the transferred data
by Nblk times and thus we can hide the slow data transfer rate.

60

cut of wave number of the plane

3.6

4.0

4.8

5.0

5.4

6.4

FFT mesh

723

803

963

1003

1083

1283

Xeon X5690 [s]

378

549

994

1188

1583

2255

Radeon HD 6950 [s]

169

297

342

500

534

749

acceleration

2.23

1.84

2.91

2.37

2.96

3.01

wave basis [a.u.]

Table 1: 1 SCF time for Si 216 atom system

Based on this theoretical analysis, we adopted AMD Radeon 6950 (26,000 JPY) and OpenCL
language because of its cost benefit.
Table 1 shows the comparison of 1 SCF time of Si 216 atom system (Г point sampling) between
GPGPU and CPU(Intel Xeon X5690; 140,000 JPY). Nblk was 20. 8 GPGPU or 8 CPU were usedin parallel.
The higher the cut of the plane wave basis set becomes, the higher the obtained acceleration
ratio is in general. Up to 3 times acceleration was obtained. Because the cost of the Radeon
GPGPU was rather low, this is meaningful number. The depressions at FFT mesh of 803 and 1003
may be because the Radeon GPGPU is not good at computation of radix 5.
xTAPP only treats valence electrons using pseudo-potentials. Therefore a pseudo-potential
library is indispensable to make it adopted by a wide range of users. In this project libraries for(ultrasoft pseudo-potential / PBE type XC potential), (ultrasoft pseudo-potential / Ceperley-AlderPerdew-Zunger type XC potential), (norm conserving pseudo-potential / PBE type XC potential)
were prepared.
These libraries contain all elements from H to Bi, except for radioactive elements (Tc, Pm) andlanthanoids other than La, Ce, Nd, Gd.
The libraries were checked by developed test system for pseudo-potentials: the bulk band
diagrams to detect the ghost states, the reproducibility of lattice constants, bulk moduli, cohesiveenergies, vibration frequencies and equilibrium inter-atomic distance of diatomic molecules. The
result is included in the library.
The other extension of xTAPP includes effective screening medium method by M. Otani and
O. Sugino and computation code of maximally localized Wannier orbitals by K. Nakamura. To
integrate these functions, we have to check the soundness of existing functions. For this purpose,
we developed xTAPP-test, a test package with a specialized code to compare the results. xTAPPtest resolves the too many false-positive issue in the comparison between the results before andafter the integration of the target function.
Thus we can easily confirm the soundness ofD0 [10-6 m2/s] Ea [kJ/mol]
existing
functions.
xTAPP-test
is
PBE
3200
46
indispensable to keep the quality of xTAPP.
PBE0
70
31
The application of xTAPP includes themodeling of the low energy bands of dmit and
B3LYP
48
29
BEDT-TTF systems, organic semiconductor
D3LPY + DFT-D3
6.6
23
PTCDA on Si(001) surface (in cooperation
experimental [5]2.517with an experimental group) and modeling ofwater systems by a classical force fields using
Table 2: Self diffusion coefficients of water
thermodynamic downfolding method. The
up to 360 K
obtained force field for water was applied to the61self diffusion coefficients of water (Table 2), where diffusion constant D as a function oftemperature T is D = D0 exp(-Ea/kBT). To obtain good classical force fields both the hybrid XC
potential and dispersion forces are important.
The number of unique users registered at the xTAPP download site from April 2013 to March
2015 was more than 120.
3. Anharmonic lattice model and the lattice thermal conductivity from first principles (S.
Tsuneyuki)
Lattice thermal conductivity of crystals is governed by the anharmonicity of interatomic
potentials. It is an essential ingredient of the figure of merit for thermoelectric materials, where
lower thermal conductivity is preferred. On the other hand, higher thermal conductivity ispreferred in electronic devices for thermal stability. From the viewpoint of materials design forthese materials, we have developed a new scheme to calculate lattice thermal conductivity fromfirst principles.
So far three methods have been proposed for computational study of thermal conductivity: amethod based on Boltzmann’s transport equation and diagrammatic evaluation of lifetime ofphonons, molecular dynamics (MD) simulation with the Kubo-Greenwood formula and nonequilibrium MD simulation of heat transfer with temperature gradient. In any case, first-principles
simulation is highly difficult because of the large system size and long-time simulation or many
sampling points in k space integration necessary for reliable calculation. Thus we decided todevelop an accurate, efficient and versatile method for modeling anharmonic interatomic
potentials with first-principles MD based on DFT.
The model potential is just a Taylor expansion of the total energy of the system calculated by
DFT,
1
2

1
3!

Φ
,

Φ

⋯.

, ,

denotes the displacement of each atom in xyz direction from its potential minimum, Φharmonic force constant and Φ

⋯

is a

is called an anharmonic force constant. Practically the Taylor

expansion is terminated at a low order and the force constants are determined so that the model
potential minimizes the deviation of the force acting on each atom from that calculated from firstprinciples at some sampling structures under crystalline symmetry constraints [6]. In this study,
we adopt up-to the sixth-order force constants for the parameter fitting. For efficient sampling of
the potential energy hyper-surface, we use the locus of atoms obtained by first-principles MD at
a fixed temperature [7]: the temperature should be high enough to reflect anharmonic characterof the potential but low enough to avoid unphysical sampling. We find the third-order force
constants determined in this way are as accurate as those carefully obtained by numericaldifferentiation of the potential energy.
Once the force constants are determined, phonon dispersion, group velocity and the lifetime ofeach phonon mode are calculated, with which lattice thermal conductivity and its temperaturedependence is obtained within the relaxation-time approximation. We applied the scheme to Si,
Mg2Si, PbTe, Bi2Te3 and Ba8Ga16G30 and found that material dependence and temperature

62

Fig. 1 Temperature dependence of the lattice thermal conductivity of various materials.
Experimental data were taken from R. Kremer et al., Solid State Commun. 131, 499 (2004) (Si);J. J. Martin, J. Phys. Chem. Solids 33, 1139 (1972) (Mg2Si); I. Ravich et al., Semiconducting leadchalcogenides, Plenum Press (1970) (PbTe); C. B. Satterthwaite et al., Phys. Rev. 108, 1164 (1957)(Bi2Te3); M. Avila et al., Phys. Rev. B 74, 125109 (2006) (Ba8Ga16G30).

dependence of the thermal conductivity are quantitatively reproduced in a wide range from 100 to
104 W/mK as shown in Fig.1.
An apparent advantage of the use of the model potential instead of direct calculation of thermal
conductivity is that we can adopt system size large enough to include the effect of phonon
scattering by those with long wave length (typically, more than 104 atoms for MD or similar
number of sampling points in the reciprocal space for lifetime calculation), and MD simulation
long enough to match the life time of phonons (much more than 102 ps), although the modelingneeds only 102 atoms and a few ps MD simulation
for sampling.
Another advantage is that the system property
can be controlled by changing the configuration of
the model. For example, in case of Ba8Ga16G30, aclathrate containing rattlers inside, an effect of therattlers for its extremely low thermal conductivity
can be clarified by investigating the thermal
conductivity of an imaginary clathrate compound
without the rattlers. By comparing the simulations
with and without the rattlers, we found that the
rattlers cause tenfold reductions in the relaxation
time of phonons at low frequency by scattering
phonons (see Fig.2), while their impact on thegroup velocity is secondary [8].

63Fig. 2 Frequency dependence of
calculated life time of phonon modes for
Ba8Ga16G30 with (green) and without(purple) rattlers in the cage.

The program package ALAMODE was developed by T. Tadano for the present procedure andit was opened to the public.
http://github.com/ttadano/alamode; http://alamode.readthedocs.org
http://ma.cms-initiative.jp/ja/listapps/alamode/alamode

4. Extension of the effective screening medium method (M. Otani)
4-1 Introduction
An electrochemical reaction at the electrode-electrolyte interface is one of the most important
issues on performance and durability of energy harvesting devices such as a fuel cell, a secondary
battery, a photovoltaic cell and a photoelectrochemical cell. Although the first-principles
calculation technique is a reasonable choice to study the electrochemical reaction, the threedimensional periodic boundary condition, which is usually employed in a conventional firstprinciples calculation program, is not compatible with the electrochemical system. To make theprogram compatible with the system, we have developed the effective screening medium (ESM)
method [9] which allows us to simulate the electrochemical system by modifying the boundary
condition of the Poisson equation. Using the ESM method, we can calculate many
physical/chemical properties of the electrochemical systems in operando conditions and cananalyze the experimental result [10].
Although the ESM method enables us to simulate electrochemical system, there is a room toimprove the modeling of the system. For example, firstly the original ESM method needs a
vacuum region between a slab and the ESM to avoid the electronic wave function penetration into
the ESM region. It is difficult to define the applied bias potential between an electrode and theESM owing to the existence of the vacuum. Secondly conventional first-principles calculations
are done under fixed total number of electron (constant-N calculation), whereas theelectrochemical system is governed by an external potentiostat. Thus the calculation should bedone by the fixed Fermi energy (constant-μ calculation).
In this project we have been trying to develop the ESM method to solve above issues. In thefollowing subsections, we will describe how to remove the vacuum region and control the Fermi
energy during the first-principles calculations.
4-2 Smooth-ESM method
The reason why we need to introduce the vacuum region between the slab and the ESM is that
there is a discontinuity in the permittivity constant [see Fig.3 (a)]. When the electronic wave
function locates in the ESM region, we cannot solve the Poisson equation. To avoid this issue, we
introduce the following function form for the permittivity in the ESM region [see Fig.3 (b)]: (z)  e 2 a(zz ),1

where a denotes the screening length of the ESM region [11]. The value of the permittivity
smoothly changes from unity to infinity; we call this the smooth ESM. With this function form,
we can still solve the Poisson equation analytically and obtain the Green’s function in advance.
Thus the calculation cost remains comparable to that of the conventional first-principles
calculation.
Figure 3(c) shows a proof test calculation for a H atom approaching to the smooth ESM [12].
In the region far from the smooth ESM, the H atom does not feel any interaction from the ESM
as expected. Whereas it approaches to the ESM, there is an attractive interaction and it turns to a
repulsive interaction according as the H atom penetrates to the smooth ESM region. The originof the attractive interaction is the dipole-dipole interaction between the H atom and the ESM. The

64

ESM

ESM

(d)

(c)

Fig. 3 (a) Discontinuous permittivity constant change in the original ESM method and (b) smoothtransition of the permittivity constant in the smooth ESM method. The permittivity changes fromunity to infinity. (c) The total energy profile of an H atom approaching the ESM region. (d) Charge
redistribution of the H atom. The color of lines indicates the position of the H atom in (c).

magenta and blue color lines in Fig.3 (d) shows there is an induced dipole moment on the H atom.
The green and red color lines indicate that an electron on the H atom is delocalized when the Hatom penetrates to the ESM region. The delocalization of the charge leads instability to the Hatom; consequently there is a repulsive interaction between the atom and the ESM. Since theelectronic wave function can penetrate to the smooth ESM region, we do not need to introduce
additional vacuum region.
4-3 Constant-μ method
It is well known that, to realize the constant Fermi energy (constant-μ) calculation, we cannot
fix the Fermi energy during the self-consistent-calculation (SCF) loop. This intuitive strategy will
fail within a few SCF steps. To realize stable and robust calculation, we employed the extended
system technique which is usually used in the constant temperature and constant pressure
molecular dynamics simulation. We assume that the charge in the simulation cell is a dynamicalvariable; we call this the fictitious charge particle (FCP) [13]. This means that the system isconnected to a charge reservoir and can keep the Fermi energy constant by exchanging the FCP
with the reservoir. By solving the dynamics equation for the FCP, we can realize grand canonicalensemble with the following grand potential:  Etot   nFCP ,where Etot, μ and nFCP indicate the total energy and the Fermi energy, and the charge of the FCP.
By taking the derivatives of the grand potential, we can calculate the force acting on atoms and
FCP.
As a proof test calculation of the constant-μ method, we calculate an H atom diffusion on
Al(001) surface [see Fig.4 (a)] by combining the constant-μ method with the nudged elastic band
(NEB) method [12]. Figure 4 (b) shows the energy profile and the Fermi energy variation of the
H diffusion with the conventional constant-N calculation. The activation barrier for the diffusion
is about 0.3 eV. During the diffusion, the H atom is slightly polarized by the interaction between
the surface, thus the Fermi energy of the system varies as the diffusion. Figure 4 (c) shows theenergy profile and nFCP along with the diffusion path under constant-μ condition (three different
target Fermi energies (μext) are shown). Although overall energy profiles depending on the target
potential are consistent with the constant-N calculation, the activation barriers and nFCP slightly

65

(b)

(c)

constant−N
ext=−4.5 v
ext=−5.0 v
ext=−4.0 v

0.5
0.4

 (eV)

0.4
E (eV)(a)constant−N

0.5

0.3
0.2

0.33
0.32
0.31
4

0.3
0.2

0.1

0.1

0.0

0.0
0.050

nFCP (e/surf)

Fermi energy (eV)

−3.5
−4.0
−4.5

0.025
0.000
−0.025−5.0
AB
Diffusion path

C

A

B

C

Diffusion path

Fig. 4 (a) H atom diffusion on Al(001) surface. A and C sites are the most stable bridge site, B site is
the saddle point of the path. (b) The energy profile and the variation of the Fermi energy along thepath with constant-N calculation. (c) The energy profile and the variation of the excess charge of thesurface along the path with constant-μ calculation. The origin of the nFCP is the neutral system.

depend on the target potentials. This means that application of a bias potential affects the diffusion
path and activation energy.
4-4 Summary
In this project, we have developed the smooth-ESM and the constant-μ methods to improve themodeling of the electrochemical system and successfully shown simple proof test calculations
using the state of the art first principles calculation program. It is expected that we can simulate
more realistic electrode-electrolyte interface system and give a deep insight into theelectrochemical system experiments.
5. First-principles core-level X-ray photoelectron spectroscopy calculation of defects insemiconductors (J. Yamauchi)
For several decades, the behaviors ofdefects in semiconductors have been
investigated actively owing to industrial aswell as fundamental interest. However,atomic-scale phenomena are not yet
sufficiently understood. Although the mostfundamental information at this scale is theatomic structure of defects, it is usually very
difficult to determine the structure. This ismainly for two reasons. One is that defects
are located in the substrate and cannot bedirectly detected. The other is the weakFig. 5 X-ray photoelectron spectroscopy.
signals in measurements. The number of
impurity atoms is very low compared withthat of matrix atoms. Furthermore, the ratio of the number of defects of interest to the total numberof impurity atoms is also very small. Recently, to compensate for the weak signals, detailed Xray photoelectron spectroscopy (XPS) measurements (Fig. 5) have been performed using highintensity X-ray beams generated by large synchrotron radiation facilities such as SPring-8.

66

Therefore, the XPS has been expected to enable highly accurate measurements than before.
Since the XPS signal itself does not uniquely determine the defect structure, its identification
requires theoretical analyses for the XPS binding energies of the suggested models with highaccuracy. On the other hand, there have been few reliable first-principles core-level XPS
calculations for impurity defects in semiconductors, because the local potential boundary
condition of defect model systems has not yet been sufficiently evaluated. To obtain chemical
shifts in XPS binding energy with high accuracy, it is necessary to take a sufficiently large
supercell for a defect so as not to affect the local potential at the boundary. We report the firstprinciples core-level XPS calculations on the defects in silicon (Si) and silicon carbide (SiC)
considering the careful evaluation of the boundary condition. The tests for the supercell size
dependence revealed that the 512- and 1728-atom supercells for Si and SiC are required to achieve
the accuracy of 0.1 eV for the XPS binding energy. The XPS binding energies are calculated bythe SCF method. To calculate the XPS binding energy, special pseudo-potentials are necessary
to deal with the core state, because usual pseudopotentials ignore the core state for the saving of
the computational cost. There are two types of such potentials. One is the screened core holepseudopotential (SCH PP), which is generated using the atomic reference removing the electronof the core state. The other is the pseudopotential with core (PPwC), which deals with the corestate explicitly. We adopt the PPwC for As 3d and the SCH PPs for the other dopant elements.
Boron has exotic features and is the most important p-type dopant element for Si. Boron atom
is so small that it tends to make three-center bonding and prefers triangular shape. In nature,polyhedral units of boron clusters such as octahedral B6, icosahedral B12, and cubo-octahedral B12,
are available in elements and compounds. Thus, it is expected that the polyhedral B clusters exist
in Si crystals. We calculated the XPS binding energies for the defect models, which are suggestedby theories and/or experiments. Among them, we plotted the binding energies of B 1s near theexperimentally observed spectra in Fig. 6. In this figure, the vertical lines indicate the calculated
values for icosahedral B12 (ICO), substitutional B, <001> B-Si and octahedral B6 (B6), and thecurves are observed and deconvoluted experimental spectra. This figure clearly shows that theexperimental three peaks correspond to the ICO, substitutional B, and <001>B-Si, respectively.

Fig. 6 B1s core-level XPS binding energy ofB clusters in Si. Experimental anddeconvoluted data are from Mizushima andcoworkers. The vertical lines are calculated
binding energies. The substitutional B isadopted for the origin of the energy.

Fig. 7 As 3d core-level XPS binding energy ofdefects in Si. The energy origins are the neutral
and charged substitutional As for (a) and (b),respectively.

67

These results are consistent for the other experimental properties such as electric activity [14].
In Fig. 7, the calculated XPS binding energies of As 3d for As defects in Si are indicated in theneutral state (a) and the charged state. In this system, experimentally observed peak is -1.2 eV
relative to that of substitutional As. Within the neutral state only (a), where the neutral
substitutional As is set to the energy origin, we cannot find the defect suitable for the experimental
one. Including the charged states, where the energy origin is the binding energy for thesubstitutional As+, it is found that the vacancy related defects are good candidates for theexperimentally observed defects.
To investigate the dependence of the XPS binding energy on the substrate semiconductors, we
also performed the XPS calculation for the various dopants (B, Al, P, As) defects in SiC. It isfound that the relative range of XPS binding energy in SiC is about 4 eV, which is much larger
than that of 1 eV in Si. This is because, while the Si is the elemental semiconductor, the SiC is
the compound semiconductor and the deviation of the local potential is much larger than that in
Si. The SiC has many polymorphs. We calculated the defects in 3C- and 4H-SiC, and found thatthe dependence of the XPS binding energy on the polymorphs is not large.
References[1] K. Nakamura, H. Kagaku, 29, 432 (2008)[2] M. Otani and O. Sugino, Phys. Rev. B, 73, 115407 (2006)[3] S. Grimme, S. Ehrlich and L. Goerigk, J. Chem. Phys, 132, 154104 (2010)[4] Atsushi Togo, Fumiyasu Oba, and Isao Tanaka, Phys. Rev. B, 78, 134106 (2008)[5] H.Z. Weingärtner, Phys. Chem. 132, 129 (1982)[6] K. Esfarjani and H.T. Stokes, Phys. Rev. B77, 144112 (2008); Phys. Rev. B86, 019904 (2012).
[7] T. Tadano, Y. Gohda and S. Tsuneyuki, J. Phys. Condens. Matter 26, 225402 (2014).
[8] T. Tadano, Y. Gohda, and S. Tsuneyuki, Phys. Rev. Lett. 114, 095501 (2015).
[9] M. Otani and O. Sugino, Phys. Rev. B 73, 115407 (2006).
[10] M. Bagge-Hansen, et al., Adv. Mater. 27, 1512 (2015).
[11] I. Hamada, O. Sugino, N. Bonnet, and M. Otani, Phys. Rev. B 88, 155427 (2013).
[12] We implemented the smooth-ESM method and the constant-μ method into the PWscf
program in the Quantum ESPRESSO package: http://www.quantum-espresso.org/.
[13] N. Bonnet, T. Morishita, O. Sugino, and M. Otani, Phys. Rev. Lett. 109, 266101 (2012).
[14] J. Yamauchi, Y. Yoshimoto, and Y. Suwa, Appl. Phys. Lett. 99 191901 (2011).

6. Collaborators
Takashi Nakayama (Chiba University), Osamu Sugino (The University of Tokyo), Yoshitada
Morikawa (Osaka University), Kazuto Akagi (Tohoku University), Yoshitaka Tateyama (NIMS),
Yuji Suwa (Hitachi-Co), Yoshihiro Gohda (Tokyo Institute of Technology/The University ofTokyo)
7. Publications
 T. Suzuki, Y. Yoshimoto, K. Yagyu and H. Tochihara, “Adsorption of PTCDA on Si(001)-2 x
1 surface”, J. Chem. Phys. 142, Art. No. 101904 (2015).
 K. Nakamura, Y. Yoshimoto and M. Imada, “Ab initio two-dimensional multiband low-energy
models of EtMe3Sb[Pd(dmit)2]2 and κ-(BEDT-TTF)2Cu(NCS)2 with comparisons to single-

68band models”,

Phys. Rev. B86, Art. No. 205117 (2012).

 J. Yamauchi, Y. Yoshimoto and Y. Suwa, “Identification of boron clusters in silicon crystal by
B1s core-level x-ray photoelectron spectroscopy: A first-principles study”, Appl. Phys. Lett.
99, Art. No. 191901 (2011).
 Y. Yoshimoto et al., Software Package “xTAPP”;
http://xtapp.cp.is.s.u-tokyo.ac.jp
http://ma.cms-initiative.jp/ja/listapps/xtapp
 T. Tadano, Y. Gohda, and S. Tsuneyuki, “Impact of Rattlers on Thermal Conductivity of a
Thermoelectric Clathrate: A First-Principles Study”, Phys. Rev. Lett. 114, 095501 (2015).
 T. Tadano, Y. Gohda and S. Tsuneyuki, “Anharmonic force constants extracted from firstprinciples molecular dynamics: applications to heat transfer simulations”, J. Phys. Condens.
Matter 26, 225402 (2014).
 T. Tadano, Software Package “ALAMODE”;
http://github.com/ttadano/alamode
http://alamode.readthedocs.org
http://ma.cms-initiative.jp/ja/listapps/alamode/alamode M. Kawamura, Y. Gohda and S. Tsuneyuki, “Improved tetrahedron method for the Brillouinzone integration applicable to response functions”, Phys. Rev. B 89, 094515 (2014).
 I. Hamada, O. Sugino, N. Bonnet, and M. Otani, “Improved modeling of electrified interfaces
using the effective screening medium method”, Phys. Rev. B 88, 155427 (2013).
 N. Bonnet, T. Morishita, O. Sugino, and M. Otani, “First-principles molecular dynamics at aconstant electrode potential”, Phys. Rev. Lett. 109, 266101 (2012).
 J. Yamauchi and Y. Yoshimoto, “X-ray Photoelectron Spectroscopy for the Boron Impuritiesin Silicon: a First-principles Study”, AIP Conf. Proc. 1399, 89 (2011).
 J. Yamauchi, Y. Yoshimoto, and Y. Suwa, “A first-principles core-level XPS study on the boron
impurities in germanium crystal”, AIP Conf. Proc. 1566, 41 (2013).
 H. Kishi, M. Miyazawa, N. Matsushima, and J. Yamauchi, “First-principles core-level X-ray
photoelectron spectroscopy calculation on arsenic defects in silicon crystal”, AIP Conf. Proc.
1583, 226 (2014).
 N. Matsushima and J. Yamauchi, “First Principles XPS Calculation for the B defects in SiC”,
JPS Conf. Proc. 1 012027 (2014).
8. Invited Talks
 Yoshihide Yoshimoto, “Development and application of plane wave based first-principles
electronic structure calculation code "xTAPP"”, 4th International Workshop on Massively
Parallel Programming Now in Quantum Chemistry and Physics - Toward post-K computers,
Nov. 23 - 24, 2014, University of Tokyo.
 S. Tsuneyuki, “Toward Accurate Calculation of Electronic and Structural Properties ofMaterials from First Principles”, The 9th General Meeting of ACCMS-VO, OIST, Okinawa,Dec. 20-22, 2014.
 S. Tsuneyuki, “Atomistic Modeling of Materials Based on First-Principles Calculation”, The
10th NOBUGS conference, KEK, Tsukuba, Sep. 24-26, 2014.

69

 S. Tsuneyuki, “Computer Experiments for Materials Science”, International Symposium on
Recent Trend of Interdisciplinary Research of Physics, Earth and Space Science, Osaka Univ.,
Dec. 17-18, 2013.


S. Tsuneyuki, “Atomistic Modeling of Materials Based on First-Principles Calculation”, theSeventh General Meeting of ACCMS-VO, Tohoku Univ., Sendai, Nov. 23-25, 2012.



M. Otani, “Computational study of structure, vibrational property and electrochemical reaction ona biased metal-water interface”, International Symposium of Quantum systems in chemistry andPhysics, September 11-14, 2011, Kanazawa, Ishikawa, Japan。.



M. Otani, “First-principles molecular dynamics study of electrochemical reactions at electrodeelectrolyte interfaces”, ICMR Workshop on Charged Systems and Solid/Liquid Interfaces, July 611, 2014, Santa Barbara, CA, USA.



M. Otani, “First-principles molecular dynamics simulations on electrochemical reactions using
effective screening medium method”, 248th ACS National Meeting & Exposition, August 10-14,
2014, San Francisco, CA, USA.



M. Otani, “First-principles molecular dynamics study of electrochemical reactions at electrodeelectrolyte interfaces”, APS March meeting 2015, March 2-6, 2015, San Antonio, TX, USA.

70

Nanoscale Non-Equilibrium Electric Transport Dynamics Based on
Density Functional Theory
S. Watanabe1, K. Watanabe2, S. Souma3, T. Ono4
The University of Tokyo, 2Tokyo University of Science, 3Kobe University,
4
Osaka University (Present affiliation: University of Tsukuba)

1

1. Introduction
Nanoscale electric transport and related phenomena, in particular dynamical processes
involving realistic complex atomic structures, non-equilibrium electron/ion movements underapplied high local electric field, etc. are important in the light of both fundamental science andpractical applications. Our understanding on them, however, is still insufficient.
Our team has been conducting computational studies aiming at deeper understanding on
nanoscale electric transport phenomena, especially transport dynamics of various aspects. Our
research subjects include the analyses of interplay of electric transport with phonon/heat, ion
transport, spin, electronic excitation, etc., analyses on models more realistic than thoseexamined previously, and development of computational methodologies and codes for these
purposes. In this report, we describe the highlights of our research activities.
2. Overview
As mentioned above, our researches in this project include various topics. In this article, wewill briefly describe our achievement for six selected topics.
The first topic is the AC transport properties. From our study on the subterahertz AC responseof metallic carbon nanotubes using the nonequilibrium Green’s function (NEGF) method, we
have found many interesting features of the AC response, especially in the case of nanotubes
with an atomic vacancy. Combining the results for the nanotubes and single molecular bridges,
we have got a unified picture of the AC response of nanostructures.
The second one is the transient transport behavior. Since in this case we need much heavier
computation than in the cases of DC and AC transport behaviors, we have concentrated on very
simple models, such as a quantum dot with a single level between electrodes. On the other hand,
we have examined the effects of various factors such as the switching speed of the applied bias
voltage, electron-phonon interaction, and local heating.
The third one is the characteristics of graphene-based novel nanoscale devices. Firstly, we
have examined transport properties of graphene nanoribbons. More specifically, we haveexamined the effects of strain induced pseudo magnetic field on the locally strained graphene
channel field-effect-transistor operation quantitatively. Next, we have proposed a new type of
the pure spin current generation device that utilizes the quantum pumping effect and the edge
spin polarization in zigzag edged graphene nanoribbons.
The fourth one is the issues related to tantalum oxide based resistive switching devices. In
this device, the formation of conduction filaments is crucial in the device operation. So we haveexamined the features of the conduction filaments and ion movements.
The fifth one is the light-induced electronic excitations and dynamics of nanostructures.
Using sophisticated methodologies such as the Bethe-Salpeter equation and time-dependent
density functional theory (TDDFT), we have examined optical activation of dark excitons incarbon nanotubes, laser-assisted field emission from graphene nanoribbons and silicene
nanoribbons, excited-state nuclear forces and femtosecond laser reaction dynamics of a71

molecule, and optical properties of graphene nanoribbons and boron nitride nanoribbons.
Finally, a few methodologies and codes have been developed. The first one is a novel but
simple approach for the consideration of bias voltage within the Kohn-Sham formalism ofdensity functional theory. The second one is TDDFT methods to efficiently calculatesecond-order nonadiabatic couplings (NAC). For the computational code, we have developed
first-principles electronic-structure and transport calculation code based on real-space
finite-difference method. In the code, the problem of heavy computation due to the direct
inversion of large matrices to obtain the surface Green’s functions and self-energy terms ofelectrodes has been overcome by drastically reducing the matrix size using novel algorithm.
3. Research Results(Note: The numbers of cited references correspond to those in “5.[1](b) Selected publications.”)[1] AC Transport Properties
Considering high potential of metallic carbon nanotubes (M-CNTs) as interconnects in next
generation electronic devices, we have examined the subterahertz AC response of MCNTs using
the nonequilibrium Green’s function (NEGF) method. We have found several interesting
features of AC response, especially for MCNTs with an
atomic vacancy. First, using the NEGF method
combined with a simple tight-binding model, we havefound that the susceptance (exactly speaking, emittanceis examined instead of susceptance) does depend on theposition of the vacancy, which makes a strong contrast to
the position independence of the DC conductance (seeFig. 1).1) Next, using the NEGF method based on thedensity functional theory (DFT), we have found that thetwo states induced by the vacancy, the π-orbital-origin
vacancy state and the σ-orbital-origin dangling-bondstate, show different susceptance behaviors at firstsight.2) That is, besides capacitive peaks seen in both of Fig. 1. Emittance and DC conductancethe two states, satellite inductive peaks are clearly seen (inset) of a metallic carbon nanotube
adjacent to the main capacitive peak only around the with an atomic vacancy. Here, ddenotes the distance from the center ofdangling-bond state. Our analysis with a simple resonant the tube between the electrodescattering model reveals that the origin and the regions.1)
magnitude of these satellite inductive peaks can beunderstood by just one parameter, i.e., the lifetime of electrons at a defect state.
We have also examined AC transport properties of 1,4-Benzenedithiol molecule sandwiched
between semi-infinite one-dimensional gold electrodes using the NEGF based on DFT. In thecalculated susceptance spectrum, we have found two types of features; one corresponding toconductance peaks/dips and the other not related to those. We have found that the former can beunderstood similarly to the case of the above MCNTs, while the latter, which is seen at theenergies having small conductances, correlates with the DOS of the electrodes. This correlation
with the DOS is considered to be the same as the one seen in mesoscopic capacitors.
[2] Transient Transport Properties
As well as the AC transport behaviors, the transient current dynamics is also important inunderstanding the current behaviors under practical operations of novel nanoscale electronic
devices. We have examined the transient current dynamics using simple models and the NEGF
method.

72

First, we examined the transient current dynamics in a resonant tunneling model having asingle energy level with considering the switching-speed of the applied bias voltage.3) We foundthat with the decrease of the switching speed, the amplitude of the current overshoot decreases.
We also found that the crucial factor determining the relaxation time changes from the dwell
time of an electron in the resonant level to the voltage rise time.
Next, we have examined the effects of electron-phonon interaction and local heating on thetransient currents in a single-level quantum dot system weakly coupled to a localized vibration
degree of freedom using the NEGF method
under the wide-band-limit and lowest-orderexpansion approximations.4) We calculated
the time dependent phonon number using aphenomenological method employing thetime-dependent power transfer. We havefound that the dynamical behaviors in thissystem can be grouped into two responses: if
the energy corresponding to the applied bias
voltage eV is smaller than or equal to theFig. 2. Schematic illustration of the model structure
phonon energy Eph, first the system of graphene field effect transistor. The single layer
temperature T increases and then decreases; graphene is stretched along the armchair direction
alternatively, if eV is larger than Eph, T only over the gated channel region. The left and theincreases monotonically until a steady state right unstrained semi-infinite graphene regions are
assumed to be doped into n-type or p-type, while
is reached. The total electrical current is
the central strained graphene channel region issuppressed by phonon heating, while the applied by the gate voltage
heat transferring between dot andenvironment mitigates the effects of suchheating.
[3] Characteristics of Graphene Based
Novel Devices(a) Strained graphene field effect transistor
incorporating the pseudo magnetic field
effectRecently, the possibility of using lateralstrain to control the electrical conduction insingle layer graphene (SLG) has been
attracting great attention. Experimentally,such strain can be applied by bending or
stretching SLG on flexible substrate. From
the theoretical view point, it is important tonote that there are two distinct mechanisms
in the strain induced modulations ofelectronic properties in SLG. The first one isthat caused by the pseudo magnetic field at
the interface between unstrained and strained
regions of SLG. The second one is thatoriginated from the strain induced bandgap
opening. The former idea stimulated various
theoretical and experimental studies such as

Fig. 3．Gate voltage dependence of the drain current
density for two different doping configurations(top: p-i-p, and bottom: p-i-n) and three different
strain ratios.

73the quantum Hall effect and valley filtering device, and switching device. In the latter case,shear type strain is especially important since it allows SLG to possess the bandgap with theexperimentally achievable strain ratio. While the effect of such strain induced bandgap opening
in the strained graphene channel FET operation is similar to that in conventional semiconductor
MOSFET, the possible application of the former idea (pseudo magnetic field effect) to the FET
device operation has not been quantitatively explored theoretically so far. With such motivation,
we study numerically the performance of locally strained graphene based FET (Fig. 2) paying
special attention to the role of the pseudo magnetic field, on/off ratio of the drain current, andthe sub-threshold slope at the room temperature. By employing the non-equilibrium Green’s
function and the atomistic tight-binding methods, we have numerically studied the performanceof strained graphene based field effect transistors, where the strain around 8% is applied overthe channel region of graphene along the armchair direction to induce the pseudo vector
potential effect. As shown in Fig. 3, we have predicted that the gate voltage applied to thecentral strained graphene region can switch the drain current on and off with high on/off ratio
more than six orders of magnitude at the room temperature in spite of the absence of the
bandgap in the strained channel region. Steeper sub-threshold slope below 60 mV/decade is also
predicted to be achieved at the room temperature due to the mechanism similar to theband-to-band tunneling FET.5)(b) Graphene based pure spin current generator based on quantum pumping effectProactive use of the spin degree of
freedom in semiconductor is one of thepromising pathway for further developmentof the semiconductor technology. One of themost important subjects in such rapidly
developing field of spintronics is theefficient generation or injection of the spins Fig. 4. Illustration of ZGNR-based pure spininsemiconductors.
Especially,
the generator. Time-oscillating potentials are applied togeneration of pure spin current (i.e., four locally gated regions independently with eachspin-flow without charge current) is other.
important since the pure spin current does
not accompany the Joule heating and thus
enable us to transmit information at very
low energy consumption. So far various
types of devices have been proposed anddeveloped to generate the pure spin current,
including the spin Hall effect, the adiabatic
pumping in graphene, and the one using the
microwave induced magnetization dynamics.
We propose another type of the pure spincurrent generation device that utilizes thequantum pumping effect and the edge spin Fig. 5．Pumping phase dependence of the spinpolarization in zigzag edged graphene dependent pumped charges, where the pumping
nanoribbons (ZGNRs).6) ZGNR is known to phases (see Fig. 4) are set as φ1=φ2=0, φ3=φ, andshow the partly flat electronic band structure φ4= −φ, and the value of φ is varied.
near the Fermi energy, and thecorresponding wavefunction is localized near the edges of the ZGNR. Since such edge localizedstates give high density of states at the Fermi energy, more precise calculations taking into74

account the spin dependence of the electron-electron interaction predict the appearance of theedge spin polarization with opposite spins along the opposite edges. Moreover it has also been
predicted that the half metallic band structure can be induced by applying the transverse electricfield. Recent experiment has demonstrated the presence of edge spin polarization in ZGNR bymeans of the scanning tunneling spectroscopy. Our proposal is based on the idea to utilize suchedge spin polarization in ZGNR by means of the adiabatic quantum pumping effect to generate
the pure spin current. Quantum pumping effect is the idea to generate a dc current by applying
the local time periodic potentials to the conductor without applying the dc bias.
By employing the spin-density-functional tight-binding method and the adiabatic quantum
pumping theory, we have shown theoretically that the pure spin current can be generated inzigzag edged graphene nanoribbons (ZGNRs) through the adiabatic pumping by edge selective
pumping potentials (Fig. 4). The origin of such pure spin current is the spin splitting of the edge
localized states, which are oppositely spin polarized at opposite edges. In the proposed device,each edge of the ZGNR is covered by two independent time periodic local pumping gate
potentials with a definite phase difference, inducing the edge localized spin polarized current.
By making the pumping phase difference opposite between two edges, the total pumped charge
currents are canceled and then generates the pure edge spin current (Fig. 5). Such edge selective
time-dependent local potential assumed in the proposed device should be able to be applied bymeans of the scanning gate microscopy. The proposed method of generating pure spin current isuseful in the development of graphene spintronics.
[4] Conductive Filament Structures and Ion Movements in Tantalum-Oxide-Based
Resistive Switching Devices
Oxide-based resistive switching devices haveattracted much attention because of its potential
as next-generation memory cells. In particular,
amorphous-tantalum-oxide based devices show
good endurance and switching performances.
Their switching behavior is understood based on
the formation/rupture of conductive filaments(CFs), but, their atomistic structures andmicroscopic formation/rupture processes have notbeen well clarified yet.
We have examined the conduction paths inthe tantalum-oxide-based atomic switch using the
DFT calculations. In the Cu/amourphous-TaO2.5(a-TaO2.5)/Pt heterostructure, where Cu is
believed to be responsible for the CFs, Cu
single-atom chains have been found unstable. On
the other hand, Cu nanowires with widths larger
than the single atom have been found stable
during the molecular dynamics (MD) simulation
at 500 K for 15 ps, and can form conductive paths
Fig. 6. Atomic structures of Cu/a-TaO2.5/Pt(see Fig. 6).7) In the Pt/amorphous-TaOx/Pt
and local density of states near the Fermi
heterostructures, we have found the stronglevel. From top to bottom: the case with nocorrelation among Ta/O coordination number,
Cu wire, with a disconnected wire, with a
Ta–Ta/Ta–O bond lengths, and O concentration,
continued wire, and with a thicker continued
wire in TaO2.5.7)
and with the decrease of O concentration, Ta

75

atoms tend to merge together and finally form a continued Ta-rich region. This suggests that not
O vacancies, but the Ta–Ta bonding mainly contributes to the CF.8)
We have also examined the ion migration behaviors in TaOx using ab initio molecular
dynamics and nudged elastic band method. For the oxygen diffusion coefficient in TaOx, weshow that it strongly depends on x. We also show that at low O content (i.e., x = 1), the diffusion
coefficient of Ta becomes only ~0.5 order lower than that of O at room temperature. So the
diffusion of Ta cannot be ignored at low O content and at high temperature. For Cu at grainboundaries in TaOx, our calculations using surface models instead of grain boundaries suggestthat the presence of water strongly promotes its diffusion.
[5] Light-Induced Electronic Excitations and Dynamics of Nanostructures(a) Optical activation of dark excitons in carbon nanotubes
The optical properties of CNTs with hydrogen adatoms were investigated theoretically (Fig. 7).
We have shown that adsorbed hydrogen atoms make the triplet-exciton states optically active.
This effect is due to enhancement of the spin-orbit interaction as a result of distortion of sp2
orbitals so that they become more like sp3 orbitals. We
investigate the effects of spin-flipping on exciton statesby solving the Bethe-Salpeter equation under thetight-binding approximation. The absorption spectrum
was calculated using the solution of the Bethe-Salpeter
equation. It shows a satellite peak that is attributed totriplet excitons. Most importantly, we determined themicroscopic mechanism for the optical activation of
spin-triplet exciton states by adsorbed impurities, which Fig. 7. Photo absorption9)of H-adsorbed
offers a solution to the recent issue regarding the satellite (20,0) carbon nanotube.
peak observed in photo luminescence measurements.9)(b) Laser-assisted field emission from graphene nanoribbons and silicene nanoribbons
The energetics and dynamics of LAFE from nanoribbons were clarified by thetime-dependent density functional theory (TDDFT) simulations (Fig. 8). The emission
mechanism, which is common to the SiNR 10) and GNR 11), is found to be governed by threefactors: the electronic dipole matrix element, the orbital characteristics of the excited states, andthe energy levels of the excited states relative to the potential hump. However, the emission
currents from the SiNR are found to be much larger than from the GNR for the same laserparameters in spite of the larger work
function of the SiNR. This can be interpretedby the higher density of states, or morechannels for dipole transition in SiNRs thanthat of GNRs. We demonstrated the
dynamical correlation among the laser pulse,
the Kohn-Sham potential and emission
currents wiggling under the laser field in realFig. 8. Time evolution of emission currents
time and space on an atomic scale, andfrom SiNR at different points.10)
observed emission current being driven backand forth in the early stage of emission.
(c) Excited-state nuclear forces and femtosecond laser reaction dynamics of a molecule
We developed a simple and computationally efficient method to calculate excited-state76

nuclear forces on adiabatic potential-energy surfaces(APES) from linear-response TDDFT within areal-space framework.12) The Casida ansatz, which has
been validated for computing first-order nonadiabatic
couplings in previous studies, was applied to thecalculation of the excited-state forces. Our method isvalidated by the consistency of results in the lower
excited states, which reproduce well those obtained by
the numerical derivative of each APES. The
femtosecond laser reaction dynamics of biphenyl
molecule was investigated using TDDFT-MD
Fig. 9. Time evolution of torsional
simulation.13) The results (see Fig. 9) confirm that theangle of a biphenyl molecule.13)
probe pulse triggers a short-duration Coulomb explosion
and the kick pulse induces torsional motion of the two phenyl rings for a long duration by
selection of the laser parameters. The Coulomb explosion dynamics simulation confirms that the
F and Br atoms dissociate to the ion detector while maintaining their initial alignment withrespect to the phenyl rings, which is the fundamental basis for Coulomb explosion imaging ofmolecular torsion. Since the TDDFT-MD method takes account of the electric dipole-laserinteraction without assumptions, the simulation enables quantitative understanding oflaser-induced ultrafast molecular dynamics at a microscopic level.
(d) Optical properties of graphene nanoribbons and boron nitride nanoribbons
Dielectric function of BNRs and GNRs were calculated by the TDDFT.14) Dimensionality
dependence of dielectric functions has been clarified,indicating the signatures of the transition of plasmon excitaion
to particle-hole excitation in lower dimensions. We found an
apparent difference in low-energy absorption spectra between
BNRs and GNRs, reflecting their energy-band structures. We
carried out a systematic study on the quasiparticle band gapsof armchair boron nitride nanoribbons (ABNNRs) as afunction of the ribbon width, using a first-principles
many-body approach based on the GW approximation.15)
Because of the quasi-one-dimensional nature of ABNNRs, theenhanced Coulomb interaction effects and the reduced
screening greatly influence the quasiparticle band gaps, giving
rise to the GW correction in a range 2.5~3.0 eV (see Fig. 10).
Our GW calculations validate the qualitative correctness of the Fig. 10. Width-dependent GW
quasiparticle band gaps of
DFT study on BNNRs, together with the demonstration of the
H-terminated armchair boron
necessity of many-body approaches for quantitative nitride nanoribbons. 15)
understanding of quasiparticle band gaps.
[6] Developments of Methodologies and Codes and Their applications(a) Orbital-separation approach for considering bias voltage
We have developed a novel but simple approach, named orbital-separation approach, for theconsideration of bias voltage within the Kohn-Sham formalism of DFT.16) In the approach, theKohn-Sham orbitals around the Fermi level are separated into anode or cathode parts, anddifferent Fermi levels are applied in the determination of occupation numbers. This method canbe readily implemented in conventional first-principles codes.

77

We have applied this method to theelectronic charging of Au/vacuum/Au andAu/MgO/Au capacitors.16) Our results forvarious dielectric thicknesses have revealed
that the bulk optical and static dielectric
constants can be obtained accurately. We havealso performed finite-bias calculations on the
SrRuO3/BaTiO3/SrRuO3(SRO/BTO/SRO)
capacitors with 9 and 4 BTO unit cells. Figure
11 shows the calculated local inverse
permittivity profiles. In both systems, theinverse permittivity inside SRO converges tozero indicating a metallic response. On theother hand, a decrease in the permittivity isobserved at the SRO/BTO interfaces (deadlayer effect). When comparing the region
inside the BTO film, a clear difference is seen:Fig. 11. Inverse permittivity profiles of the SRO
for the 9-layer BTO, the permittivity is /BTO/SRO capacitors with (a) 9 BTO unit cells
positive as usual, but for the 4-layer BTO, theand (b) 4 BTO unit cells.
permittivity is found to be negative. Thisconfirms that ultrathin FE films with thickness of the order of a few unit cells exhibit negative
capacitance, at least if ferroelectric domain formation is suppressed. Since a layer of a few unit
cells is too thin to suppress tunneling current to a manageable amount in actual devices, we havebeen exploring the possibility of capacitance boost in the metal/PE/metal by sandwiching BTO
at the metal/PE interface.
(b) TDDFT methods for efficient calculation of nonadiabatic couplings (NAC)
We proposed a TDDFT method to efficiently calculate second-order NAC, using the Casida
ansatz adapted for the computation of first-order NAC. Calculations in the immediate vicinity ofJahn-Teller and Renner-Teller intersections showed that the results agreed well with theprediction from the Jahn-Teller/Renner-Teller models.17) We also presented extensive TDDFT
calculations on the quantization behaviors of first-order NAC in polyatomic systems and theangular NAC was found to show an oscillatory feature in the small-displacement limit (see Fig.
12), instead of the quantized value of 0.5 in the D3h symmetry.18) We further presented an
improved method for accurately calculating NAC from TDDFT, by the analytic evaluation of
the Kohn-Sham derivative matrix elements on the basis of density functional perturbation
theory.19) We elucidated the fact that the use of fractional
occupation, while being a natural extension for getting the
ground-state total energies or excitation energies, is not sostraightforward for getting NAC.20) Contrary to theconjecture that the Tamm-Dancoff (TDA) approximation
might cause the NAC results to deteriorate and violate thesum rule, the surprisingly good performance of the TDA
for NAC was revealed and attributed to that the TDA canpartially compensate for the local-density-approximation Fig. 12. Oscillating behavior oferror and give better excitation energies in the vicinity of angular nonadiabatic18) couplings inpolyatomic systems.
intersections of potential energy surfaces.21)78

(c) First-principles electronic-structure and transport calculation code based on real-space
finite-difference method
The nonequilibrium Green’s function (NEGF) approach has been used extensively inconnection with tight-binding models and first-principles methods employing localized basis
sets. However, the NEGF method has not been combined with the real-space formalism, whichis advantageous to massively parallel computer architectures and thus enables us to carry out
large scale transport simulations. This is because the direct inversion of Nx×Ny×Nz-dimensional
matrices to obtain the surface Green’s functions and self-energy terms of electrodes iscomputationally demanding due to the large numbers of grid points. Here, Nx, Ny, and Nz are
the numbers of grid points along the x-, y-, and z-directions in the unit cell of the electrodes andelectrons flow along the z-direction. The overbridging boundary-matching (OBM) method has
been employed with real-space approaches. In the formalism of the OBM method, the effect ofelectrodes is treated by the matching formula using Nx×Ny×Nf-dimensional ratio matrices,where Nf is the order of the finite-difference approximation for the kinetic energy operator in the
Kohn-Sham equation and is much smaller than Nz (Nf«Nz).
We have developed the real-space finite-difference (RSFD) NEGF scheme, in which thesurface Green’s functions and self-energy terms of the electrodes required in the NEGF method
can be obtained from the ratio matrices in the OBM method.22-26) The dimension of the matrices
for the surface Green’s functions and self-energy terms, which are directly inverted, issignificantly reduced from Nx×Ny×Nz to Nx×Ny×Nf in the present scheme while keeping the
rigorousness of the mathematical formulation. In order to demonstrate the applicability of the
RSFD NEGF method and the importance of the interpretation using scattering wave functions,the transport property of the C/BNNT where one carbon ring of (9,0) CNT is replaced with a
BN ring is examined.23,27,28) Inset of Fig. 13 shows the computational model. The central
finite-difference case, i.e., the case of Nf=1, is used. To determine the Kohn-Sham effective
potential, we use a conventional supercell under a periodic boundary condition in all directions
with a real-space grid spacing of ~ 0.24 Å; the dimensions of the supercell are Lx=13.34 Å,
Ly=13.34 Å, and Lz=4.32 Å for the electrodes and Lx=13.34 Å, Ly=13.34 Å, and Lz=8.64 Å forthe transition region, where Lx and Ly are the lateral lengths of the supercell in the x- andy-directions perpendicular to thenanotube axis, respectively, and Lz is
the length in the z-direction. The sizeof the matrices for the self-energy
terms is reduced from 75264 to 3136
using the present method.
The conductance spectrum of
the C/BNNT is shown in Fig. 13. We
have also calculated the conductancespectrum and channel transmissions
by the OBM method and found thatthese perfectly agree with the results
obtained by the present method
except for rounding error ofnumerical calculation. From Fig. 13, Fig. 13. Channel transmissions as functions of energy ofincident electrons. (Inset) Computational model where
we found that two channels actually
one BN zigzag ring is sandwiched between (9,0) CNT
contribute to the transport in theelectrodes. Large dark, small dark, and small light balls
are N, C, and B atoms, respectively. Reprinted withvicinity of the Fermi level and no
permission from Ref. 23).
significant peaks due to the resonant

79

tunneling through the edge states are observed in the conductance spectrum. The wave function
matching at the interface reveals that the rotational symmetry of wave functions with respect tothe tube axis plays an important role in electron transport. Since the states coming from andgoing to electrodes show threefold rotational symmetry, the states in the vicinity of the Fermi
level, whose wave function exhibits fivefold symmetry, do not contribute to the electrontransport through the BN ring. This result indicates that the real-space picture of the scatteringwave function, which is not necessary to be taken into account to calculate the transport
property in the NEGF formalism, helps us to interpret transport phenomena.
The spatial maps of the local density of states obtained by scanning tunneling spectroscopy(STS) can give us the images of standing waves, which provide important information about thedispersion relation of the electron scattering process at the potential barrier. By employing the
newly developed computational code in this project, we have carried out first-principles
calculation for obtaining the scattering potential of the defects on Ge(001) surfaces using acomputational model shown in Fig. 14.29) The Ge-Ge dimer at the center of the scattering region
is replaced by Ge-Si or Ge-Sn dimer as a defect. When the Si and Ge atoms are located at thelower and upper sides of the dimer, respectively, the dimer is referred as an SiL dimer. Other
dimers are named in a similar manner. By calculating the scattering wave functions using theOBM method, the standing waves in the spatial map of the local density of states are examined;
the waves correspond to the image of the differential conductance obtained by STS.
The charge density distribution of the scattering wave functions for the electrons
propagating from both the left and right electrodes is investigated with an energy of EF+0.55 eV.
To examine the period and phaseshift of the standing waves, thedensity of the standing waves is fittedby α(x)=Acos(2kxx+φ), where A, φ,and kx are the amplitude of thestanding waves, phase shift of thestanding waves, and Bloch vector inx direction, respectively. The fitting
is carried out using the density of thestanding waves above the lower
atoms of the dimers. The period ofFig. 14. Schematic image of computational model. Dark
the standing wave and its phase shiftspheres are Ge atoms and light spheres represent theare shown in Table I, in which they
dimer replaced by a Ge-Si or Ge-Sn dimer, which isagree with those obtained by theindicated by the arrow. Atoms are denoted by large andexperiment using STS. The scattering
small spheres according to the distance from the surface.
Reprinted from Ref. 29).
potential acts as a barrier when theelectronegativity of the upper atom
Table I. Amplitude and phase shift of the standing wavesof the dimer is larger than that of thearound the Ge-Si and Ge-Sn dimers.
lower atom, while it becomes a wellModelin the opposite case. The scattering
SiL
SiU
SnL
SnU
potential is related to the stabilization
Amplitude
3.908 1.692 7.169 1.031
of the π bands of the Ge(001) surface-7
3(10 e/Å /eV/spin)
due
to
the
differenceinPhase shift
0.221 -0.602 -0.650 0.142
electronegativity between Ge and the(πrad)
impurity.

80

4. Members(Affiliation at (the beginning, if later moved to anywhere else, and) the end of the period when the
person participated in our team is shown.)[1] Leader and principal members
Satoshi Watanabe (Professor, Graduate School of Engineering, The University of Tokyo)
Kazuyuki Watanabe (Professor, Faculty of Science, Tokyo University of Science)
Satofumi Souma (Associate professor, Graduate School of Engineering, Kobe University)
Tomoya Ono (Assistant professor, Graduate School of Engineering, Osaka University⇒ Associate professor, Center for Computational Sciences, University of Tsukuba)[2] Collaborative members
Akira Sakai (Professor, Graduate School of Engineering, Kyoto University)
Tomofumi Tada (Assistant professor, Graduate School of Engineering, The University of Tokyo⇒ Associate professor, Materials Research Center for Element Strategy, Tokyo Institute ofTechnology)
Takahiro Yamamoto (Assistant professor, Graduate School of Engineering, The University ofTokyo ⇒ Junior associate professor, School of Engineering, Tokyo University of Science)
Satoru Konabe (Postdoctoral fellow, Graduate School of Pure and Applied Science, Universityof Tsukuba)
Chunping Hu (Assistant professor, Faculty of Science, Tokyo University of Science)
Yasunobu Ando (Assistant professor, Graduate School of Engineering, The University ofTokyo)
Kanji Sasaoka (Assistant professor, Organization of Advanced Science and Technology, Kobe
University)
5. Publications and Invited Talks[1] Publications(a) Total number: 72 (English: 69, Japanese: 3)(b) Selected publications
1) D. Hirai, T. Yamamoto, and S. Watanabe, “Theoretical Analysis of AC Transport in
Carbon Nanotubes with a Single Atomic Vacancy: Sharp Contrast between DC and AC
Responses in Vacancy Position Dependence”, Appl. Phys. Exp. 4, 075103 (3 pages)(2011).
2) D. Hirai, T. Yamamoto, and S. Watanabe, “Anomalous satellite inductive peaks inalternating current response of defective carbon nanotubes”, J. Appl. Phys. 115, 174312(6 pages) (2014).
3) K. Sasaoka, T. Yamamoto, and S. Watanabe, “Wavelet Analysis of Quantum Transient
Transport in a Quantum Dot”, Appl. Phys. Lett. 102, 233107 (4 pages) (2013).
4) W. Liu, K. Sasaoka, T. Yamamoto, T. Tada, and S. Watanabe, “Inelastic transient
electrical currents and phonon heating in a single-level quantum dot system”, J. Appl.
Phys. 113, 123701 (9 pages) (2013).
5) S. Souma, M. Ueyama, and M. Ogawa, “Simulation based design of strained graphene
FET incorporating the pseudo magnetic field effect”, Appl. Phys. Lett., 104, 183103(2014).
6) S. Souma and M. Ogawa, “Pure spin current induced by adiabatic quantum pumping inzigzag-edged graphene nanoribbons”, Appl. Phys. Lett. 104, 213505 (2014).
7) B. Xiao, T. Gu, T. Tada and S. Watanabe, “Conduction paths in Cu/amorphous-Ta2O5/Pt
atomic switch: First-principles studies”, J. Appl. Phys. 115, 034503 (7 pages), 2014.

81

8)

B. Xiao and S. Watanabe, “Oxygen vacancy effects on an amorphous-TaOx-based
resistance switch: a first principles study”, Nanoscale 6, 10169-10178 (2014).
9) S. Konabe and K. Watanabe, “Mechanism for optical activation of dark spin-triplet
excitations in hydrogenated single-walled carbon nanotubes”, Phys. Rev. B 83, 145407(2011).
10) T. Higuchi, C. Hu, and K. Watanabe, “Energetics and Dynamics of Laser-Assisted Field
Emission from Silicene Nanoribbons: Time-Dependent First-Principles Study”, e-J. Surf.
Sci. Nanotech. 13, 115 (2015).
11) D. Utsugi, C. Hu, and K. Watanabe, “Laser-Driven Field Emission from Graphene
Nanoribbons: Time-Dependent Density-Functional Theory Simulations”, Appl. Phys.
Express 5, 105101 (2012).
12) J. Haruyama, T. Suzuki, C. Hu, and K. Watanabe, “Excited-state nuclear forces on
adiabatic potential-energy surfaces by time-dependent density-functional theory”, Phys.
Rev. A 85, 012516 (2012).
13) J. Haruyama, C. Hu, and K. Watanabe, “First-principles molecular-dynamics simulationof biphenyl under strong laser pulses by time-dependent density-functional theory”, Phys.
Rev. A 85, 062511 (2012).
14) S. Hagiwara, H. Goto, C. Hu, and K. Watanabe, “Optical Properties of Boron Nitride andGraphene Nanoribbons: A Time Dependent Density Functional Theory Simulation”, JPS
Conf. Proc. 1, 012072 (2014).
15) C. Hu, R. Ogura, N. Onoda, S. Konabe, and K. Watanabe, “Quasiparticle band gaps ofboron nitride nanoribbons”, Phys. Rev. B 85, 245420 (2012).
16) S. Kasamatsu, S. Watanabe, and S. Han, “Orbital-separation approach for considerationof finite electric bias within density-functional total-energy formalism”, Phys. Rev. B 84,
085120 (11 pages) (2011) (Editor’s suggestion).
17) C. Hu, O. Sugino, and K. Watanabe, “Second-order nonadiabatic couplings fromtime-dependent density functional theory: Evaluation in the immediate vicinity ofJahn-Teller/Renner-Teller intersections”, J. Chem. Phys. 135, 074101 (2011).
18) C. Hu, R. Komakura, Z. Li, and K. Watanabe, “TDDFT Study on quantization behaviors
of nonadiabatic couplings in polyatomic systems”, Int. J. Quant. Chem. 113, 263 (2013).
19) C. Hu, T. Tsukagoshi, O. Sugino, and K. Watanabe, “Nonadiabatic couplings fromtime-dependent density functional theory: Formulation by the Kohn-Sham derivative
matrix within density functional perturbation theory”, Phys. Rev. B 87, 035421 (2013).
20) C. Hu, O. Sugino, H. Hirai, and Y. Tateyama, “Reply to Comment on ‘Nonadiabatic
couplings from the Kohn-Sham derivative matrix: Formulation by time-dependent
density-functional theory and evaluation in the pseudopotential framework’ ”, Phys. Rev.
A 88, 056502 (2013).
21) C. Hu, O. Sugino and K. Watanabe, “Performance of Tamm-Dancoff approximation on
nonadiabatic couplings by time-dependent density functional theory”, J. Chem. Phys.
140, 054106 (2014).
22) T. Ono, S. Tsukamoto, Y. Egami, and Y. Fujimoto, “Real-space calculations for electrontransport properties of nanostructures”, J. Phys.: Condens. Matt. 23, 394203 (13 pages)(2011).
23) T. Ono, Y. Egami, and K. Hirose, “First-principles transport calculation method based onreal-space finite-difference nonequilibrium Green’s function scheme”, Phys. Rev. B 86,
195406 (13 pages) (2012).
24) T. Ono, Y. Fujimoto and S. Tsukamoto, “First-principles calculation methods for
obtaining scattering waves to investigate transport properties of nanostructures”, Quant.

82

Matt. 1, 4 (16 pages) (2012).
25) M. Heide and T. Ono, “Convergence of the Broyden density mixing method innoncollinear magnetic systems”, J. Phys. Soc. Jpn. 82, 114706 (10 pages) (2013).
26) T. Ono, “First-principles electronic-structure and transport calculation formalism using
real-space grid based method,” AIP Conference Proceedings 1558, 1524 (4 pages)(2013).
27) T. Kojima and T. Ono, “First-principles study on transport property of peapods,” Curr.
Appl. Phys. 12, S100 (5 pages) (2012).
28) H. D. Nguyen and T. Ono, “Doping Effect on Magnetism and Transport Property ofHeterojunction between Carbon and Boron Nitride Nanotubes”, J. Phys. Chem. C 117,
24115 (6 pages) (2013).
29) T. Ono, “First-principles calculation of scattering potentials of Si-Ge and Sn-Ge dimers
on Ge(001) surfaces”, Phys. Rev. B 87, 085311 (6 pages) (2013).
30) S. Souma, “Atomistic tight-binding simulation of spin-orbit coupled semiconductor
devices”, in “Spintronics in Nanoscale Devices” edited by E. R. Hedin and Y. S. Joe (Pan
Stanford Publishing), 101 (20 pages) (2013).
31) S. Souma, Y. Ohmi, and M. Ogawa, “Effect of lateral strain on gate induced control ofelectrical conduction in single layer graphene device”, J. Comput. Electron. 12, 170,(2013).
32) A. Mehdipour, K. Sasaoka, and M. Ogawa, and S. Souma, “Strain-induced modulationof anisotropic photoconductivity in graphene”, Jpn. J. Appl. Phys. 53, 115103 (2014).
[2] Invited talks(a) Total number: 35 (international: 25, domestic: 10)(b) Selected invited talks
1) S. Watanabe, T. Tada, S. Kasamatsu and T. K. Gu, “Nanoscale simulations on electronic
and atomic conduction in solid electrolyte/metal junction systems”, IUMRS 11th
International Conference in Asia (Qingdao, China, September 25-28, 2010).
2) S. Watanabe, T. Tada, S. Kasamatsu and T. K. Gu, “Ab Initio Based Simulations on
Electronic and Atomic Transport in Solid Electrolyte/Metal Junction Systems”, Materials
Research Society 2011 Spring Meeting (San Francisco, U. S. A., April 27, 2011).
3) T. Ono, “Spin-polarized current through graphene nanoflake”, The 6th Japan-Sweden
Workshop on Advanced Spectroscopy of Organic Materials for Electronic Applications(Kagaonsen, Japan, November 23-26, 2011).
4) C. Hu, O. Sugino, Y. Tateyama, and K. Watanabe, “Nonadiabatic couplings fromtime-dependent density functional theory: Progress and challenges”, ISSP-CMSI
international symposium on MAterial Simulation in Petaflops era (MASP2012)(Kashiwa, Japan, July 2, 2012).
5) S. Watanabe, B. Xiao, and S. Kasamatsu, “First-Principles Simulations on Electric andDielectric Properties of Metal-oxide Heterostructures for Novel Nanoscale Devices”,
IUMRS International Conference in Asia 2013 (IUMRS-ICA-2013) (Bangalore, India,
December 19, 2013).
6) Tomoya Ono, “First-principles electronic-structure and transport calculation formalism
using real-space grid based method” (Plenary talk), Computational and theoreticalanalysis of grid-based quantum many-body theory (Rhodes, Greece, September 21-27,
2013).
7) Tomoya Ono, “First-principles study on transport property of defects at surface and83interface”, The 16th Asian Workshop on First-principles Electronic Structure
Calculations (Beijing, China, October 28-30, 2013).
8) Tomoya Ono, “First-principles calculation on transport properties of carbon nanotubes
and fullerenes”, International Workshop of Computational Nano-Materials Design on
Green Energy, JSPS Core-to-Core Program Workshop (Osaka, Japan, June 1-3, 2014).
9) S. Watanabe and B. Xiao, “Density Functional Study on the Structures of Conductive
Filaments and Ion Migration Behaviors in Tantalum Oxide based Resistive Switching
Devices”, IEEE International Nanoelectronics Conference (INEC) 2014 (Sapporo, Japan,
July 30, 2014).
10) S. Watanabe and B. Xiao, “Density Functional Study concerning Tantalum Oxide based
Resistive Switching Devices”, 9th International Conference on Computational Physics(ICCP9) (Singapore, January 7-11, 2015).

84

New properties of materials probed by proton and muon, and their quantum
dynamics
H. Nakanishi 1, H. Goto 1, M. Geshi 1, M. Wilde 2,
W. Dino1*, H. Kasai1,2,3*, K. Fukutani2*, H. Kikuji1*
Osaka University 1, The University of Tokyo 2, National Institute of Technology, Akashi college3
We have been developing the first principles simulation methods and novel experimental
methods for the positive muon and proton states as hydrogen isotope nuclei states in thematerials, and investigating their behaviors and their induced new properties of materials. In
Chapter 1, we report our developing first principles simulation code “Naniwa”, for the positive
muon, proton and other small mass nuclei in the material environments, and its applications toreal material systems. In Chapter 2, we report a new algorithm for electron-electron correlationenergy calculations by superposition of nonorthogonal Slater determinants. In Chapter 3, wereport the physical properties of metallic hydrides under high pressure. In Chapter 4, we report
our experimental methods and their results for the catalytic reaction, diffusion, and desorption
dynamics of hydrogen in the near-surface region of palladium.

Ch.1 The first principles simulation code “Naniwa” and its applied results
1.1 Introduction
The first principles calculation based on the density functional theory is one of the mostsuccessful and powerful methods in the materials physics. And also the first principles
molecular dynamics methods have been used for various dynamical behaviors. In the case ofsmall mass atoms like hydrogen atoms, we should treat their nuclei (proton) in a quantummechanical manner, in addition to electrons. The quantum behaviors of the nuclei have crucial
roles to play in the materials related to today’s energy technology: fuel cell and lithium-ion
rechargeable battery, and also various catalytic reactions to produce hydrogen fuel, not only
from their academic interests. Positive muon is also one of our target quantum particles, because
it has been used as a magnetic probe particle in materials, -SR. The positive muon has thesame spin and same charge as a proton and behaves as the very light isotope of hydrogen which
has ninth mass of proton. It is important to analyze the quantum behavior of these particles in
the materials. In this chapter, we report our developing simulation codes “Naniwa” and its
application examples to real material systems.
1.1 Simulation code “Naniwa” and its algorithm.
We have been developing the quantum simulation code “Naniwa” for the small mass atom
nuclei, proton and positive muon on solid surfaces, in subsurfaces and bulk crystals. These
particle-case situations are different from that of electron case in the materials. We propose thefollowing suitable methods for the quantum state calculation for these particles in materials.
Here, we consider that the material are constructed from the nuclei and electrons. If weknow how these particles behave, we can know the almost material properties. The total
Hamiltonian of the electrons and nuclei in material is given byN 2  2 n  2  2(1)
   V (r,R )   H  

  2M 
n c .

I 1



I



  2m 
e

I

i 1



e



i

where MI and me are masses of the I-th nucleus and electron. Numbers of nucleus and electron
are N nc. and ne. The positions of the electrons and nuclei are indicated by(2)
r 1r ,2r ,3r ,, ri, rn  and R  R 1 , R 2 , R 3 ,, R I ,, R N ,enc.

* Co-Investigators (renkei-kenkyūsha).

85

where ri is the i-th electron position vector and R I is the I-th nucleus position vector. The
potential energy is given by the coulomb interaction between these particles;Nn N
n i 1I 1ZJ ZI e 2
 ZI e 2(3)e2V (r,R )   rR  r r   R R

n c .

e

i 1 I 1

i

n c .

e

i 1 j 1

IjI 1 J 1iJI

where Zl is atomic number of the I-th nucleus, and e is the elementary charge.
The total Schrödinger equation of electrons and nuclei is(4)
H  (r, R )  E  (r, R ) ,where E and  (r, R ) are the total eigen energy and the eigen wave function describing the stateof this material system. When we adopt the adiabatic approximation between the electrons andnuclei, the wave function, (r, R ) , can be written by,(5)r(R, ) n; R r( ) ; n (R )n ,and the total Schrödinger equation (4) can be divided into coupled two equations:(6)        V (r, R )  (r )  U (R )  (r ),     U (R )  (R )  E  (R )   2M 
 2m 
ne



N nc.

2

2
i

i 1



e

n ;R

n

n ;R



2

2
I

I 1

n



I

 ;n

 , n  ;nfor electron system and for nucleus system. Here,  n;R (r ) is the n-th eigen wave function ofelectron system with its eigen energy U n (R) in the case of the fixed nucleus positon R. By theuse of conventional ab initio electron states calculations or coming electron state calculation inCh.2 for various configurations of R, we can obtain the eigen energy U n (R) as a function of
R. And we solve the latter part of equation (6) and we can obtain the -th eigen function
 ;n (R ) of nucleus system in the case of electron system in its n-th state, and eigen energyE ;n , which is appeared as E in the eigen equation (4).
In the case of single small-mass-nucleus in the host materials, we described  ;n (R ) bylinear combination of the 3D-Gauss functions, which are located at mesh grid points   ,  ,   with its decay factors ( x ,  y ,  z ) :.
  x y z  exp   x x   2   y  y   2   z z    2
3



1

NG

 ( x, y, z )   C , 
 1



4



(7)

By use of the variation method, latter part of eq. (6) becomes matrix equation:
H  E S C  0, H  T  U .




 

 ,0

 

 

 ,

 

 

(8)

In the case of Gauss function based set, the overlap integral matrix elements, S  , and the
kinetic energy matrix elements, T , are analytically given by
y
 

2
   2   z    2 ,S  exp  x     
 




2









2

2





(9)




 2 
  S       2  1       2  1       2  1 .
T   
x
x


y
y


z
z


 2M  



 











(10)

When we use the discrete Fourier transform (DFT) of the potential energies, U n ( X j1 , Y j2 , Z j3 ) ,at sampling points ( X j , Y j , Z j ) , j1  1 N1 , j 2  1 N 2 , j3  1 N 3 :
1

2

3

~

 U n (k1 , k 2 , k 3 ) ,

(11)

DFT

U n ( X j1 , Y j2 , Z j3 )the potential energy matrix elements is also analytically given by
U    N1 1 / 2
S  

N 1 N 2 N 3 k1    N1 1 / 2

 N 2 1 / 2

k 2   N 2 1 / 2

 N 3 1 / 2~

k3   N 3 1 / 2

n

1

2

3



2

k 

k 
k 
1  2 k1 
1  2 k 2 1  2 k 3    i 1        i 2       i 3      . (12) L 
8 x  L y 
8 z  L z x x  Lz 
 Lx  y 

  U (k , k , k ) exp  8  L2

2

Hence the all matrix elements are given, and we can solve eq.(8) efficiently in Naniwa code [1].

86

1.2 Quantum states of hydrogen isotope adsorbed on metallic surface.
By use of our simulation code “Naniwa”, we investigate the hydrogen isotope states on themetallic surfaces. In the Table 1, we show the numerical results for the vibrational excitedenergies. Our simulation results show the good agreement with the experimental results. Theirdifferences are less than 10 %. The ratio of the excitation energy between deuterium andprotium is less than 2 . This reduced ratio is also shown in experiment. Even for suchfundamental physical quantity, the simple harmonic approximation around the minimum energy
point is failed, and such ab initio quantum simulation is necessary for the small mass atom
states.
NaniwaExperiment

Error

H on Pd(111)// 91 meV⊥ 114 meV//
96 meV [2]⊥ 124 meV [2]// 5.2%⊥ 8.1%

H on Cu(111)⊥ 135 meV⊥

129 meV [3]⊥ 4.7%

D on Cu(111)⊥ 104 meV⊥

96 meV [3]⊥ 8.3%

Isotope effect

1.29

1.34

3.4%

Table 1. Excitation energies of hydrogen isotope atoms adsorbed on metal surfaces for parallel (//) andperpendicular (⊥) vibrational modes.

In collaboration with the other group of (MEXT) Grant-in-Aid for Scientific Research on
Innovative Areas: “Frontier of Materials, Life and Particle Science Explored by Ultra Slow
Muon Microscope”, we investigate the positive muon and proton states on graphene [4].
Naniwa result for the hydrogen adsorbed energy, 0.58 eV, shows the good agreement with thatfrom TDS (Thermal Desorption Spectroscopy) experiments, 0.59 or 0.65 eV [5]. Only fromconventional electron states calculation, the calculated adsorbed energy is over estimated,because of lack of the zero-vibrational energy of proton. We found that an adsorbed state of
positive muon is also stable on graphene with lower adsorbed energy, 0.22eV. On graphene, apositive muon catches single electron on its 1s-orbital and becomes non-spin-polarized Mu(muonium), which will be observed by the coming ultraslow muon microscope.
In association with the experimental parts Ch.4, we investigate the hydrogen atom
absorption in hydrogen-covered Pd(110) (1 × 2) missing-row surface [6]. On this reconstructedsurface, the absorption of initially adsorbed hydrogen atoms is entirely assisted by the cominghydrogen molecule from outside, instead of the assistance of initially adsorbed H atoms. The
dissociation of hydrogen molecule is preferred to occur on H-vacant ridge site than on troughsite. Origin of such difference between these sites is clarified by tracing the position of thederived anti-bonding state in the transition states. We found that, for both cases, the dissociation
process is the rate-limiting step and hydrogen absorption is a non-activated process on thissurface.
Furthermore, we have been also developing the other version of Naniwa codes for scattering
problems, and investigate the dynamics of hydrogen isotopes (Mu, H, D, T) absorption into
Pd(111) subsurface [7]. We found the quantum correlation effects between hydrogen isotope
atom and surface lattice vibrations in adsorption process.
1.3 Quantum state of the hydrogen isotope impurity in the covalent bond crystals
After the achieve a measure of success in the case of metallic surface, we try to investigate
the quantum states of impurity hydrogen isotopes in covalent crystals, diamond structure crystalof silicon (Si) and -quartz (SiO2). In the case of Si, we found the impurity hydrogen state in
BC site as its ground state, and that in T site as its excited state, which correspond to those87

reported with the aid of the first principles path integral simulation by Miyake [8]. We noted that
correct results for these hydrogen impurity sites require the larger size of supercell in thesimulation, because of the impurity induced strong lattice stress. In this case, 3x3x3 supercell isneeded at the least. This simulation methods can be applied for revealing the hydrogen
behaviors in the metallic hydrides under high pressure appeared in Ch.3.
Nevertheless -SR experimental results show that a positive muon exist as a muonium in
SiO2 crystal, as a results of previous conventional ab initio study, the neutral muonium andneutral hydrogen atom impurity states are unstable in SiO2. We calculate the quantum states ofmuonium, hydrogen, deuterium and tritium atoms in -quartz by use of Naniwa code (Fig.1).
As a result of the 3x3x3 supercell calculation, which includes 81 silicon atoms and 162 oxygen
atoms, these neutral states are stable, whose ground state energies are -1.03eV, -1.15eV, -1.18eVand -1.20eV. The wave function is localized in SiO2 lattice cage. Calculated hyperfine constantis 4.47GHz, which are good agreement with experimental value [9]. In Fig.1, we found thesignificant quantum effects of Muonium as compared with other hydrogen isotope atoms, forexample, three degenerate ground states and larger vibrational excitation energy, which can beseen in energy gap from quantum number 3 to 4.

Fig.1. Eigen energies of a muonium (Mu), Hydrogen (H), Deuterium (D) and Tritium (T) atoms in -quartz
crystal. Upper insets show the wave functions of the 3 degenerate ground states of Mu. Lower right inset shows thewave function of the ground state of H. Cyan balls indicate silicon atoms. Red balls indicate oxygen atoms.

1.4 Conclusions
We have been developing the first principles simulation code “Naniwa” for positive muonand proton in various material environments. We have verified practical effectiveness of oursimulation methods for metallic surfaces, and for covalent bond crystals, against theexperimental given data. And we found some typical new quantum effects derived from small
mass of nuclei coupling with material environments. As for experimental methods by probe ofmuon being energetically developed in J-PARC (Japan Proton Accelerator Research Complex),
our simulation can provide the necessary corroborating information about muon site, muonstates (its motion, its spin, its valence electron and spin), their differences from proton(hydrogen), etc. in the various target materials. The quantum simulation must be powerful andnecessary tools to reveal the new properties of materials.
1.5 References[1] Japanese patent 4774523, US patent US8140467[2] H. Conrad, et al, J. Vac. Sci. Technol. A5, 452(1987).
[3] G. Lee, et al., Surf. Sci. 498 (2002) 229.
[4] A. D. Pant, et al., JPS Conf. Proc. 2, 010313(2014)[5] X. Zhao, et al., J. Chem. Phys. 124(2006)194704.

[6] A. A. B. Padama, et al., J. Chem. Phys. 140,
244707 (2014)[7] K. Shimizu et al.,, J. Phys. Soc. Jpn. 83, 013601(2014)[8] T. Miyake, et al., Phys. Rev. Lett. 81 (1998) 1873
[9] S. F. J. Cox, Rep. Prog. Phys. 72 (2009) 116501

88

Ch.2 A new algorithm for electron-electron correlation energy calculations bysuper- position of nonorthogonal Slater determinants
2.1 Introduction
In this study, a reliable and accessible algorithm for calculating electron-electron correlationenergies of few-particle systems with continuously controllable accuracy by the superposition ofnonorthogonal Slater determinants (SDs) [1] is presented. The key points of the proposed
procedure are updating of all the one-electron wavefunctions by employing correction functions
and optimizations on the basis of the variational principle without constraints on theorthogonality and normalizations. The accuracy and applicability of the present algorithm aredemonstrated through calculations of the ground- and excited-state energies for atoms andmolecules.
2.2 Optimization algorithm
An N-electron wavefunction Ψ(𝐫1 , 𝜎1 , 𝐫2 , 𝜎2 , ⋯ , 𝐫𝑁 , 𝜎𝑁 ) is expressed by a linear
combination of nonorthogonal SDs as follows:𝐿Ψ(𝐫1 , 𝜎1 , 𝐫2 , 𝜎2 , ⋯ , 𝐫𝑁 , 𝜎𝑁 ) = ∑ 𝐶𝐴 Φ 𝐴 (𝐫1 , 𝜎1 , 𝐫2 , 𝜎2 , ⋯ , 𝐫𝑁 , 𝜎𝑁 ) .

(1)

𝐴=1

Here, 𝐫𝑖 and 𝜎𝑖 represent the position and spin index of the ith electron, respectively. L is thenumber of SDs and Φ 𝐴 (𝐫1 , 𝜎1 , 𝐫2 , 𝜎2 , ⋯ , 𝐫𝑁 , 𝜎𝑁 ) is the Ath SD constructed by one-electron
wavefunctions(2)
𝜓𝑖𝐴 (𝐫, 𝜎) = 𝜙𝑖𝐴 (𝐫)𝛾𝑖 (𝜎)𝐴with 𝜙𝑖 (𝐫) and 𝛾𝑖 (𝜎) being nonorthogonal and unnormalized one-electron spatial
wavefunctions and spin orbital functions, respectively. The one-electron wavefunction 𝜙𝑖𝐴 (𝐫)is constructed as a linear combination of Gaussian basis functions. In the present procedure, theith one-electron wavefunction 𝜙𝑖𝐴 (𝐫) in the Ath SD is updated by
𝑁𝑐
𝐴(𝑛𝑒𝑤)(𝐫) = 𝐶𝐴 𝜙𝑖𝐴(𝑜𝑙𝑑) (𝐫) + ∑ 𝐶𝐿+𝜇 𝜉𝜇 (𝐫),
𝜙𝑖
𝜇=1

(3)

where 𝜉𝜇 (𝐫), 𝐶𝐿+𝜇 and Nc are a correction function, the expansion coefficient and the numberof correction functions, respectively. 𝜉𝜇 (𝐫) is also expressed as a linear combination ofGaussian basis functions. Thus, we have a linear combination of L+Nc SDs as the new
N-electron wavefunction. The coefficients 𝐶𝑖 (𝑖 = 1,2, … , 𝐿 + 𝑁𝑐 ) are obtained by solving thegeneralized eigenvalue equations obtained by adopting the variational principle with respect tothe total energy. Iterations of this updating procedure for all one-electron wavefunctions
belonging to all the SDs lead to the ground state with the superposition of nonorthogonal SDs.
This algorithm is the main result of this study. After the convergence of the ground state, an
excited state can be obtained by adding new SDs and updating the new one-electron
wavefunctions by the same procedure.
2.3 Applications to few-electron systems
The total energy for a carbon atom by the present algorithm is shown in Fig. 1. The ground-stateenergy is obtained using less than 100 nonorthogonal SDs with an error of 0.001%. The convergenceproperty is so smooth that the accuracy of the total energy is controllable by the number of employed SDs.
In contrast, the full configuration interaction (CI) method requires over 105 orthogonal SDs, andthis reduction in the numbers of SDs is a notable advantage of adopting nonorthogonal SDs [1].
Fig. 2 illustrates the total energy convergence of a Be atom for different values of 𝑁𝑐 . The
convergences are improved by multiplying the correction vectors, since the volume of the89search space for a one-electron wavefunction increases with 𝑁𝑐 . Figs. 3 and 4 show thenumbers of SDs to count 98% of the electron-electron correlation energy for few-electron
systems. Both sets of results illustrate that the number of nonorthogonal SDs to determine theground state by the present algorithm gradually increases with the system. Fig. 5 shows thecalculated potential energy curve of a HF molecule. Although for short bond lengths, the errors
obtained by coupled-cluster theory with singles and doubles (CCSD) and plus perturbative
triples (CCSD(T)) are a few milliHartrees, at longer bond lengths, the accuracy appears to
become depleted [2]. In contrast, the present calculation ensures practical exact ground states atall bond lengths, since no approximations are employed. In the case of 90 degree twisted
ethylene around the C-C bond axis, the same problem on counting the static correlation energy
arises. Fig. 6 indicates the noticeable advantage of the present algorithm. Non-negligible errors
in the total energy difference between the singlet and triplet states at 90 degree torsion angle
given by CCSD(T) and CAM-B3LYP are shown.

Fig. 1. Total energy convergence as a function of thenumber of SDs for a C atom with 3 correction
functions.

Fig. 2. Convergence performance of the total energy
for a Be atom with different numbers of correction
functions.

Fig. 3. Required number of SDs to determine theground state of atoms with 6-31G* basis set.

Fig. 4. Required number of SDs to determine theground state of small diatomic molecules.

Fig. 5. Potential energy curve of a HF molecule obtainedusing proposed algorithm with 6-31G** basis set.

90

Fig. 6. Total energy variation depending on thetorsional angle of ethylene.

2.4 Conclusion
A new calculation algorithm for searching the ground- and excited-state wavefunctions by thesuperposition of nonorthogonal SDs is proposed. The accuracy and applicability of the present
algorithm are demonstrated through calculations of the ground- and excited-state energies for
few-electron systems.
2.5 References[1] H. Fukutome, Prog. Theor. Phys. 80 (1988) 417.
[2] P. J. Knowles, et al.,, J. Chem. Phys. 133 (2010) 224106, K.Shimizu et. al.,J. Phys. Soc. Jpn. 83, 013601 (2014)

Ch. 3 Physical properties of metallic hydrides under high pressure
3.1 Introduction
Hydrogen at high pressure has attracted many physicists for long time, for examples,
metallization and superconductivity. In addition, Ashcroft’ suggested that metallic hydrides
might be metallic and realized the superconducting state at lower pressure than pure hydrogen[1,2]. Many researchers expected that the superconducting transition temperature (T c) ofmetallic hydrides might be higher than that of the previously found materials. Firstly, this wasinvestigated by means of first-principles calculations based on Density Functional Theory(DFT) using Allen-Dynes formula based on BCS theory. Many reports showed promising
results. However, experimental maximum Tc was 17 K of SiH4 [3]. The difference between
theoretical predictions from the DFT calculations and experimental results discourages theresearchers to study H-rich metals in view point of promising superconductors.
We focus on H-rich metals from different points of view. One is Metal-to-Nonmetal transition,and the other is effects of hydrogen for elastic properties of H-rich materials.
Basic calculations of all studies are performed using Quantum-Espresso code [4] to relax
atomic positions and cells and calculate phonon dispersions and elastic constants. The elastic
constants are calculated by means of my developed method [5]. To analyze accurate electronic
structures, we use Wien2k code [6].
3.2 Pressure induced Metal-to-Nonmetal transition of AlH3
AlH3 is a R3c structure at ambient pressure. With increasing pressure, it transforms to a
Pm3 n structure through an intermediate structure, a P 1 structure [7]. The electronic structureof the Pm3 n structure is semimetallic. Normally, band dispersion becomes wide and strongly
overlaps with increasing pressure. However, this semimetallic band structure changes tononmetallic ones and the band gap is open at 300GPa within the GGA result in spite of the factthat the band dispersion becomes wide. In order to obtain more accurate estimation of theMetal-to-Nonmetal transition pressure, we have performed higher accurate calculation using themethod of one-shot GW approximation [8-10]. From this result, we have estimated thetransition pressure of about 200GPa as shown in Fig.1. Using the leading-edge technique of ahigh pressure measurement this may be verifiable.
The reasons of pressure induced band gap opening are (1) the moderately large difference ofelectronegativity between aluminum and hydrogen and (2) the orthogonality between the 3s
states and 2s states of Al.. We have also examined several materials by replacing Al with B, Ga,
In, Tl, N, P, As, Sb, and Bi, and by replacing H with F assuming the same structure. However,Pressure induced band gap opening with the same mechanism did not found in those synthetic
materials.
The structural stability of higher pressure region than 164 GPa is confirmed by calculating91

phonon dispersion and enthalpy compared with the Pm3 n structure and many type of
optimized structures. This is the first finding of pressure induced band gap opening of hydrides
and the mechanism is different from Metal-to-Nonmetal transition of high pressure Li.

Fig.1: Band dispersion of AlH3 with Pm3n structure at 200 GPa. Black solid (Red dashed) lines indicate
GGA (GW approximation) results.

3.3 Chemical trend of elastic constants of metallic hydrides
It is difficult to identify positions and numbers of hydrogen in hydrides from experiments
except for neutron diffraction measurement. We therefore have calculated elastic constants for
hydrides with changing the number of hydrogen and have investigated the chemical trend andsome properties from the electronic structure analysis. The calculated elastic constants can becompared with experimentally observed ones by means of Brillouin scattering measurement.
We have calculated RH2 (R=Sc, Y, La, Ti, Zr, V, Nb, Ta) assuming the structure being the
CaF2 structure which is the typical structure of this chemical composition. In this structure theatom of R is at 4a site (0, 0, 0) and hydrogen does at 8c site. When hydrogens are added, theyoccupy the 4b site (1/2, 1/2, 1/2). When hydrogens are removed from RH2, they are done fromthe 8c site (1/4, 1/4, 1/4; 3/4, 3/4, 3/4). We have calculated the elastic constants for each numberof hydrogen from n=-4 to 4 with respect to RH2 (RH2+; -1 ≤  = n/4 ≤1).
(a)
(b)
(c)

(d)

(e)

(f)

Fig.2: The elastic constant C11-C12 for (a) YH2+(-1≤≤１;=n/4), (b) ZrH2+, and (c)NbH2+, and C44 for (d) YH2+,(e) ZrH2+, and (f) NbH2+.

The trend of the elastic constants depends on the group of metals. Figure 2 shows the elastic

92

constants, C11-C12 and C44, for YH2+, ZrH2+, and NbH2+ as representatives. Note that for n=-2
and n=2 their structures are always tetragonally distorted although the data is plotted in Fig. 2(a),(b), and(c). The origin of the tetragonal distortion is the crystal symmetry of RH2.5 and RH1.5. In
the positive region of C11-C12, the value of C44 is also positive. These show the existing regionof these metallic hydrides within the harmonic approximation, which is consistent with the Joint
Committee on Powder Diffraction Standards (JCPDS) data [11]. These results can be used toestimate the number of hydrogen and their positions for RH2+.
A general outline of the electronic structures of these materials can be understood that they
are quite similar with those having D4h symmetry. This means that these materials essentially
includes the electronic structure to distort tetragonal structure by changing the amount ofhydrogen. In fact, several RH2+ type materials are tetragonal structures [11].
3.3 Summary
We have found pressure induced Metal-to-Nonmetal transition for AlH3. This transition is thefirst finding for hydrides. The elastic constants have been calculated for several metallic
hydrides. If the elastic constants are measured from experiments, then the number of hydrogenand their positions can be estimated.
3.4 References
Universitaet Wien, Austria),2001.
[7] I. Goncharenko et al., Phys. Rev. Lett. 100, (2008)
045504.
[8] T. Kotani, M. van Schilfgaarde, Phys. Rev. B 81
(2010) 125117.
[9] M. van Schilfgaarde, T. Kotani, S.V. Faleev, Phys.
Rev. B 74 (2006) 245125.
[10] T. Kotani, M. van Schilfgaarde, S.V. Faleev,
Phys. Rev. B 76 (2007) 165106.
[11] http://www.icdd.com/[1] N.W. Ashcroft, Phys. Rev. Lett. 92 (2004)
187002.
[2] J. Feng et al., Phys. Rev. Lett. 96, (2006) 017006.
[3] M. I, Eremets, et al., Science 319 (2008)1506.
[4] P. Giannozzi, et al., J.Phys.:Condens.Matter 21,(2009) 395502.
[5] M. Geshi, Physica B 405, (2010) 517.
[6] P.Blaha, et al., WIEN2k, An Augmented plane
Wave þ Local Orbitals Program for Calculating
Crystal Properties Karlheinz Schwarz, Techn.

Ch.4. Investigation of the catalytic reaction, diffusion, and desorption
dynamics of hydrogen in the near-surface region of palladium
4.1 Introduction
In the final year of this project, we have continued our investigation into the hydrogen (H)transportation dynamics through palladium (Pd) surfaces, which are of crucial fundamental
importance for hydrogen storage and purification applications in hydrogen energy technology as
well as in industrial hydrogenation catalysis. Our previous research has provided detailed
insight into the near-surface hydride nucleation process and into the atomic-level hydrogen
absorption mechanism at the H2-exposed Pd(110) single crystal surface [1-4]. This established
our ability to systematically vary the spatial distribution of Pd-absorbed hydrogen underneaththe Pd(110) surface over a wide depth range. We also obtained evidence that the hydrogen
absorption kinetics are surface structure-sensitive. Based on this knowledge, we further pursued
our research following two specific objectives: 1.) To clarify the role of palladium-dissolvedhydrogen in the mechanism of Pd-catalyzed olefin hydrogenation, which has been subject ofcontroversial discussion in the literature for many years; and 2.) to explore the possibility tomanipulate the hydrogen transport between the interior and the surface of palladium throughdeliberate surface structural modification.
4.2 Clarification of the role of Pd-dissolved hydrogen in olefin hydrogenation catalysis on
palladium surfaces
Palladium is the most extensively applied industrial catalyst for the partial hydrogenation of93

unsaturated hydrocarbons (olefins) in petroleum refining and in organic synthesis. This reaction
adds two hydrogen atoms to the C=C double bond of the olefin adsorbed on the catalyst surface.
Surprisingly, this surface reaction is known to require hydrogen dissolved in the interior of thepalladium catalyst, but no consensus on the particular role of the Pd-absorbed hydrogen in the
catalytic mechanism has yet been reached in the literature. On one hand, it is possible that
Pd-absorbed H atoms become directly involved in the hydrogenation after they emerge from themetal interior onto the catalyst surface in an energetic state, because H in Pd bulk interstitialsites is ~0.3-0.4 eV less stable than in chemisorption sites on the surface [5]. This argument isanalog to the rather well-accepted explanation for the particular hydrogenation reactivity ofsubsurface hydrogen underneath alkyl-adsorbed Ni surfaces [6, 7]. On the other hand, one may
consider that – if present in sizeable populations (>50 %) - hydrogen in subsurface sites may
indirectly activate co-adsorbed reactants on the surface by altering the electronic structure of thecatalyst surface [8].
To elucidate this important mechanistic problem in hydrogenation catalysis on Pd, we here
applied our unique combination of hydrogen depth profiling via resonant 1H(15N,)12C nuclear
reaction analysis (NRA) and thermal desorption spectroscopy (TDS) [9] to reveal the hydrogen
distribution on and beneath a Pd(110) model catalyst surface under hydrogenation reaction
conditions for a typical conversion of cis-2-butene (C4H8) to butane (C4H10) and characterized
the reaction behavior of hydrogen/C4H8 co-adsorption systems on Pd(110) by means of TDS. A
full account of this study is published in Ref. [10].
Initially, we prepared different amounts and depth distributions of absorbed hydrogen (Habs)
in Pd(110) by controlling the H2 dosage and the Pd crystal temperature during the H2 exposure,then post-adsorbed a monolayer of C4H8 molecules at 115 K. The TDS traces of the C4H10hydrogenation product in Fig. 1 (a) show that the catalytic reaction proceeds efficiently between
160 and 250 K when absorbed hydrogen has been pre-charged into the Pd(110) surface, and thatthe product yield increases with the amount of pre-dosed H2. Notably, surface-adsorbed H on
Pd(110) (obtained after H2 exposure of 1 L = 1.33×10-4 Pa ∙ s) alone does not achieve any C4H10
production. This result is similar to observations at Pd nanoparticle catalysts [11] and forPd(111) [12, 13] and showcases the indispensable role of Pd-absorbed hydrogen for the catalytic
reactivity. Fig. 1 (b) summarizes the results of TDS reactivity measurements by showing thedependence of the butane yield on the amount of absorbed H (controlled by the H2 dosage) for
three different Pd crystal temperatures during the H2 exposure (Te = 115, 160, and 200 K).

Fig. 1: (A) Series of C4H10 TPD spectra recorded after sequential exposure to various amounts of H2 and to 1.25 L
C4H8 at 115 K. (B) Butane (C4H10) reaction yield as a function of the amount of Habs prepared at Te = 115 K (circles),
160 K (rectangles), and 200 K (diamonds). The solid lines denote the H 2 quantity desorbing in TPD measurementsfrom bare Pd(110) below 250 K. (B) is adapted from Ref. [10].

Evidently, the butane reaction yield depends linearly on the quantity of Pd-absorbedhydrogen at all Te’s and larger hydrogenation yields are obtained when Habs is prepared at lower
temperatures. The NRA H depth profiles of H2-exposed Pd(110) in Fig. 2 (a) reveal that this94

behavior relates to the initial depth distribution of the absorbed hydrogen, which tends to belocated closer at the surface at lower Te. The NRA H profiles in Fig. 2 (b) – (d), however,evidence that although the depth distributions of absorbed hydrogen prepared at the three Te’sare initially very different, the potentially large initial H concentration in the subsurface region
vanishes when the butene/hydrogen co-adsorption system on Pd(110) is stepwise annealed to
the reaction temperature of the catalytic hydrogenation (maximum at 218 K, Fig. 1 (a)).
Complementary TDS measurements detect only little H2 desorption during annealing to 218K,
hence the loss of the H in the near-surface region is due to diffusion into the deeper Pd bulk.
The remaining NRA profiles at 218 K (Fig. 2 (d)) reflect the signal of the saturated H
chemisorption layer on the Pd(110) surface at a coverage of 1.5 monolayers (ML).[4]Fig. 2: (a) Near-surface NRA H-depth profiles from Pd(110) exposed to H2 to prepare an equivalent of 10 ML ofabsorbed hydrogen at Te = 115 K (circles), 160 K (squares), and 200 K (diamonds). Triangles and a corresponding
Gaussian fit (solid line) indicate the resonance profile of surface hydrogen at saturation coverage (1.5 ML). (b)-(d):Evolution of the near-surface H distributions after co-adsorbing 1.25 L C4H8 at 115 K and briefly annealing to (b) 150
K, (c) 190 K, and (d) to the hydrogenation reaction temperature, TR = 218 K. The -yield of H in co-adsorbed C4H8
has been subtracted from the data in (b)-(d).

The combined data of Figs. 1 and 2 thus signify that the catalytic hydrogenation reaction canproceed efficiently although the H concentration in the Pd subsurface region is as small as 0.5
at. % (evaluated in depths larger than 5 nm, where surface hydrogen does no longer contributesignificant NRA signal). This clearly rules out the proposed indirect scenario that large H
concentrations in subsurface sites would influence the hydrogenation reactivity by activating
surface-adsorbed reactants through alterations of the surface electronic structure. On the other
hand, the solid lines in Figure 1 (b) denote the amount of absorbed H that desorbs from theclean Pd(110) surface in the temperature range of the hydrogenation reaction (up to 250 K). This
indicates that the butane reaction yield is linearly proportional to the number of absorbed H
atoms arriving at the Pd surface by diffusion from the Pd bulk at the reaction temperature.
Our results strongly support the interpretation that re-emergence of bulk-dissolved hydrogen
onto the H-saturated Pd surface triggers the catalysis by supplying reactive H species for thehydrogenation reaction, whereas the hydrogenation catalysis does clearly not depend on large
stationary H concentrations in Pd subsurface sites. We hence reach a clear decision in favor ofthe direct scenario for the role of Pd-dissolved H in Pd-catalyzed olefin hydrogenations, where
the Pd-absorbed hydrogen provides a reservoir of reactive hydrogen species that entertain thehydrogenation reaction after resurfacing from the Pd bulk.
4.3 Release control of Pd-dissolved hydrogen through surface structural modification
Our previous research into the atomic-level hydrogen absorption pathways at H2-exposed
Pd(110) with 15N NRA H depth profiling and thermal desorption spectroscopy withisotope-labeled surface hydrogen [4] has demonstrated that two H2 absorption pathways exist on
the Pd(110) surface: One is related to surface defects, whereas the other one involves regular95

terrace sites. In comparison to H2 absorption at Pd(100) [14, 15] and Pd(111) [16], where only
surface defects (such as step edges and terrace pits) appear to be active sites for hydrogen
ingress, the efficient absorption at regular terraces of Pd(110) seemed to suggest that hydrogen(H2) absorption is a structure-sensitive process, and that certain properties of the particular
H-induced pairing-row reconstruction of the Pd(110) surface enhance the hydrogen uptake
kinetics relative to the atomically more close-packed (111) and (100) surfaces. In order toexplore this hypothesis further, we have looked into the possibility to deliberately influence thehydrogen transport through palladium surfaces by structural modifications, exploiting the factthat the Pd(110) surface is susceptible to several CO (carbon monoxide) adsorption-induced(de-)reconstructions. While a detailed account of this investigation is published in Ref. [17], weonly provide a brief summary of the main results here.
The experimental study was performed by dosing 1000 L of H2 onto the clean Pd(110)
surface at either 120 or 160 K in order to H-saturate the surface chemisorption sites and to
populate the H absorption states [4] with a few MLs of hydrogen. Subsequently, various
amounts of CO (up to 3 L) were co-adsorbed at the same surface temperature and the H2desorption behavior was examined with TDS. The resulting structural phases of the Pd(110)
surface and the associated effects on the H2 thermal desorption spectra are summarized in
Figure 3. We verified that the H2 pre-dosage of Pd(110) has no influence on the CO-induced
structural modifications and that CO adsorbs on this surface with a constant sticking probabilityof 0.5 until it saturates after dosage of 2 L at a maximum coverage of 1.0 ML.[17]The bare low-temperature (160 K) H2-exposed Pd(110) surface initially exhibits a H-induced(2×1) pairing-row (PR) reconstruction. The low temperature region of the H2 TDS trace isdominated by two features (1 at 160 K and 3 at 200 K), which are due to desorption ofabsorbed H through surface defects and regular terrace sites, respectively [4]. Preferential
adsorption of small CO amounts (below 0.4 L or 0.2 ML) at defects eliminates the 1 desorption
channel at 160 K by blocking the exit sites for absorbed H, leaving now only one dominant
desorption feature of absorbed H from the (2×1) PR reconstructed terraces at 200 K (1).
A second step of CO-induced modification occurs in the dosage/coverage regime of 0.4 – 1.2
L (0.2 – 0.6 ML), which lifts the original H-induced PR reconstruction and restores a bulk
truncated (1×1) surface. This is accompanied by a second high temperature shift of the H2desorption feature from 200 K (1) to 270 K (2).

Fig. 3 (A) Ball models of the CO-induced surface (de-)reconstructions of Pd(110). White, gray and dark balls denotesurface, first and second subsurface Pd atoms, respectively. PR: (2×1) pairing-row; MR: (1×2) missing-row structures.
(B) Three steps of H2-TPD modification with increasing CO post-dosage. Pd(110) is sequentially exposed first to
1000 L H2 and various amounts of CO. Gas dosage is carried out (a) at 120 K, or, (b) and (c) at 160 K. Adapted from
Ref. [17].

A final stage of CO-induced structural modification takes place during the TDS heating ramp,
when the Pd(110) surface holding 0.3 – 1.0 L CO is heated above 340 K. This results in a (1×2)

96

missing-row (MR) reconstruction of the surface, which in turn leads to another substantial
high-temperature shift (by 105 K!) of the H2 desorption that now takes place in a dominant 3feature at 375 K. Remarkably, this final desorption temperature is higher than that of surfacechemisorbed hydrogen from the clean Pd(110) surface (~300 K), and because post-dosed CO
pushes chemisorbed H into the Pd interior [17], a distinction of surface and Pd-absorbed H as in
the H2 TDS trace from clean Pd(110) [4] is no longer possible after CO-modification.
A further noteworthy observation is that all H2 desorption features of the Pd(110) surface
described in Figure 3 occur while CO is still present on the surface (CO desorbs at even higher
temperatures than H2). With exception of the suppressed 160 K 1 feature, this clearly
distinguishes the present manipulations of the H2 desorption behavior as actually being due tosurface structural modification rather than as resulting from mere CO site blocking effects asreported for a few other surfaces [18-21]. We further revealed through NRA H depth profilingthat prior to desorption through the CO-modified surface above 200 K, all near-surface absorbedhydrogen, including H in first-layer subsurface sites, diffuses into the deeper Pd bulk [17].
In summary, we succeeded in demonstrating the possibility to deliberately raise thedesorption temperature of Pd-dissolved hydrogen in three distinct steps from 160 K of the clean
Pd(110) surface to 200 K, 270 K, and even up to 375 K through well-defined CO-induced
surface structural modifications. The individual H2 release modes (related to distinct surface
structural phases) are easily selectable by controlling the CO coverage. The largest achieved
temperature increase by remarkable 215 K shifts the H2 release from a cryogenic regime (160
K) to a range significantly above room temperature (375 K), which may open novel
opportunities for hydrogen storage technology of much reduced cooling energy cost.
4.4 Summary
Through direct visualization of the hydrogen distribution on and below a Pd single crystal
surface during catalytic conversion of butene (C4H8) to butane (C4H10) with NRA hydrogen
depth profiling, we have succeeded in finally clarifying the long-debated mechanistic role ofPd-dissolved hydrogen in Pd-catalyzed olefin hydrogenation. Pd-dissolved hydrogen is
identified as a resource for reactive hydrogen species after it emerges onto the H-saturated
surface by diffusion from the Pd bulk. Large stationary H concentrations in subsurface sites, on
the other hand, are not necessary to sustain the catalytic hydrogenation reactivity [10].
We further demonstrated the possibility to control the desorption dynamics of Pd-dissolvedhydrogen through well-defined modifications of the Pd(110) surface structure, achieving the so
far largest reported desorption temperature shift (215 K) of absorbed hydrogen from a cryogenic
regime (160 K) to above room temperature (375 K) [17]. The temperature at which Pd-absorbedhydrogen re-emerges at the Pd surface to either desorb as H2 or to induce a catalytichydrogenation reaction is a critical parameter that has the potential to improve process
conditions and catalytic selectivity.
In conclusion, we believe that the fundamental insight into the atomic-level dynamics ofhydrogen in catalytic reactions, diffusion, and desorption processes at palladium surfaces
obtained in this project will contribute significantly to the development of energy-efficientmaterials and process conditions in hydrogen storage applications and in industrialhydrogenation catalysis.
4.5

Referencesmaterials probed by proton and muon, and theirquantum dynamics”, Ch.4.

[1] The 2011 annual report on “New properties ofmaterials probed by proton and muon, and theirquantum dynamics”, Ch.4.

[3] The 2013 annual report on “New properties of[2] The 2012 annual report on “New properties ofmaterials probed by proton and muon, and their97

quantum dynamics”, Ch.4.

10853.

[4] S. Ohno, et al., J. Chem. Phys. 140 (2014)
134705.

[13] A. M. Doyle, et al., Angew. Chem. Int. Ed. 42(2003) 5240.

[5] Y. Fukai, The Metal Hydrogen System, Springer,
Berlin, New York, 2005.

[15] M. Wilde, et al., Surf. Sci. 482-485 (2001) 346.

[14] H. Okuyama, et al., Surf. Sci. 401 (1998) 344.

[6] A. D. Johnson, et al.,, Science 257 (1991) 223.

[16] G. E. Gdowski, et al., J. Vac. Sci. Technol. A 5(1987) 1103.

[7] S. T. Ceyer, Acc. Chem. Res. 34 (2001) 737.
[8] H. A. Aleksandrov, et al., Angew. Chem. Int. Ed.
53 (2014) 13371.

[17] S. Ohno, et al., J. Phys. Chem. C., submitted.

[9] M. Wilde, et al., Surf. Sci. Rep. 69 (2014) 196.

[19] G. Rupprechter, et al., Surf. Sci. 554 (2004) 43.

[10] S. Ohno, et al., J. Phys. Chem. Lett., submitted.

[20] M. D. Marcinkowski, et al., Nature Materials 12(2013) 523.

[18] C. Nyberg, et al., Surf. Sci. 256 (1991) 9.

[11] M. Wilde, et al., Angew. Chem. Int. Ed. 47(2008) 9289.

[21] S. Ogura, et al., J. Phys. Chem. C 117 (2013)
9366.

[12] M. Morkel, et al., J. Chem. Phys.119 (2003)

Ch.5 Refereed papers & Invited talks
5.1 Refereed papers
1. H. S. Kuncoro, M. Sakaue, H. Nakanishi, H. K. Dipojono, H. Kasai, J. Phys. Soc. Jpn. 80(2011) 024601.
2. M. K. Agusta, W. A. Diño, M. David, H. Nakanishi, H. Kasai, Surf. Sci. 605 (2011)1347.
3. Y. Kunisada, H. Nakanishi, W. A. Diño, H. Kasai J. Vac. Soc. Jpn. 55 (2012) 115.
4. A. Sarhan, O. Y. Ching, H. Nakanishi, K. Fukutani, H. Kasai, J. Appl. Phys. 113 (2013) 023703.
5. K. Shimizu, W. A. Dino, H. Kasai , J. Phys. Soc. Jpn. 83 (2014) 013601.
6. A. A. B. Padama, B. Chantaramolee, H. Nakanishi, H. Kasai, Inter. J. Hydrogen Energy 39(2014) 6598.
7. H. Goto and K. Hirose, J. Nanosci. Nanotechnol. 11 (2011) 2997.
8. A. Sasaki, M. Kojo, K. Hirose, H. Goto, J. Phys.: Condens. Matter 23 (2011) 434001.
9. A. Sasaki, K. Hirose and H. Goto, Curr. Appl. Phys., 12 (2012) S96-S99.
10. H. Goto, M. Kojo, A. Sasaki, K. Hirose, Nano. Res. Lett. (2013), 8:200
11. M. Geshi, T. Fukazawa, Physica B 411 (2013) 154.
12. S. Ohno, M. Wilde, K. Fukutani, J. Chem. Phys. 140 (2014) 134705.
13. M. Wilde, K. Fukutani, Surf. Sci. Rep. 69 (2014) 196-295.
Other referred papers: 53

5.2 Invited talks
1. H. Nakanishi, “Quantum states of the muon on solid surfaces and in subsurfaces”, JPS 2011 Autumn Meeting
Symposium: “Ultra slow muon spectroscopy: its innumerable possibilities”, Toyama University, Toyama, Japan,
September 23, 2011.
2. M. Geshi and T. Fukazawa, “Pressure Induced Band Gap Opening of AlH 3”, International Workshop ofComputational Nano-Materials Design on Green Energy (Joint Workshop of Interactive Materials Science
Cadet Program (IMSC), Osaka University and S-1 JSPS Core-to-Core Program (A) Advanced Research
Networks) Awaji Yumebutai International Conference Center, June 16-19, 2013
3. M. Wilde, “Subsurface hydride formation mechanisms at Pd(110)”, 9th International Conference on Diffusion
in Solids and Liquids (DSL-2013), Madrid, Spain, June 24-28, 2013.
4. H. Nakanishi, “Quantum states of impurity hydrogen isotopes in covalent crystals”, 10th International
Conference on Diffusion in Solids and Liquids (DSL-2014), Paris, France, June 23-27, 2014.
5. M. Wilde, “Atomic-level mechanism of hydrogen absorption at palladium surfaces”, Seminar at Chemical
Physics Group (Prof. Dr. H.-J. Freund), Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany,
July 1, 2014.
6. H. Nakanishi, “First-principles calculations of probe quantum positive muon”, JPS 70th Annual Meeting（2015)
Symposium: Current status and perspective of first-principles calculation methods, Waseda University Tokyo,
Japan, March 21, 2015.
Other invited talks: 22

98

Reaction Analysis and Conformational Sampling forMultidimensional Large Scale Systems

1

T. Yamato, 2A. Mitsutake
1
Nagoya University, 2Keio University

AFM force-distance curve of membrane protein: A coarce-grained dynamics simulation
Regarding the structure and dynamics of single-biomolecules, atomic force microscopy (AFM)
measurements provide us detailed information we would not obtain otherwise. For example,
during the forced unfolding of a bacteriorhodopsin (bR) molecule with typicalseven-transmembrane architecture, we observe force-distance (F-D) curves with multiple peaks,
which have attracted a broad attention from many researchers both in experimental andtheoretical expertise. Unfortunately, however, the physicochemical mechanisms of theseprocesses have not been fully elucidated yet. To address the issue, we conducted a molecularsimulation study with a novel coarse-grained model.
From a theoretical viewpoint, the abovementioned peaks are thought to be direct reflectionsof energy barriers along the unfolding pathways of bR on its complex energy surface. Regarding
the energy landscape of membrane proteins, Popot and Engelman proposed a famous model
describing the protein folding process as consisting of two independent steps: (1) formation ofindividual helices and their insertion into the membrane and (2) the subsequent helix-helix
association within the membrane environment. Here, it is very likely that the interactions thatare responsible for the first step mainly characterize of the F-D curves with multiple peaks.
Based on the working hypothesis, we conducted computer simulations of bR with thecoarse-grained (C-G) model with rigid-sphere representation for peptide units. The surrounding
waters and lipid membrane were treated as implicit continuum environment. As a result, theexperimental peak positions of the F-D curves in the literatures were reproduced well by our
computer simulations, indicating that the essential features of the molecular interactions
involved in the forced unfolding processes of bR by the AFM apparatus were well captured in
our C-G model.
Figure 1.
We
havedevelopedanewcoarse-grained model of membraneproteins. Our simulation reproduced
experimental peak positions observedin the AFM force-distance curves ofbR. The overall system (left), F-D
curve (middle), and bacteriorhodopsin
molecule (right).

Energy exchange network of inter-residue interactions within a thermally fluctuating
protein molecule: A computational study
Molecular dynamics (MD) allows us to “see” how the protein behaves under physiologicalconditions. To study molecular mechanisms involved in protein functions, it is important to99

develop good tools to extract useful information from MD trajectories.
Here we propose our method to analyze the residue-residue interactions based on the energy
flow within a thermally fluctuating protein molecule. The “crosstalk” among interacting
residues was represented as a graph of energy exchange network (EEN). As an example, we
analyzed the properties of a small globular domain, PDZ3, which is well known to exhibit
single domain allostery. The removal of its C-terminal helix is known to decreases ligand
affinity by 21-fold without changing the overall protein structure; nevertheless, wedemonstrated that the helix constitutes an essential part of the EEN graph, indicating that theinter-residue interactions play crucial roles in the protein’s function.
Our computer program called “CURP” (CURrent calculatioin for Proteins), which was usedpreviously to analyze the atomic stress tensors in a small protein molecule, has been extended toinclude the energy flow analysis in this study.
N363

R312

T321

G329

I336

I338

V362

V315

G345

F337

I359

G356

G364

D366

P346

V365

D332

S371

R368

A375

E373

Q374

G324

A376

I377

A378

I327

K380

N381

A382

G333

T385

Ligand binding pocket
G322

H372

L379

S339

I341

E401

K355

Y397

E331

G335

E334

F400

E396

P394

E395

K393

R399

A402

S398
I314

E310

P311

S320

L349

R354

D357

R309

Q358

Q391

Y392

A390

S361

R313

D348

E352

L360

A347

S350

I316

T387

I389

R318

G319

Q384

G351

L353

Figure 2.
The structure of PZD3 domain (left) and its energy exchange network (EEN) (right).
Each node represents an amino acid residue, and interacting residue pairs with irEC greater than 0.015(0.008) {0.006}

are connected by thick red (thin blue) {thin green} edges. The

ligand-binding pocket was indicated by yellow box. Black rounded rectangles represent amino acidresidues located in the α3 helix.

CURP (CURrent calculation for Proteins)
The physical properties of condensed matter systems can be illustrated at the microscopic scaleby evaluating the continuum variables in atomistic simulations. Among condensed mattersystems, native protein molecules are particularly interesting in that they realize biological
functions via an energy relaxation process from the non-equilibrium state to the equilibrium
state in response to external perturbations such as light illumination and ligand binding. We cancharacterize native proteins in terms of continuum variables and provide biophysical grounds
for the molecular mechanisms of protein functions. The values of continuum variables vary100

from site to site in a protein molecule of interest, reflecting its inhomogeneity and anisotropy.
Therefore, we can expect to find functionally important sites by analyzing the 3D field ofcontinuum variables in a protein molecule. For instance, we analyzed electron-tunnelingcurrents in proteins and discovered a key residue for the electron transfer reaction in DNA
photolyases[1]. Other examples are the analysis of the energy-transfer pathway in photoactive
yellow protein[2,3] and the identification of the “epicenter” of the protein quake in photoactive
yellow protein via stress tensor analysis[4]. Note that the first quantity is related to the electron
flow, the second is related to the energy flow, and the third is related to the linear momentum
flow. The CURrent calculation for Proteins (CURP) program is written in Python and
FORTRAN, reads (1) the parameters of the force-field functions and molecular topology dataand (2) the atomic coordinates and velocities from the molecular dynamics trajectory, and thencalculates the flow of physical quantities. The AMBER format is supported for the current
version[5]. In the future, we plan to distribute an advanced version of the CURP program, andthe supported formats will be extended to include those of other molecular simulation packages.
References:[1] Y Miyazawa, H Nishioka, K Yura, T Yamato, Biophys J 94 (2008) 2194-203.
[2] T Ishikura, T Yamato, Chemical Physics Letters 432 (2006) 533-37.
[3] T Yamato, in: D.M. Leitner, J.E. Straub (Eds.), Proteins : energy, heat and signal flow,
Taylor and Francis, New York, 2009, p. 129-47.
[4] K Koike, K Kawaguchi, T Yamato, Phys Chem Chem Phys 10 (2008) 1400-5.
[5] T Ishikura, T Hatano, T Yamato, Chemical Physics Letters 539 (2012) 144-50.

Figure 3.
The Logo of the CURP program (left), calculation
flow (upper right), and an example of CURP
calculations (bottom right ) in combination with
conformational sampling by conventional MD
simulation.

Computational study on the roles of amino acid residues in the active site formation
mechanism of blue-light photoreceptors
The cryptochrome and photolyase families have different biological functions, despite sharing
high degrees of sequence identity and structural similarity between them. From the structural
point of view, there is no doubt that their enzymatic activities are particularly sensitive to thefine-tuning of their active site conformation.
It has been accepted that the active site methionine (hereafter denoted as M-site) and glutamic
acid (E-site) residues play important functional roles in the enzymatic activity of thecyclobutane-pyrimidine dimer (CPD) photolyase. To examine the functional roles of the M-site101and E-site residues, we performed in silico mutation at the M-site using MD simulation in asystematic manner, and focused on the hydrogen bonding between the E-site and the CPD
substrate. Fragment molecular orbital calculations with electron correlations demonstrated that
substitution of the M-site methionine with either alanine or glutamine always destabilized theinteraction energy between the E-site and the CPD by more than 12.0 kcal/mol, indicating thatthe methionine and glutamic acid residues cooperatively facilitate the enzymatic reaction in theactive site.
Figure 4.
The E-site glutamic acid and the
M-site methionine residue
cooperatively facilitate the hydrogenbonding formation between the CPD
and E-site, which is thought to beimportant for efficient electron transfer
reaction in the active site of CPD
photolyases.

Ligand migration in myoglobin: A combined study of computer simulation andtime-resolved x-ray crystallography
Ligand migration in myoglobin (Mb) is a fundamental biophysical process in which theinterplay between dynamics, thermal fluctuation, and ligand-protein interaction plays a crucialrole. Nevertheless, the details of the molecular mechanism involved have not been fully
understood. From structural point of view, it has been accepted that the hydrophobic cavities
called Xe pocket and Distal pocket (DP) play important roles in ligand migration in Mb.
However, no x-ray structure exhibits broad pathways for ligand migration movements
especially at the bottlenecks between different internal hydrophobic cavities, indicating that thethermal fluctuations around the average structure are essential for regulating the molecularfunction under the physiological conditions.
So far, a large number of studies have been devoted to illustrate ligand migration in Mb withexperimental techniques, computer simulation techniques and other theoretical approaches. By
using time-resolved X-ray crystallography at high resolution under the low-temperature condition,
Tomita and colleagues recently demonstrated the structural changes and the breathing motion
associated with the ligand migration movement of carbon monoxide in the wild-type sperm whale
myoglobin. Laser flash photolysis induces the structural change of the protein from thecarbon-monoxide-bound form (MbCO) to the carbon-monoxide- unbound form (Mb…CO). Under
cryogenic conditions, temperatures are low enough for high-resolution crystallography, and eachligand is supposed to reside inside each protein.
To illustrate the ligand migration mechanism, they proposed the self-opening model, in which theligand-protein interaction broadens the bottleneck between cavities and facilitates efficient ligand
movement. Here, we developed a new computational method: homogeneous ensemble displacement(HED), which effectively approximates the statistical ensemble of Mb…CO based on that of MbCO.
Using this method, we demonstrate the importance of the ligand-protein interaction for the ligand
migration. Although the structural changes were small, the presence of the ligand molecule in102the protein matrix significantly affected the 3D scalar field of the potential of mean force for theligand-protein interactions, in accord with the self-opening model proposed in the previous
x-ray study.

Figure 5.
Flash photolysis of myoglobin. Upon flash
photolysis, the CO molecule (red) is detachedfrom the heme group (blue). There areseveral internal cavities: four Xe-bindingsites (Xe1, Xe2, Xe3, Xe4), the distal pocket(DP) and the phantom site (Ph), indicated bydotted lines (green). In the Mb…CO form,
the ligand molecule migrates from one cavity
to another.

Figure 6.
PMF map for MbCO (left) and Mb…CO(right). (a,b) Xe1, (c,d) Xe2, (e,f) Xe3, (g,h) Ph,
and (i,j) DP and Xe4. Value of PMF, W, is
indicated by blue

, cyan, white, pinkand red. A 3Dinterpolation between grid points provided thescalar field of PMF for the molecular interior
space. Isoenergetic contour

in

Mb…CO (right) is indicated by broken lines in
MbCO (left). We indicate the protein interior inblack.

Atomic stress tensor analysis of proteins
We performed stress tensor analysis of polypeptides at the atomic level by molecular
dynamics simulations. Most of the approaches to stress tensor analysis of molecules in theliterature assume that the interatomic forces are pairwise; however commonly used force-field103

functions contain multi-body interactions. To address this issue, we derived new mathematicalformulae for atomic forces based on force-field functions, in which the total force acting oneach atom is expressed as a summation of pairwise interatomic forces. Then, a computer
program for stress tensor analysis was developed, and it successfully characterized themechanical features of molecules at the atomic level.
Figure 7.
We
derivedmathematicalexpressionsforpairwiseinteratomic forces based onforce-field functions containing
multi-body interactions. Then,
atomic stress tensors were
calculated based on Hardy’s
formula.

Normal Mode Analysis of Compressibility of Evolutionary Lysozymes
According to X-ray crystal structures, globular proteins have a precisely defined compact
structure, but there are many packing defects or cavities in the interior of a protein molecule
which cause internal motions or flexibility response to thermal or mechanical forces. Suchcavities are easily compressed by pressure and hence isothermal compressibility βT is an
important measure of protein dynamics or volume fluctuation. However, the direct measurementof βT is generally difficult for protein as seen in limited reports because the volume of protein
molecule is only slightly reduced by pressure and high pressure induces conformational change
or denaturation of protein. Therefore, most compressibility studies of protein have been carriedout with the adiabatic compressibility βs that can be more easily and accurately determined bysound velocity measurements. An important finding of these compressibility studies is that only
single amino acid substitution induces large changes in βs and that the mutant having larger βsvalue has higher enzyme activity. This means that the local structural changes by mutation
cause significant modification of overall protein dynamics to affect its function.
The isothermal compressibilities (βT) of chicken lysozyme and its six evolutionary mutants at
Thr40, Ile55, and Ser91 were calculated from their X-ray structures by means of a normal mode
analysis at 300K. The energy-minimization was carried out by a Newton’s method using the
program FEDER/2 and an energy function ECEPP. The βT value was calculated as a sum of thevolume fluctuation from individual normal modes within the potential energy of harmonic range.
The βT values of two extant lysozymes from chicken and quail (bobwhite) were 1.61 and 1.59
Mbar-1, respectively, but other ancestral mutants showed the larger βT values up to 2.08 Mbar-1.
These results suggest that the ancestral mutants were highly flexible and that such mutation
followed a non-neutral evolutionary pathway. No visible change was found in the tertiary
structure of all the mutants but most ancestral mutants induced a large increase in the total
cavity volume (Vcav). An observed positive linear correlation between βT and Vcav predicts thatcavity or atomic packing is an important determining factor of the volume fluctuation inmolecular evolution of protein.

104

Table 1 Compressibility and volume fluctuation of extant and ancestral lysozymes.
a) The values in parentheses represent the ratio (%) of <V> to total molecular volume.
b) Mean total cavity volume estimated with the probe radii of 1.05–1.20 Å.
c) Taken from BA Malcom et al. Nature 345 (1990) 86-88.

Molecular mechanism of long-range synergetic color tuning between multiple amino acidresidues in conger rhodopsin
The synergetic effects of multiple rhodopsin mutations on color tuning need to be completely
elucidated. Systematic genetic studies and spectroscopy have demonstrated an interesting
example of synergetic color tuning between two amino acid residues in conger rhodopsin’s
ancestral pigment (p501): —a double mutation at one nearby and one distant residue led to asignificant λmax blue shift of 13 nm, whereas neither of the single mutations at these two sites led
to meaningful shifts.
To analyze the molecular mechanisms of this synergetic color tuning, we performed
homology modeling, molecular simulations, and electronic state calculations. For the double
mutant (DM), N195A/A292S, in silico mutation analysis demonstrated conspicuous structuralchanges in the retinal chromophore, whereas that of the single mutant (SM), A292S, was almost
unchanged. Using statistical ensembles of QM/MM optimized structures, the intrinsic excitationenergy of retinal chromophore was evaluated forthe three visual pigments. As a result, the λmax
shift of DM from p501 was –8 nm, while that of
SM from p501 was +1 nm. Moreover, principal
component analysis successfully identified three
determinants for color tuning: bondlength
alternation, counterion displacement.
Figure 8. (Left) Protonated Schiff-base of retinal and amino acid residues at the sites 195 and 292
in rhodopsin. Although these two amino acid residues are separated far away, they cooperatively
work for the color tuning of rhodopsin. (Right) Average structures of the protonated Schiff-base ofretinal and the surrounding amino acid residues are shown. The thermal average structure wasobtained from MD simulations for p501 (red), SM(orange), and DM (green).

Relaxation mode analysis of proteinsIn this project, we have applied generalized-ensemble algorithms to the water confined toslit nanopores to investigate the liquid-solid phase transition of the system. We also have apply
relaxation mode analysis to the protein system to investigate the dynamics and kinetics. Here we
explain the results of relaxation mode analysis.
Biopolymers have flexible structures and several varieties of functions. The functions arederived from not only structures but also the dynamics of structural fluctuations. Therefore, the105

dynamic properties of structural fluctuations of biopolymers are important for understanding theinterrelationship between its movement and functions. Classical molecular dynamics (MD)simulations are a popular and powerful method for describing the structure, dynamics, andfunction of biomolecules in microscopic detail. Recent technological advances have allowed for
simulations on the timescales of the order of microsecond. Because longer MD simulations havebeen feasible in recent years, it is more important to develop an analysis method to extract goodorder parameters for identifying local-minimum-energy states automatically, and investigate
dynamics and kinetics of proteins.
Relaxation mode analysis (RMA) has been developed to investigate ``dynamic'' propertiesof spin systems and homopolymer systems. We applied RMA to biomolecular system in the
project. The equilibrium time correlation functions of the relaxation modes, Xp satisfy
X p (t)X q (0) = δ p,q e

where− λ ptX p (t)X q (0) denotes the equilibrium correlation of Xp at time t and Xq at time 0 and λp

is called the relaxation rate of Xp. The relaxation modes and rates are also given as left
eigenfunctions and eigenvalues of time-evolution operator of the master equation of the system,
respectively. For single linear polymers represented by the Rouse model, which has no excluded
volume interaction and no hydrodynamic interaction, the relaxation modes are identical to the
Rouse modes, which have been playing an important role in the theory of the polymer dynamics.
In the case of linear polymers, the relaxation phenomena have been studied systematically interms of the relaxation modes and rates.
In RMA, the relaxation modes and rates are estimated by solving a generalized eigenvalue
problemN∑ C (t + τ ) f
j=1

i, j

N

N

i=1

j=1 p,i

∑ ∑

0

p, j

=e

− λ ptN∑ C (t ) f
j=1

i, j

0

p, j

f Ci, j (t0 + τ ) fq, j = δ p,q ,Figure 8. (Left) Protonated Schiff-base of retinal and amino acid residues at the sites 195 and 292 inrhodopsin. Although these two amino acid residues are separated far away, they cooperatively workfor the color tuning of rhodopsin. (Right) Average structures of the protonated Schiff-base of retinal
and the surrounding amino acid residues are shown. The thermal average structure was obtained
from MD simulations for p501 (red), SM(orange), and DM (green).

, where Ci, j (t) denotes the equilibrium time-displaced correlation function of the position of
the i-th segment relative to the center of mass of the polymer. RMA is formulated as avariational problem equivalent to the eigenvalue problem of the time-evolution operator of thesystem, where a relaxation mode Xp is approximated by a trial function, which is constructed asa linear combination of relevant physical quantities that are time-evolved for t0/2. The parametert0 is introduced in order to reduce the relative weight of the faster modes contained in thephysical quantities. The slow relaxation modes and rates are obtained approximately. The
optimization of the normalized equilibrium autocorrelation function of the trial function
time-displaced by τ leads to the generalized eigenvalue problem. In practice, the timecorrelation matrices of structural fluctuations for two different times (t0 and t0+τ) arecalculated through simulations. Then, by solving a generalized eigenvalue problem for these106matrices, the relaxation rates and modes are obtained from the eigenvalues and eigenvectors,
respectively. Thus, we call this method the RMA method using a single evolution time t0/2.
We applied RMA to the Monte Carlo simulation for a heteropolymer, peptide, system witha small number of degrees of freedom and its effectiveness was demonstrated. In theapplications to "homo"polymer, polymer systems, the translational degrees of freedom areremoved from the conformations of the polymer sampled in a simulation. However, therotational degrees of freedom are remained because they are interested in the slow rotational
relaxation of the polymer. For "hetero"polymer, biomolecule systems, in contrast, both thetranslational and rotational degrees of freedom are removed from sampled conformations of abiomolecule because the structural fluctuations around its average conformation are interested.
We explained how to remove the contribution of the rotational degrees of freedom in RMA andapplied RMA to a five-residue-peptide, Met-enkephalin in gas phase because it is known tohave several metastable or stable conformations.
A long Monte Carlo simulation of Met-enkephalin in gas phase was performed. The results
were analyzed by the principal component analysis (PCA) and RMA. PCA extracts modes withlarge conformational fluctuation and is a static analysis method. We compared the results ofboth methods and showed the effectiveness of the relaxation mode analysis. From thesimulation, we observed three groups due to different hydrogen bond patterns of backbone
atoms, A and B, C and D, E and F. The clusters A and B in the same group have same hydrogenbonds between backbone atoms H2-5 and the global-energy-minimum state. The cluster C andD have H1-4 and are the second lowest-energy-minimum state and the cluster E and F haveH1-5 and are the third lowest-energy-minimum state. Difference between A and B, C and D, or
E and F is the arrangement of side chain of Tyr1 (see Fig.9). We obtained the different view ofthe free energy surfaces between PCA and RMA. In Fig.1 the free energy surfaces obtained by
RMA are shown. The directions of slow relaxation modes obtained by RMA correspond to slow
movements (transitions) between local-energy-minimum states. The free energy surface interms of the coefficients of the first, second, and third relaxation modes distinguished theclusters because they have long relaxation times due to their stabilities. The first relaxationmode, which is similar to the first principal component axis, corresponded to the transitions
between clusters A and C or clusters A and D. The second relaxation mode, which is notobserved in PCA, represented the movement of the side chain of Tyr1 or the transition between
clusters C and D. The third relaxation mode, which is similar to the second principal component
axis, corresponded to the transitions between clusters C and E or between clusters D and F. We
find that the transition between compact structures of H1-4 and H1-5 is faster than the
movement of the side
chain of Tyr1 or thetransition between
cluster C and D. From
the free energy
surfaces obtained by
RMA, we identify theclusters andinvestigate thetransitions between
these clusters while
Figure 9. The free energy surfaces along the first and second slowest
PCA gives only static
relaxation mode axes (a) and along the second and third slowest relaxation
information. RMA ismodes axes (b) obtained by RMA and six typical structures.
a powerful analysis

107method to investigate the dynamics and kinetics of protein systems.
Although RMA is a powerful method to extract slow modes, it requires a relatively highstatistical precision of time correlation matrices. Owing to this requirement, RMA needs a muchlong simulation than to occur many transitions between local-minimum-energy states, which
may not be a problem because very long simulations have been feasible in recent years.
Moreover, it cannot treat a large number of degrees of freedom directly. Therefore, thereduction of the degrees of freedom is necessary for the application of RMA to protein systems.
To apply RMA to a protein system by reducing its degrees of freedom, we proposed an analysis
method, which is referred to as the principal component relaxation mode analysis (PCRMA)
method. In this method, PCA is carried out first and then RMA is applied to a small number ofprincipal components with large fluctuations. This method can reduce the degrees of freedom
systematically. Even if we succeed in reducing the degrees of freedom by using PCA, it issometimes difficult to obtain reasonable relaxation modes and times by RMA using a single
evolution time t0/2. This occurs when we cannot make t0 so large that the fast modesin the selected principal components time-evolved for t0/2 become negligible, because the valueof t0 should be chosen so that the statistical precision of the correlation matrices C(t0) and C(t0 +τ) is maintained sufficiently high. Note that the statistical precision of C(t) becomes worse forlarger t. In such a case, the selected principal components that are time-evolved for t0/2 containfast relaxation modes that are not well described by a linear combination of the selectedprincipal components. To solve this problem, we also proposed the RMA method using multiple
evolution times, which can reduce the contribution of the fast modes efficiently. We used the
combination of the two proposed methods, which is the PCRMA method using multiple
evolution times.
We performed an all-atom molecular dynamics simulation of human lysozyme in aqueous
solution for 100 ns at 300 K. PCA was carried out on the mass-weighted coordinates for 1029
heavy atoms of the protein. We used 10 lowest PC modes for RMA. We reduced the degrees of
freedom from 3081 (3087-6) to 10 to apply
RMA. In Fig. 10, the three-dimensional
vectors in the first and second PC modes andin the first and second slowest PCRMA
modes are shown. Black lines represent the
average structure and arrows represent thedirections of the modes. For the first PC
mode, the residues with large fluctuations
are Pro103 and Gln104, which are located at
an exposed turn part. The first PC mode
corresponds to a local movement of the turnpart. On the other hand, for the first slowest
PCRMA mode, there is no local large
fluctuation near Pro103 and Gln104 andFigure 10. Three-dimensional vectors at Cα, C
the mode seems to be a collective mode.
β, and Cγ atoms for the first (a), second (c) PC
PCA sometimes extracts local movements
modes obtained by PCA and the first (b) andwith large and fast fluctuations located atsecond (d) slowest RM modes obtained byexposed parts (e.g., turn parts) as
PCRMA. The vectors are divided by the mass
lower-order PC. PCRMA succeeds inweight and multiplied by 8. The Cα atoms ofextracting a collective mode without local
Pro103 and Gln 104 are colored in yellow.
and large fluctuation as the slowest
relaxation mode.

108

PCRMA can reduce the degrees of freedom systematically. The combination method of
PCRMA and multiple evolution times can extract slow relaxation modes.
Finally, we applied PCA and RMA to the system, in which large conformational changes
are observed. PCA is difficult to extract order parameters to identify the local-minimum-energy
states for the system with large conformational changes because PCA extracts the modes withlarge structural fluctuation around an average structure. PC modes with large structuralfluctuations do not correspond to the transitions between the local-minimum-energy states. On
the other hands, RMA extracts slow relaxation modes. The local-minimum-energy states areusually stable and stay long time during a simulation. The order parameters with slow
relaxations may correspond to the direction between local-minimum-energy states. Slowrelaxation modes may correspond to good order parameters to identify local-minimum-energy
states.
We performed a simulation of chignolin at a transition temperature. Chignolin consists often amino acid sequences and is the test peptide to develop simulation methods.
There were many simulations for chignolin. From previous researches, it is found thatchignolin has the stable state (native structure) and a misfolded state. We consider that byincreasing temperature, many transitions between two states may occur in the order of hundred
ns simulation. The simulation at a transition temperature corresponds to a long time simulation.
We have performed a 750 ns molecular dynamics simulation of chignolin in aqueous
solution at 450K. Many transitions among the native, misfolded, and unfolded structures wereobserved. In Fig. 3 the free energy surfaces along the first and second lowest PC axes (a) andalong the first and second slowest RM axes (b) are shown. We obtained the different view of thefree energy surfaces of PCA and RMA. From the free energy surfaces of RMA, we identified
not only the stable and misfolded states but also intermediate state automatically. The native andmisfolded structures have hairpin-line structures. The stable and misfolded states have slightly
different hydrogen bond patterns of backbone atoms. The intermediate structures havecharacteristic structure; turn structure from Asp3 to Glu5. RMA neglects the conformationalchanges with fast relaxation of the terminal residues and extract the intermediate state while
PCA dose not identify the intermediate state. The stable and misfolded structures have the sameturn structure. From the results of RMA, it is found that chignolin folds to the native or
misfolded structures through the turn structure. From RMA, we clearly understand the folding
process and kinetics of the system. RMA is powerful and efficient to analyze the system withlarge conformational changes such as folding/unfolding and long simulations and investigate
dynamics and kinetics of the system.

10
5
0 2nd

Unfolded

15

Intermediate

10

Stable

5 2nd
0

-5
-10
-5

0

5 10 15
1st-5

Misfolded

-10

-5

0
1st

5

10

Figure 11. The free energy surfaces along the first and second lowest PC axes (a) and along thefirst and second slowest RM axes (b)109Research publications (Total # of papers and book chapters: 23)
T. Kaneko, J. Bai, K. Yasuoka, A. Mitsutake, and X.C. Zeng, “Liquid-solid and solid-solid
phase transition of monolayer water: High-density rhombic monolayer ice", Journal ofChemical Physics, 140, 184507 (2014)
T. Yamato and K. Yura, “Combinatorial approach of molecular dynamics simulations anddatabase analysis for the studies of protein structure and function”, SEIKAGAKU (The Japanese
Biochemical Society Journal), 85 (8) pp. 646-655, 2013.
T. Kaneko, J. Bai, K. Yasuoka, A. Mitsutake, and X.C. Zeng, “New Computational Approach to
Determine Liquid-Solid Phase Equilibria of Water Confined to Slit Nanopores", J. Chem. Theo.
Compt. 9 (2013) 3299
T. Tsuduki, A. Tomita, S. Koshihara, S. Adachi, T. Yamato, “Ligand migration in myoglobin:
A combined study of computer simulation and X-ray crystallography”, J. Chem. Phys., 136(16)165101 (9 pages) (2012)
Ishikura, T. Hatano, T. Yamato, “Atomic stress tensor analysis of proteins”, Chem. Phys. Lett.
139-140, pp. 144-150, (2012).
A. Mitsutake, H. Iijima, H. Takano,” Relaxation mode analysis of a peptide system: comparison
with principal component analysis” J. Chem. Phys.135, 164102(15 pages), 2011.
Invited talks (Total #: 22)
Ayori Mitsutake, “Effective Sampling Algorithms and Analysis Methods for Protein
Simulations’’, The 14th KIAS Conference on Protein Structure and Function, September 19,
2014, Korea
T. Yamato, “Role of reorganizable interactions between native residue contacts on the allostericcommunication in proteins: A computational study by the inter-residue energy conductivity
analysis”, Protein dynamics, Telluride research science workshop, Telluride, CO, Aug. 5-9,
2013.
A. Mitsutake, “Development of effective sampling algorithm and analysis method forbiomolecular simulations”, 4th Japan-Korea Seminar on Biomolecular Sciences Experiments andSimulations, Jan.2012, Nara
T. Yamato, “Ligand migration in myoglobin: A combined study of computer simulation andx-ray crystallography”, 4th France-Japan Joint Seminar, Imaging of spatiotempral hierarchies inliving cells -- an overview of dynamics from molecules to cells – , Hyogo, Japan, Jan. 6 --11,
2012.
T. Yamato, “Intramolecular Communication Chart of Proteins: Computational Analysis of
Energy Transfer Pathways”, Thermal Transport at the Nanoscale, Telluride Science ResearchCenter Workshop, Telluride, CO, USA, Jun. 21-25, 2010.
Awards (Total #: 2)
A. Mitsutake, Young scientist award of the Physical Society of Japan (2013).

110

Developments of first-principles multiscale simulation
for coupled dynamics of light-wave and electrons in dielectrics
Kazuhiro Yabana
Center for Computational Sciences, University of Tsukuba

1. Introduction
In this project, we have developed a first-principles computational approach to describeinteractions between light and matter based on time-dependent density functional theory.
Interactions between light and matter are usually described by two theories: Macroscopic
Maxwell equations describe propagation of a light wave in a medium, while quantum
calculation of susceptibilities such as dielectric function is one of central issues infirst-principles condensed matter calculations. Recent progresses of laser technologies,
however, require theories beyond them. Ultrashort laser pulses of even a few cycles are often
used, and pump-probe measurements are carried out in time domain. They require theories intime-domain, solving the time-dependent Schroedinger equation. Strong electromagnetic fields
of a laser pulse induce extremely nonlinear electron dynamics which no more allows
perturbative separation between macroscopic electromagnetic fields and microscopic electron
dynamics. As our solution to the problems, we have recently developed a multiscale theory forlight-matter interactions, describing electron dynamics in a solid using real-time time-dependent
density functional theory (TDDFT) and coupling it with macroscopic Maxwell equations in a
multiscale strategy. The theory provides a quite general and computationally feasible basis for anumber of problems, including ordinary macroscopic electromagnetism in a weak field limit
and being applicable to problems involving intense and ultrashort laser pulses.

2. Multiscale theory for coupled dynamics of electrons and light-wave
In our simulation, we combine two computations of different spatial scales. One is the
microscopic electron dynamics whose spatial scale is less than a nano-meter. The other is themacroscopic dynamics of light-wave whose spatial scale is about a micrometer. We start withthe explanation of the former.
2.1 Microscopic electron dynamics
In a microscopic spatial scale, we consider electron dynamics in a unit cell of a solid under aspatially-uniform, time-varying electric field. A core solver in our approach calculates
time-evolution of Bloch orbitals under the electric field:
2δE
1 ⎡ ! ! e ! ⎤ !
+
+
(
)
A
t
u nk − eφunk! + xc unk!
p
k
⎢
⎥
δn
∂t
2m ⎣
c
⎦
,
(1)
!
!
!
where the electric field is described using the vector potential A(t ) as E(t) = −(1 / c)dA (t ) / dt .

i"∂u nk!

=.
Before the irradiation of the electric field, the system is given by a ground state of static
Kohn-Sham equation. From the time-evolved Kohn-Sham orbitals, we may calculate electric111

Figure 1. Left panel shows the ground-state electron density of Si in [110] plane. The middle and right panels show
the change in the electron density from that in the ground state by the laser pulse. In the middle and right panels, thered color indicates the increase in the electron density while blue color indicates the decrease. Taken from [8].

current density flowing in the unit cell,

!
! !
*
!! !
−e
1 ' !* ! ! ! e !$ ! !
	
 
A
ψ
(
r,
t)
p
+
ψ
(
r,
t)
+
c.c.
j
(
r,
t)
=
(
,
)
,
I (t ) =
d
r
j
r
t
#
&
∑
)
,.
i
i
"
%
c
2m
Ω ∫Ω
(
+
i
(2)
!
Integrating the current over time, we may! obtain the polarization, P (t ) . !Thus our microscopic
solver provides us with the polarization P (t ) for a given electric field E(t) . We may regard
this microscopic calculation as a numerical constitutive relation. In fact, we may extract
information of dielectric function using this solver [10].
In Fig. 1, we show electron density in a typical time evolution calculation, an ultrashort laser
pulse irradiation on crystalline silicon. The laser pulse of 2.5 eV frequency is applied in [001]direction. The left panel shows the electron density in [110] plane in the ground state. The
middle panel shows a change of electron density from the ground state under irradiation of thelaser pulse. The red region indicates increase of electron density from the ground state, and theblue region indicates decrease. Electrons in the bond region are showing dipole oscillation. The
right panel shows electron density change after the laser pulse ends. The figure indicateselectrons in the bond region decrease by excitations.
2.2 Maxwell + TDDFT multiscale simulation
A propagation of light wave
is usually described by macroscopic! in! a! medium!
! ! Maxwell
we assume that B = H and there
equations for the four fields, D, E!, B, H!
! . In the! following,Eholds a local relation
betweenandasusual.
Namely, the macroscopic
D = E + 4πP! ! !
polarization
at point R , P R, t is determined by the electric field of the same point in the past,! !
E R, t ' , t ' < t . When the electric field is weak, the polarization and the electric field are relatedby the linear suceptibility χ αβ (t − t ') . When the polarization field is strong but still expressedin power series of electric field, we may use, for example, the third order susceptibility tensor,( 3)(t − t ' , t − t ' ' , t − t ' ' '). If the field is further strong, polarization may not be expressed as a
χ αβγδ
power series. We then need an approach in which we do not assume power series expansions.
For this problem, we have proposed a multiscale scheme, solving the coupled equation of

( )

( )

Figure 2. Coordinate system adopted
in multiscale simulation. At eachmacroscopic grid points shown left,
microscopic grid points shown rightare used.

112

Maxwell and time-dependent Kohn-Sham equations. The macroscopic equation to be solved isan ordinary wave equation and is given by

4π e
1 ∂ 2 AZ (t ) ∂ 2 AZ (t )−=−J Z (t )
2
2
2
c
c
∂t
∂Z
,

(3)

where we assume the propagation of the light wave is in Z-direction. We solve this equation in
macroscopic grid points, which is shown in the left side of Fig. 2. At each macroscopic grid
point, we prepare a microscopic grid points, shown in the right side of Fig. 2. The microscopic
grid points are used to solve the time-dependent Kohn-Sham equation (1).
As an example, we show a calculation of propagation of a laser pulse irradiating on a Si
surface [10]. In Fig. 3, we show snapshots of the time evolution. In solving Eqs. (2) and (1), themacroscopic coordinate Z is discretized into 256 grid points with the grid spacing of 250 au forthe medium region, Z > 0 . At each grid point, microscopic time-dependent Kohn-Shamequation (1) is solved.
The initial laser pulse at t = 0 has a peak intensity of 1×1011 W/cm 2 , the pulse length is
18 fs, and the average frequency is 1.55 eV. This is shown in the upper panel of the figure. The
middle panel shows the field when the center of the pulse has just reached the surface. In thebottle panel, one can see a transmitted and the reflected waves. In the right panels, electronic
excitation energy per atom is shown. The excitation is seen in the spatial region wheretransmitted wave exists. Although the laser frequency is far below the direct band-gap energy,
the excitation is seen after the transmitted pulse went away in the right-bottom panel. This iscaused by multiphoton excitations.

3. Physics applications
We have been applying the method to various problems. Among applications, laser damage
processes which are intimately related to laser machining are one of important areas that thepresent method will be useful. If a laser pulse of long pulse duration, picoseconds and more, isFigure 3. Snapshots of the vector potential divided by light speed, A / c < 0 (left panel), and of electronic
excitation energy per atom (right panels) at different times are shown as a function of macroscopic position. The
vacuum is at Z < 0 and the Si crystal is at Z > 0 . Top panels show initial starting field with a pulse on left
moving toward the Si surface. Middle panels show the field at a time when the middle of the pulse reaches thesurface. Lower panels show the field when reflected and transmitted pulses are well separated. The maximum
intensity of the incident laser pulse is set at 1×1011 W/cm 2 . Taken from [10].

113

used, avalanche mechanism is considered to dominate for electron excitations. In recent
researches, it has been realized that nonthermal, much cleaner processing is possible using
femtosecond laser pulses. In this case, the initial excitation process is dominated by one-electron
process such as multiphoton and tunneling excitations. Since the present multiscale simulation
may describe energy transfer from laser pulses to electrons in solids, we expect the present
simulation will be useful to understand basic mechanism of nonthermal laser processing.
We have made calculations of energy transfer from a laser pulse to a medium solving thecoupled Maxwell + TDDFT simulation. As the material to be investigated, we chose α-quartz
which is of practical importance. A few-cycle, intense laser pulse of 20 fs duration is irradiatednormally to the α-quartz. In Fig. 4, we show energy deposited to the α-quartz as a function of
the distance from the surface. The energy deposition to the medium is shown in a unit ofeV/atom. Calculations are achieved for various laser intensities around 1014W/cm2.
Experimentally, it has been known that ablation process starts to occur at around the intensity of
2x1014 W/cm2.
As shown in Fig. 4, the energy deposited to electrons in the medium increases as theintensity of the laser pulse increases. However, the amount of the energy deposition saturates ata certain value. Electrons inside the surface cannot be excited much even if we increase the laser
intensity. This is because the laser pulse is strongly reflected at the surface when the number of
excited electrons at the surface exceeds a critical density. As a measure to know what kind ofprocess will take place after the energy deposition to electrons, two horizontal lines, ablationand melting, are drawn. The line 'ablation' is drawn at the energy corresponding to the averagecohesive energy of α-quartz. It can be seen that the deposited energy exceeds the ablationthreshold at the surface when the intensity of the laser pulse exceeds 2.5x1014W/cm2. We
consider that this roughly coincides with measured threshold. At stronger intensities, the energy
deposition exceeds the ablation line to the depth of about 100-150 nm from the surface. Thisvalue is again consistent with the observed ablation depth. We thus consider that the present
approach succeeds to describe basic aspects of the initial stage of laser damage processes.

Figure 4. Energy deposited from a laser pulse of various intensities to α-quartz is shown as a function of distancefrom the surface. Two horizontal lines, ablation and melting, are shown to indicate damage thresholds.

114

4. Summary and future prospects
We consider the present approach solving Maxwell and time-dependent Kohn-Shamequations simultaneously is a quite general and comprehensive framework for light-matterinteractions. For weak electromagnetic fields, it may be regarded as a solver of Maxwell
equation with the accurate dielectric function given by microscopic TDDFT. As the intensity of
the light pulse increases, various nonlinear effects are automatically included such as second
and third order nonlinearities. It can even describe interactions of very strong laser pulses withsolids when electrons are strongly excited to form a plasma. Thus the present method may be
used for analyses of laser machining. The simulation requires, however, quite large computerresources. For the present scheme to be really useful, use of newest supercomputers underintimate collaborations with computer scientists is quite important.

Publications (Refereed journals and books)
1) M. Schultze, K. Ramasesha, C.D. Pemmaraju, S.A. Sato, D. Whitmore, A. Gandman, J.S.
Prell, L.J. Borja, D. Prendergast, K. Yabana, D.M. Neumark, S.R. Leone, Attosecond
band-gap dynamics in silicon, Science 346, 1348-1352 (2014).
2) S.A. Sato, Y. Shinohara, T. Otobe, K. Yabana, Dielectric response of laser-excited silicon at
finite electron temperature, Phys. Rev. B90, 174303 (8 pages) (2014).
3) G. Wachter, C. Lemell, J. Burgdoerfer, S.A. Sato, X.-M. Tong, K. Yabana, Ab Initio
Simulation of Electrical Currents Induced by Ultrafast Laser Excitation of DielectricMaterials, Phys. Rev. Lett. 113, 087401 (5 pages) (2014)4) M. Noda, K. Ishimura, K.Nobusada, K. Yabana, T. Boku, Massively-parallel electron
dynamics calculations in real-time and real-space: Toward applications to nanostructures ofmore than ten-nanometers in size, J. Comput. Phys. 265, 145-155 (2014).
5) S.A. Sato, K. Yabana, Efficient basis expansion for describing linear and nonlinear electron
dynamics in crystalline solids, Phys. Rev. B 89, 224305 (11 pages) (2014).
6) K.-M. Lee, C.M. Kim, S.A. Sato, T. Otobe, Y. Shinohara, K. Yabana, T.M. Jeong,First-principles simulation of the optical response of bulk and thin-film α-quartz irradiatedwith an ultrashort intense laser pulse, J. Appl. Phys. 115, 053519 (8 pages) (2014).
7) S.A. Sato, K. Yabana, Y. Shinohara, T. Otobe, G.F. Bertsch, Numerical pump-probe
experiments of laser-excited silicon in nonequilibrium phase, Phys. Rev. B 89, 064304 (8pages) (2014).
8) K. Yabana, Y. Shinohara, T. Otobe, J.-I. Iwata, G.F. Bertsch, First-Principles Calculations
for Laser Induced Electron Dynamics in Solids - Time-Dependent Density-Functional
Theory for laser matter interactions, Advances in Multi-Photon Processes and Spectroscopy,Vol. 21, pp. 209-244, Eds. S.H. Lin, A.A. Villaeys, Y. Fujimura, World Scientific (2014).
9) Y. Shinohara, S.A. Sato, K. Yabana, J.-I. Iwata, T. Otobe, G.F. Bertsch, Nonadiabatic
generation of coherent phonons, J. Chem. Phys. 137, 22A527 (2012).
10) K. Yabana, T. Sugiyama, Y. Shinohara, T. Otobe, G.F. Bertsch, Time-dependent density
functional theory for strong electromagnetic fields in crystalline solids, Phys. Rev. B85,
045134 (2012).
11) K.-M. Lee, K. Yabana, G.F. Bertsch Magnetic circular dichroism in real-timetime-dependent density functional theory, J. Chem. Phys. 134, 144106 (9 pages) (2011).

115

Conference talks (invited)
1) First-principles description of strong electromagnetic fields in solids, K. Yabana, invited
talk at focus session: Computer Simulation of Interaction of Electromagnetic fields andNanostructures, APS Meeting 2014, Colorado Convention Center, Denver, USA, Mar. 3-7,
2014.
2) Maxwell + TDDFT multiscale simulation for strong electromagnetic fields in solids, K.
Yabana, Quantum Dynamics Research Meeting, Vanderbilt University, Nashville, USA,
Mar. 10-12, 2014.
3) Multiscale description for strong electromagnetic fields in solids, K. Yabana, Gordin
Research Conference on TDDFT, Univ. New England, Biddeford, ME, Aug. 11-16, 2013.
4) Light-matter interactions in time-dependent density functional theory, K. Yabana, Advancesin time-dependent methods for quantum many-body systems, ECT*, Trento, Italy, Oct.
14-18, 2013.
5) Ab-initio theory for intense laser pulses in solids, K. Yabana, Korean Physical Society 2012
Spring Meeting, April 25-27, 2012, Daejeon, Korea.
6) Real-time electron dynamics in solids under strong electromagnetic fields, K. Yabana,
ISSP-CMSI International Workshop/Symposium on Material Simulation	  in Petaflops era(MASP2012), June 27,2012, Tokyo, Japan.
7) Time-Dependent Density Functional Theory for Electron Dynamics, K. Yabana,
BERTSCHFEST, UW, Seattle, Sept. 7-9, 2012.
8) Ab-initio description for the interaction of intense laser pulses with solids, K. Yabana,
Frontiers in Intense Laser-Matter Interaction Theory (FILMITh), Sept. 19-21, 2012, Max
Planck Institute fur Quantenoptik, Garching, Germany.
9) Multi-scale first-principles approach for strong electromagnetic fields in solids, K. Yabana,Int. Symp. on Computics: Quantum Simulation and Design,	  Oct. 11-13, 2012, Osaka,
Japan.
10) Time-dependent density functional theory for ultrafast electron dynamics in solid, K.
Yabana, Computational approaches to nuclear many-body problems and related quantum
systems, Feb. 12-16, 2013, RIKEN, Wako, Japan.
11) Real-time TDDFT Calculation in Molecules and Solids, K. Yabana, ISTCP-VII(International Symposium on Theoretical Chemistry and Physics), Waseda Univ. Sept. 2-8,
2011.
12) Real-Time TDDFT for Molecules and Solids, K. Yabana, Dynamics and Correlations in
Exotic Nuclei, YITP Kyoto Univ., Sept. 23, 2011.
13) Time-dependent density functional theory for femtosecond electron dynamics in dielectrics,
K. Yabana, The 14th Asian Workshop on First-Principles Electronic Structure Calculations,
Univ. Tokyo, Oct.31-Nov. 2.
14) Time-Dependent Density Functional Theory for Intense Laser Pulse Propagation in Solids,
K. Yabana, 3rd Int. CQSE Workshop on Atomic, Molecular and Ultrafast Science andTechnology, National Taiwan Univ., Jan. 7-8, 2012.
15) Computational Approach for Dynamics of Many-Fermion Systems - from Nuclear Physics
to Optical Science-, K. Yabana, Kyoto Univ. GCOE Symposium “Links among
Hierarchies”, Feb. 13-15, 2012.

116

Hybrid-density-functional theory for magnetic materials
Yoshihiro Gohda
Department of Materials Science and Engineering,Tokyo Institute of Technology, Yokohama 226-8502
1. Introduction
First-principles calculations based on density functional theory play an indispensable rolein materials science and condensed matter physics. While standard generalized gradientapproximation is highly successful, a better approximation is desired for some of materials
including magnetic ones with localized states. One of such approaches is hybrid density
functional theory. However, a problem of hybrid density functional theory is theadjustability of the mixing parameter. In this work, we tried to examine a scheme toremove such adjustability. As a result, we identified that the mixing parameter can be
determined using the generalized Koopmans condition, which should be satisfied by exact
single-particle states. We also found that this parameter can be highly dependent individual
electronic state, so that the reduction of the computational cost remains a problem to be
overcome. In addition, we performed first-principles calculations for various magnetic
materials rather in a standard manner: strain effect on the magnetic anisotropy in Y-Fe-B
compounds and development of a method for magnetic-anisotropy decomposition with low
computational costs; the magnetic order and magnetic anisotropy of Fe ultrathin films on
the Cu(001) surface; and gigantic magnetic anisotropy in the ε phase of Fe2O3.
2. Results
We first examined the generalized Koopmans theorem to apply the hybrid density
functional scheme. We derived first-principles mixing parameters for theexchange-correlation functional in the generalized gradient approximation and the exact
Hartree-Fock exchange. By applying our scheme for type-II antiferromagnetic NiO with adistorted rocksalt structure, we successfully reproduced its electronic structure as acharge-transfer insulator. In contrast with standard generalized gradient approximation and
HSE hybrid functional, our functional with optimized mixing parameter provide theposition of unoccupied 3d states that is consistent with experiments [Fig. 1]. On the other
hand, the type-II antiferromagnetic FeO exhibits strongly state-dependent mixing
parameters, even though the parameter determined by the states at the conduction band
minimum reproduces FeO as a Mott-Hubbard insulator. We also found that the mixing
parameters for the above compounds are larger than transition metal impurities in nitride
semiconductors due to larger locality of electronic states. Even though their charged states
are metallic, numerical calculation can be performed because wrong zero-density of statesof Hartree-Fock is caused by singular slope of density of states at the Fermi energy causing
practically no influences. Indeed, the optimized mixing parameter for bcc Fe is almost zero,117

which is consistent with the fact that the generalized gradient approximation is satisfactory
for this material. A strategy to determine the state-dependent mixing parameter more
precisely is to use a double-hybrid scheme where the correlation of density functional
theory is mixed with the MP2 correlation. However, this will significantly increase thecomputational cost, so that this problem remains to be solved. In addition to itinerant
electrons that can be appropriately described by the generalized gradient approximation,
localized electrons should be treated appropriately from first principles. For thedevelopment of a unified scheme, the knowledge obtained from the present results is
expected to be helpful. In addition, it should be pointed out that the present scheme todetermine the mixing parameters is applicable to determine the Hubbard U in the DFT+U
method, in particular for 3d transition metals where optimal U value significantly changes
depending on the chemical environment.
(b)

NiO

Density of states [arb. units]

Density of states [arb. units]

(a)

0

−10

−5

0

5

Energy relative to εVBM [eV]

10

FeO

0

−10

−5

0

5

Energy relative to εVBM [eV]10

Fig. 1: (a) Density of states for distorted-rocksalt NiO and (b) distorted-rocksalt FeO withthe type-II antiferromagnetic ordering. Solid lines are obtained with optimized mixing
parameter in hybrid density functional theory, whereas the dashed lines are results obtainedusing the generalized gradient approximation.
We also performed standard first-principles calculations for various magnetic materials,
where we focused mainly on the magnetocrystalline anisotropy. First, we calculated
Y-Fe-B compounds to examine the intersite couplings due to d electrons and the magnetic
anisotropy of Fe sublattice, because utilizing itinerant 3d electrons instead of localized 4f
electrons in exhibiting the magnetic anisotropy is an important new direction bothscientifically and technologically. In particular, the development of rare-earth-free magnets
will be made possible driven by fundamental understanding of the itinerant-electron
anisotropy. Since itinerant magnetic states are responsible to direct interactions amongmagnetic sites, d states are expected to be sensitive to lattice strain. In this study, we
examined strain effects on magnetic properties theoretically studied by first-principles
calculations for Y2Fe14B and YFe3, where Y is a prototypical f0 rare-earth element.
First-principles calculations on the basis of density functional theory within the generalized
gradient approximations are performed using the OpenMX code. The lattice constants a

118

and c of Y2Fe14B are changed from the equilibrium values independently, where we foundthe uniform compression enhances the perpendicular magnetic anisotropy. To clarify theorigin of this enhancement, we developed a method to decompose the magnetic-anisotropy
energy into contribution from each atomic site as well as from couplings among specificatomic orbitals, where the sum rule is satisfied by including off-site contributions in thesecond-order perturbation indirectly. As a result, we identified specific coupling among 3d
orbitals at the Fe j2 site to play an important role in enhancing the anisotropy, where boththe effect of the local density of states and the matrix elements among atomic orbitals are
essential [Fig. 2]. Our method enables us to study the anisotropy at microstructureinterfaces. In addition, our scheme can derive lattice spin models including the single ion
anisotropy, which can be used in micromagnetics and Monte Carlo simulations.

(a)

B

0.4
0.2
0
−0.2
−0.4

Y

LDOS (states/eV)

Fe

(b)

up

dx2-y2

down

†＊
dxy

0.4
0.2
0
−0.2
−0.4

＊
−4

−2

†

0

Energy (eV)2Fig. 2: (a) Crystal structure and spin-density distribution of Y2Fe14B. (b) Local density ofstates (LDOS) projected onto two 3d components of the Fe j2 site with (solid lines) andwithout (shades) compression. Pairs of daggers and asterisks indicate anisotropy coupling,respectively.
We also studied magnetic ultrathin films attracting attentions in fundamental surface
science. In contrast with the ground state of Fe bulk, the bcc structure with theferromagnetic order, distorted fcc Fe films have been grown onto Cu(001). In this system,
peculiar structural and magnetic properties of Fe have been reported. But its ground stateof magnetic structure is controversial. We performed first principle calculations in order tounderstand the electronic and magnetic structures of this system, where we have found thatthe ground state is not ferromagnetic but antiferromagnetic in the 4-monolayer (ML)system from the total energy analysis of allowable spin configurations. In the 5 to 7-ML
systems, an antiferromagnetic order is more stable than the ferromagnetic order, which isin good agreement with experimental results.
Furthermore, the origin of gigantic magnetic anisotropy in ε-type Fe2O3 was studied. We

119have found that the oxygen vacancies can play a significant role to exhibit magnetic
moments and large magnetic anisotropy.
3. Summary
We examined the dependence of the total energy of electronic systems on the number ofelectrons through the generalized Koopmans theorem. Deriving an exact condition to besatisfied for single-electron energy levels, we determined the mixing parameter appearing
in hybrid density functional theory. We applied this scheme for various magnetic materials
including distorted-rocksalt NiO as a charge transfer insulator and distorted-rocksalt FeO
as a Mott-Hubbard insulator.
We also performed first-principles calculations to investigate the magnetic anisotropy.
Strain effects for Y2Fe14B are clarified, where we developed a convenient and reliable
scheme to calculate single-ion anisotropy constants. This scheme is a promising tool to
combine first-principles calculations and spin lattice models for micromagnetics
simulations based on Landau-Lifshitz-Gilbert equations and Monte Carlo simulations.
4. Participants
PI: Yoshihiro Gohda
Collaborators: Zahra Torbatian, Yasutomi Tatetsu, Daisuke Hirai, Shinji Tsuneyuki, andTaisuke Ozaki
5. Publications
Original Papers (total 6 papers):
1) Z. Torbatian, T. Ozaki, S. Tsuneyuki, and Y. Gohda, “Strain effects on the magnetic
anisotropy of Y2Fe14B examined by first-principles calculations”, Appl. Phys. Lett. 105,
242403 (2014).
2) T. Nakamura, A. Yasui, Y. Kotani, T. Fukagawa, T. Nishiuchi, H. Iwai, T. Akiya, T.
Ohkubo, Y. Gohda, K. Hono, and S. Hirosawa, “Direct observation of ferromagnetism in
grain boundary phase of Nd-Fe-B sintered magnet using soft x-ray magnetic circulardichroism”, Appl. Phys. Lett. 105, 202404 (2014).
3) M. Kawamura, Y. Gohda, and S. Tsuneyuki, “Improved tetrahedron method for the
Brillouin-zone integration applicable to response functions”, Phys. Rev. B 89, 094515(2014).
Invited Talks (total 10 talks: 4 in English; 6 in Japanese):
1) Y. Gohda, “First-principles theory on magnetism at interfaces”, Collaborative Conference
on Materials Research 2014 (CCMR2014), (Incheon, Korea, Jun. 24, 2014).
2) Y. Gohda, “First-principles study of microstructure interfaces of Nd-Fe-B magnets”,
ESICMM-G8 Symposium on Next Generation Permanent Magnets, (Tsukuba, Japan, Jun.
2015, confirmed).
3) Y. Gohda, “Microstructure of Fe-based magnetic materials”, The 3rd OpenMX/QMAS
workshop, (Kashiwa, Japan, May 2015, confirmed).

120

A02: Dynamics of electron, spin and heat transport through single atomic
and molecular junctions
Manabu Kiguchi
Tokyo Institute of Technology
1. Introduction
A single molecular junction, where a single molecule bridges between metal electrodes,
is a low-dimensional material having two metal-molecule interfaces (see Fig. 1). Due toits geometrical and electronic characters, single molecular junctions can show novel
properties that are not observed in isolated molecular or bulk systems. The single
molecular junction has also attracted attention due to its potential application in
ultrasmall electronic devices. Since it is hard to see a single molecule bridging between
metal electrodes, we discuss the single
molecular junction by comparing theexperimentally obtained signal from thesingle molecular junction and calculation
results using some models. Here, we study
the dynamic properties of the carriers
Figure 1. Schematic representation of an
through single atomic and molecular atomic scale junction where a benzenedithioljunction by experiments and theoretical molecule is sandwiched between two Au
electrodes.
calculation.
2. Results[1] Single Molecular Resistive Switch
We investigated the possibility to exert dynamic control on molecular anchoring sites
and proposed a single-molecule resistive switch based on “switch of anchor in single
molecule” without altering the binding modes or chemical structures of themetal-molecule contact. For this purpose, we investigated a quaterthiophene-based
molecular wire (QT), bearing two thiophene rings at each end of the molecular
backbone as molecular anchors (T1 and T2) (Figure 2a). These two termini weresymmetrically separated by the“insulating” molecular layer, to prevent theintermolecular interactions among neighboring QT molecules and to promote themeasurement of single QT conductance. Because of this unique QT arrangement, thejunction could be switched between T1-T1, T1-T2, and T2-T2 configurations. This gave121

rise to three different conductance values: 0.05 G 0 (high-conductance state), 0.005 G 0(medium-conductance state), and 0.0005 G 0 (low-conductance state). By estimating the
distance between the contact points as well as tip-Au distance, we calculated that theresulting conductance was in line with the standard length dependence of off-resonant
tunneling, i.e. exponential decay. The most stable molecular structure of each contact
configuration was determined employing first-principles calculations (Figure 2b). The
theoretical studies demonstrated that the resistive switching was caused by varying theeffective length of the conducting π-conjugated backbone via a change in the molecularanchoring points T1 ↔ T2 (Figure 2c). The dynamic control of the three conductancestates was experimentally shown by mechanically controllable modulation. Supported
by DFT calculations we demonstrated that molecular materials bearing multiple
anchoring groups are a viable alternative for the development molecular devices withadvanced electronic functionality eg. resistive switching.

Figure 2. (a) Chemical structure of the quaterthiophene-based molecular wire. (b) One of DFT
models for electronic transport calculation (T2-T2 connection). (c) Schematic illustration ofswitch in the effective length of the conducting π-conjugate backbone via a change in theanchors.

[2] Electron transport through metal-ion wires
In recent years, electron transport though metal-atom wires has attracted the interest of
the scientific community. Their minute size and quantized electric properties makes
them especially interesting for the development of the next generation ultra-dense
electronic devices. Despite their appealing properties, electrical performance of
metal-ion wires has never been studied mainly hindered by the synthetic difficulties.
The preparation of metal-ion arrays with a fixed cross section and length between
nanogap electrodes is nontrivial. More recently, a number of synthetic protocols havebeen developed for the preparation of multinuclear complexes with ordered metal-ion

122arrays. Among them, [3 × n] gold-ion clusters, enclosed in self-assembled cages (Figure3a), are of particular interest because the stacking number n is uniquely determined byheight of the molecular cages. The molecular cages, that keep the metal ions highlyordered in a [3 × n] manner, are excellent frameworks for accommodating π-stacked
molecules and evaluating their electron-transport properties (Figure 3b).
Single-molecule conductance studies performed on the [3 × n] stacks of gold-ion
clusters n (n = 1, 2, or 3) showed a high conductance profile, in the range of 3~9 ×10-3
G 0 regardless of the stacking number. DFT studies further revealed that the metal-ion
arrays are highly conductive with a negligibly small distance dependence and anelectron transport efficiency comparable to that of metal-atom wires. The combinationof atomic scale transport experiments and DFT studies shed light on the potential
benefits of metal-ion molecular wires and on the fundamental aspects of
one-dimensional physics.

Figure 3. (a) [3 × n] gold-ion clusters, enclosed in self-assembled cages. (b) Schematic
illustration of [3 × 3] gold-ion clusters sandwiched by gold electrodes.

[3] Temperature dependence of the thermopower and its variation of the Au atomic
contact
Thermoelectric devices are of great interest because of their ability to efficiently harvest
waste heat and transform it into an electrical signal. While thermopower measurements
have been performed for various metal atomic contacts and molecular junctions, thetemperature dependence of the thermopower effect has not been satisfactorily studied.
Here, we simultaneously measured the thermopower and conductance of Au atomic
contacts during the self-breaking process in air at room temperature. These studies
showed a random fluctuation of the junction thermopower. This fluctuation was foundto be especially large and both positive and negative in sign for the junction in the lower
conductance regime. While the average thermopower was negligibly small, the standard
deviation of thermoelectric voltage linearly increased with the temperature difference123across the Au contacts. The standard deviation of the thermopower was inversely
related to the junction conductance with a dramatic increase below 1 G 0 . The increasein the standard deviation of thermopower was explained by the coherent backscatteringof the electrons near the contact. Above 320 K, the standard deviation of thermopower
was found to decrease, indicating the decrease in the density of defects for the Au
atomic contacts. The Au atomic contacts are low-dimensional nanomaterials, hence theatomic motion could be significantly enhanced above 320 K, leading to the decrease in
the density of defects near the contacts. The present study indicates that the standard
deviation of thermopower provides information about the thermopower of the Au
atomic contact and the atomic structure of the Au atomic contacts (e.g., crystallinity anddistribution of defects).
These works are done with the collaboration with Prof. Fujii and students in Tokyo
Institute of Technology, Prof. Fujita and Prof. Watanabe (Tokyo University), Dr.
Nakamura (AIST), and Prof. Tada (Tokyo Institute of Technology), and Dr. Sugiyasu(NIMS).
3. Selected publications (Total 35 publications)[1] M. Kiguchi, T. Ohto, S. Fujii, K. Sugiyasu, S. Nakajima, M. Takeuchi, and H.
Nakamura “Single molecular resistive switch obtained via sliding multiple
anchoring points and varying effective wire length” J. Am. Chem. Soc., 136,
7327-7332 (2014). Selected as the cover picture and picked up by THE NIKKANKOGYO SHIMBUN.
[2] M. Kiguchi, J. Inatomi, Y. Takahashi, R. Tanaka, T. Osuga, T. Murase, M. Fujita, T.
Tada, S. Watanabe “Highly Conductive [3xn] Gold Ionic Clusters Enclosed within
Self-Assembled Cages” Angew. Chem. Int. Ed., 52, 6202-6205, (2013).
[3] R. Matsushita, S. Kaneko, S. Fujii, H. Nakamura, M. Kiguchi “Temperature
Dependence of the Thermopower and its Variation of the Au Atomic Contact”
Nanotechnology, 26, 045709, (2015).
4. Selected invited talks (Total 12 talks)[1] M. Kiguchi, “Experimental and theoretical study of electron transport throughsingle π-stacked systems and ionic wires” 2nd International Symposium on
Computics: Quantum Simulation and Design, Tokyo, 2014/12/1.

124

Electron-Phonon Coupling Dynamics and High-Sensitive Detection of
Nano-Scale Phonon Wavepackets in Carbon-Based Materials
Jun Takeda
Department of Physics, Graduate School of Engineering, Yokohama National University
1. Introduction
To unveil the non-equilibrium dynamics far from equilibrium states in new functional materials,
ultrafast laser spectroscopy is one of most powerful tools. In this research, we have mainly utilized
three types of new spectroscopic methods we have recently developed: i.e., frequency-resolved
coherent phonon spectroscopy, THz time-domain spectroscopy and single-shot imaging spectroscopy.
Using these methods, we have investigated dynamics of nano-scale optical phonon wavepackets ingraphene, resonant enhancement of first- and second-order coherent phonons due to van-Hove
singularities in metallic single-walled carbon nanotubes (M-SWCNTs) and photoinduced
phase-changes of chalcogenide glasses. Some other related photoinduced phenomena were also
revealed.

2. Results
2.1 Nano-scale optical phonon wavepacket in graphene
Coherent nano-scale optical phonon wavepacket was excited using ultrashort laser pulses via
impulsive inter-Dirac-cone scattering at graphene edges and defects. In contrast to the normal coherent
phonons generated with first-order Raman process such as G-mode, the D-mode generated with thesecond-order Raman process showed the phonon chirp, and the amplitude and frequency strongly
changed depending on the probe wavelength. The results can be discussed on the basis of doubly
resonant Raman scattering process; the D-mode couples strongly with the electronic states near the
Fermi level, and thereby spatiotemporally modulates the electronic states with nanometer-spatial andfemtosecond-temporal resolutions. As a result, the generated D-mode coherent phonons can propagate
as nanoscale optical-phonon wavepackets. (See, Fig. 1)

2-2. Resonant properties of metallic single-walled carbon nanotubes
High-frequency coherent phonons resonantly excited in M-SWCNTs were investigated via
spectrally resolved pump-probe spectroscopy. In addition to first-order coherent phonons such as
RBM, M and G modes, we clearly observed second-order high-frequency coherent phonons of 2D and
2G modes, which can be regarded as squeezed phonons. We found that the amplitudes of the RBM, G
and 2D modes were resonantly enhanced at specific wavelengths: the maximum resides at a125

wavelength whose energy is smaller than that of the van-Hove singularities in M-SWCNTs by anamount corresponding to the phonon energy. Further, the 2D mode has stronger enhancement than theother first-order Raman modes. These results indicate that the enhancement originates from a
Stokes-stimulated Raman-scattering process at van-Hove singularities, and that efficient resonanceenhancement occurs for the 2D mode, possibly through double resonance due to the trigonal warping
effect and strong electron-phonon coupling due to the Kohn anomaly. (See, Fig. 2)

2-3. Ultrafast amorphization in chalcogenide glasses

Using broadband single-shot imaging spectroscopy, we observed an irreversible ultrafast
crystalline-to-amorphous phase transition in chalcogenide alloy thin films. The absorbancechange that accompanied the ultrafast amorphization was measured via single-shot detection
even for laser fluences above the critical value, where a permanent amorphized mark wasformed. The observed rise time to reach the amorphization was found to be 130~200 fs,
which was in good agreement with the half period of the A1 phonon frequency in theoctahedral GeTe6 structure. This result strongly suggests that the ultrafast amorphization canbe attributed to the rearrangement of Ge atoms from an octahedral structure to a tetrahedral
structure. Based on the dependence of the absorbance change on the laser fluence, we could
also discuss the stability of the photoinduced amorphous phase. (See, Fig. 3)

126

3. Members of This Research Project
Jun Takeda (Project Reader; Professor, Yokohama National University)
Maki Suemitsu (Member; Professor, Tohoku University)
Ikufumi Katayama (Member; Associate Professor, Yokohama National University)
Masahiro Kitajima (Member; Senior Researcher, LxRay Co. Ltd.)
Yauo Minami (Member; Assistant Professor, Yokohama National University)

4. Research Activities
Original Papers (total: 11 papers)
1) K. Yoshioka, Y. Minami, K. Shudo, T. D. Dao, T. Nagao, M. Kitajima, J. Takeda, and I.
Katayama, "Terahertz-Field-Induced Nonlinear Electron Delocalization in Au Nanostructures",
Nano Lett. 15, pp. 1036-1040 (2015).
2) K. Sato, K. Tahara, Y. Minami, I. Katayama, M. Kitajima, H. Kawai, K. Yanagi, and J. Takeda,"Resonant Enhancement of First- and Second-Order Coherent Phonons in Metallic Single-Walled
Carbon Nanotubes", Phys. Rev. B 90, 235435: pp.1-5 (2014).
3) Y. Minami, J. Takeda, T. D. Dao, T. Nagao, M. Kitajima, and I. Katayama, "Nonlinear Electron
Dynamics of Gold Ultrathin Films Induced by Intense Terahertz Waves", Appl. Phys. Lett. 105,
241107: pp.1-4 (2014).
4) J. Takeda, W. Oba, Y. Minami, T. Saiki, and I. Katayama, "Ultrafast Crystalline-to-Amorphous
Phase Transition in Ge2Sb2Te5 Chalcogenide Alloy Thin Film Using Single-Shot Imaging
Spectroscopy", Appl. Phys. Lett. 104, 261903: pp. 1-4 (2014).
5) Y. Minami, M. Yamaki, I. Katayama, and J. Takeda, "Broadband Pump-Probe Imaging
Spectroscopy Applicable to Ultrafast Single-Shot Events", Appl. Phys. Exp. 7, 022402: pp. 1-3(2014).

127

6) J. Takeda, I. Katayama, K. Shudo, and M. Kitajima, (Invited paper) "Coherent Phonon and
Surface-Enhanced Raman Scattering Dynamics in Solids", J. Lumin. 152, pp. 23-27 (2014).
7) T. Kawano, I. Katayama, J. Ohara, M. Ashida, and J. Takeda, "Intermolecular THz Vibrations
Relevant to Optically and Thermally Induced Magnetic Phase Transitions in the Strongly
Correlated Organic Radical TTTA", J. Phys. Soc. Jpn. 83, 014713: pp. 1-6 (2014).
8) I. Katayama, K. Sato, S. Koga, J. Takeda, S. Hishita, H. Fukidome, M. Suemitsu, and M. Kitajima,"Coherent Nanoscale Optical-Phonon Wavepacket in Graphene Layers", Phys. Rev. B 88, 245406:
pp. 1-5 (2013).
9) K. Shudo, T. Satake, T. Shimatsu, M. Uchiyama, and J. Takeda, "Electronic Excited States of aStrongly Correlated Organic Radical 1,3,5-trithia-2,4,6-triazapentalenyl (TTTA) Adsorbed on aSi(001) Surface", Phys. Chem. Chem. Phys. 15, pp. 19213-19220 (2013).
10) Y. Minami, Y. Hayashi, J. Takeda, and I. Katayama, "Single-Shot Measurement of a Terahertz
Electric-Field Waveform Using a Reflective Echelon Mirror", Appl. Phys. Lett. 103, 051103: pp.
1-4 (2013).
11) I. Katayama, S. Koga, J. Takeda, S. Hishita, D. Fujita, and M. Kitajima, "Electron-Phonon
Coupling and Defect Scatterings in Ar+-ion Implanted Graphite", J. Cer. Soc. Jpn. 121, pp.
291-294 (2013).
Selected Proceedings & Reviews (total: 13 papers)
1) J. Takeda, Y. Minami, and I. Katayama, (Review article in Japanese) "Time-Frequency
Two-Dimensional Imaging Spectroscopy Using a Reflective Echelon Mirror", Rev. Laser Eng. 43,(2015) to be published.
2) K. Maekawa, K. Sato, Y. Minami, I. Katayama, J. Takeda, K. Yanagi, and M. Kitajima,"Electrochemical Control of Coherent Phonon Generations in Single-walled Metallic Carbon
Nanotubes", Ultrafast Phenomena XIX: Proceedings of the 19th International Conference on
Ultrafast Phenomena, (Springer Proceedings in Physics), pp. 356-359 (2015).
3) W. Oba, I. Katayama, Y. Minami, T. Saiki, and J. Takeda, "Single-shot Real-time Observation of
Ultrafast Amorphization in Ge2Sb2Te5 Thin Film", Ultrafast Phenomena XIX: Proceedings of the
19th International Conference on Ultrafast Phenomena, (Springer Proceedings in Physics), pp.
352-355 (2015).
4) Y. Minami, T. D. Dao, T. Nagao, J. Takeda, M. Kitajima, and I. Katayama, "Nonlinear Carrier
Responses in Gold Thin Films Induced by Intense Terahertz Waves", Ultrafast Phenomena XIX:
Proceedings of the 19th International Conference on Ultrafast Phenomena, (Springer Proceedingsin Physics), pp. 626-629 (2015).
5) K. Araki, Y. Minami, T. D. Dao, T. Nagao, J. Takeda, M. Kitajima, and I. Katayama, "Nonlinear
Carrier Dynamics in Semi-Metal Bismuth Induced by Intense Terahertz Field", Ultrafast
Phenomena XIX: Proceedings of the 19th International Conference on Ultrafast Phenomena,(Springer Proceedings in Physics), pp. 633-636 (2015).
6) I. Katayama, Y. Minami, and J. Takeda, (Review article in Japanese) "Terahertz Time-Domain
Spectroscopy of Thin Films and Surfaces", J. Surf. Sci. Jpn. 35, pp. 680-685 (2014).
Selected Invited Talks (total: 7 talks)
1) I. Katayama, W. Oba, Y. Minami, T. Saiki, and J. Takeda (Invited Talk), "Ultrafast Dynamics ofPhase-Change Materials Observed Using Echelon-Based Single-Shot Setups", The 26th
Symposium on Phase Change Oriented Science (PCOS2014), (December 4-5, Hamamatsu, Japan).
2) I. Katayama, K. Shudo, J. Takeda, and M. Kitajima (Invited Talk), "Nanoscale and Femtosecond
Phonon Dynamics Observed with Surface Enhanced Raman Scattering", Ultrafast Surface
Dynamics 2013, (May 28-31, 2013, Colorado, USA).
3) J. Takeda, I. Katayama, K. Shudo, and M. Kitajima (Invited Talk), "Coherent Phonon and
Surface-Enhanced Raman Scattering Dynamics in Solids", 18th International Conference on
Dynamical Processes in Excited States of Solids, II-1 (August 4-9, 2013, Fuzhou, China).

128

“First-principle molecular dynamics analyses on nonlinear optical properties
change of Si nano-dot”
Yasuteru Shigeta1,3,4, Kenji Shiraishi 2, Masayoshi Nakano3
1

Graduate School of Pure and Applied Sciences, University of Tsukuba
2Graduate School of Engineering, Nagoya University
3
Graduate School of Engineering Sciences, Osaka University
4
CREST, JST

Reviewed Paper (28 including 2 review articles)
1. H. Harada, Y. Takano, T. Baba, Y. Shigeta, “Simple, Yet Powerful Methodologies forConformational Sampling of Proteins”, Physical Chemistry Chemical Physics (invited featurearticle) 17, 6155-6173 (2015).
2. H. Ando, Y. Shigeta, T. Baba, C. Watanabe, Y. Okiyama, Y. Mochizuki, M. Nakano, “Hydration
Effects on Enzyme-Substrate Complex of Nylon Oligomer Hydrolase: Inter-Fragment Interaction
Energy Study by the Fragment Molecular Orbital Method”, Molecular Physics 113, 319-326(2015).
3. R. Harada, Y. Takano, Y. Shigeta, "Enhanced Conformational Sampling Method for Proteins
Based on the TaBoo SeArch (TBSA) Algorithm: Application to the Folding of a Mini-protein,
Chignolin", Journal of Computational Chemistry 36, 763-772 (2015).
4. K. Okuno, Y. Shigeta, R. Kishi, M. Nakano, “Theoretical design of solvatochromism switching by
photochromic reactions using donor-acceptor disubstituted diarylethene derivatives with oxidized
thiophene rings”, Physical Chemistry Chemical Physics 17, 6484-6494 (2015).
5. T. Baba, M. Boero, K. Kamiya, H. Ando, S. Negoro, M. Nakano, Y. Shigeta, “Unraveling thedegradation of artificial amide bonds in nylon oligomer hydrolase: from induced-fit to acylation
processes”, Physical Chemistry Chemical Physics, 17, 4492-4504(2015).
6. T. Matsui, Y. Kitagawa, M. Okumura, Y. Shigeta, “Accurate Standard Hydrogen Electrode
Potential and Applications to the Redox Potentials of Vitamin C and NAD/NADH”, Journal of
Physical Chemistry A, 119, 369-376 (2015).
7. Y. Shigeta, H. Harada, M. Kayanuma, M. Shoji, “Quantal cumulant dynamics for real-time
simulations of quantum many-body systems”, International Journal of Quantum Chemistry(invited review), 115, 300-308 (2015). DOI: 10.1002/qua.24820
8. R. Harada, T. Nakamura, Y. Takano, Y. Shigeta, “Protein folding pathways extracted by Outlier
FLOODing method (OFLOOD)”, Journal of Computational Chemistry, 36, 97-102 (2015).
9. R. Nakamura, Y. Shigeta, K. Okuno, M. Fukushima, M. Hasegawa, S. Suzuki, M. Kozaki, K.
Okada, M. Nakano, “Substitution Effects on Optical Properties of Iminonitroxide- substituted
Iminonitroxide Diradical”, Molecular Physics 113, 267-273 (2015).
10. T. Baba, T. Matsui, K. Kamiya, M. Nakano, Y. Shigeta, "A density functional study on pKa of
small polyprotic molecules”, International Journal of Quantum Chemistry, 114, 1128–1134(2014).
11. T. Baba, R. Harada, M. Nakano, Y. Shigeta, "On the induced-fit mechanism of substrate-enzyme
binding structures of Nylon-oligomerhydrolase”, Journal of Computational Chemistry 35,
1240-47 (2014).
12. K. Kamiya, T. Baba, M. Boero, T. Matsui, S. Negoro, Y. Shigeta, “A Nylon-oligomer Hydrolase
Promoting Cleavage Reactions in Unnatural Amide Compounds”, Journal of Physical Chemistry
Letters 5, 1210-1216 (2014).

12913. R. Harada, Y. Takano, Y. Shigeta, “Fluctuation Flooding Method (FFM) for accelerating
conformational transitions of proteins”, Journal of Chemical Physics 140, 125103 (2014).
14. Y. Kitagawa, T. Matsui, Y. Nakanishi, Y. Shigeta, T. Kawakami, M. Okumura, K. Yamaguchi,“Theoretical studies of electronic structures, magnetic properties and electron conductivities of
one-dimensional Nin (n = 3, 5, 7) complexes”, Dalton Transaction, 42, 16200-16208 (2013).
15. S. Muhammad, H. Xu, Z. Su, K. Fukuda, R. Kishi, Y. Shigeta, M. Nakano, “A new type oforganic-inorganic hybrid NLO-phore with large off-diagonal first hyperpolarizability tensors: A
two-dimensional approach”, Dalton Transaction, 42, 15053-15062 (2013).
16. K. Koyanagi, Y. Kita, Y. Shigeta, M. Tachikawa, “Binding of a positron to nucleic-acid basemolecules and their pairs”, ChemPhysChem. 14, 3458-3462 (2013).
17. T. Inui, Y. Shigeta, K. Okuno, T. Baba, R. Kishi, M. Nakano, “Finite-Field Method with Unbiased
Polarizable Continuum Model for Evaluation of the Second Hyperpolarizability of an Open-Shell
Singlet Molecule in Solvents”, Journal of Computational Chemistry, 34, 2345-2352 (2013).
18. K. Okuno, Y. Shigeta, R. Kishi, M. Nakano, “Non-empirical tuning of CAM-B3LYP functional intime-dependent density functional theory for excitation energies of diarylethene derivatives”,
Chemical Physics Letters, 585, 201-206 (2013).
19. K. Okuno, Y. Shigeta, R. Kishi, M. Nakano, “Photochromic Switching of Diradical Character:
Design of Efficient Nonlinear Optical Switches”, Journal of Physical Chemistry Letters, 4,2418-2422 (2013).
20. T. Matsui, Y. Kitagawa, Y. Shigeta, M. Okumura, ”A Density Functional Theory Based Protocol
to Compute the Redox Potential of Transition Metal Complex with the Correction of
Pseudo-Counterion: General Theory and Applications”, Journal of Chemical Theory andComputation, 9, 2974–2980 (2013).
21. K. Koizumi, M. Boero, Y. Shigeta, A. Oshiyama, “Atom-Scale Reaction Pathways andFree-Energy Landscapes in Oxygen Plasma Etching of Graphene”, Journal of Physical Chemistry
Letters, 4, 1592–1596 (2013).
22. Y. Shigeta, T. Inui, T. Baba, K. Okuno, H. Kuwabara, R. Kishi, M. Nakano, “Qantal Cumulant
Mechanics and Dynamics for Multi-Dimensional Quantum Many-Body Clusters”, International
Journal of Quantum Chemistry, 113, 348-355 (2013).
23. T. Matsui, Y. Kitagawa, M. Okumura, Y. Shigeta, S. Sakaki, “Consistent Scheme for ComputingStandard Hydrogen Electrode and Redox Potentials”, Journal of Computational Chemistry, 34,
21-26 (2013).
24. M. Nakano, R. Kishi, H. Fukui, T. Minami, K. Yoneda, S. Minamide, Y. Inoue, T. Yamada, S. Ito,
S. Muhammad, Y. Shigeta, T. Kubo, B. Champagne, “Diradicalology in Third-Order Nonlinear
Optical Systems: Second Hyperpolarizabilities of Acetylene-Linked Phenalenyl Based
Superpolyenes”, International Journal of Quantum Chemistry, 113, 585-591 (2013).
25. S. Muhammad, T. Minami, H. Fukui, K. Yoneda, S. Minamide, R. Kishi, Y. Shigeta, M. Nakano,“Comparative Study of Diradical Characters and Third-Order Nonlinear Optical Properties ofLinear/Cyclic Acenes versus Phenylenes”, International Journal of Quantum Chemistry, 113,592-598 (2013).
26. K. Yoneda, S. Minamide, T. Yamada, S. Ito, T. Minami, R. Kishi, Y. Shigeta, M. Nakano,“Antidot Effects on the Open-Shell Characters and Second Hyperpolarizabilities of Rectangular
Graphene Nanoflakes”, International Journal of Quantum Chemistry, 113, 605-611 (2013).
27. A. Konishi, Y. Hirao, K. Matsumoto, H. Kurata, R. Kishi, Y. Shigeta, M. Nakano, K. Tokunaga,
K. Kamada, T. Kubo, “Synthesis and Characterization of Quarteranthene: Elucidating theCharacteristics of the Edge State of Graphene Nanoribbons at the Molecular Level”, Journal of
the American Chemistry Society, 135, 1430-1437 (2013).
28. S. Muhammad, K. Fukuda, T. Minami, R. Kishi, Y. Shigeta, M. Nakano, “Interplay between the130Diradical Character and Third-Order Nonlinear Optical Properties in Fullerene Systems,
Chemistry-A European Journal, 19, 1677-1685 (2013).
Invited talks (8 International conferences)
1. Y. Shigeta, “A Molecular Design of Nonlinear Optical Properties and Conductivity Switches on
the Basis of Open-shell Nature”, 2014 Workshop on Innovative Nanoscale Devices and Systems(WINDS), Nov. 30th-Dec. 5th 2014, Hawaii, USA.
2. Y. Shigeta, “Protein Folding Processes Detected by Enhanced Sampling Techniques”, 19thInternational Workshop on Quantum Systems in Chemistry and Physics, Nov. 11th-17th 2014,
Tamsui, Taiwan.
3. Y. Shigeta, “Towards Theoretical Design of Catalytic Activities of Enzymes”, The Asia Hub for
e-Drug Discovery Symposium 2014, Nov. 11th-12th 2014, in Sichuan University (SCU), Chengdu,
China.
4. Y. Shigeta, “First-principles analysis on enzymatic degradation of nylon”, 2nd World Congress on
Petrochemistry and Chemical Engineering, Oct. 27th-29th 2014, Las Vegas, USA.
5. Y. Shigeta, “Computational Studies on Redox Potential of Metal Complexes and Model
Cofactors”, International Conference on Synthetic Metals, June 30th-July 5th 2014, Turku, Finland.
6. Y. Shigeta, “Theoretical Studies on Reaction Mechanism of An Enzyme Cleaving Unnatural
Amide Compound”, Symposium on Molecular Science and Synthesis of Functional Molecules for
Next Generation, Mar.10th-11th 2014, Hiroshima, Japan.
7. Y. Shigeta, “Quantum chemical studies for estimation of pKa and redox potential”, World
Congress on Petrochemistry and Chemical Engineering, Nov. 17th-19th 2013, San Antonio USA.
8. Y. Shigeta, “Free Energy Analyses on Cluster Deformations by Cumulant Mechanics”, 8thCongress of the International Society for Theoretical Chemical Physics, Aug. 25th-31st 2013,
Budapest, Hungary.
Award and others (1 award and 1 press release)
1. [Award] Yasuteru Shigeta, May 2013, 2nd Young researcher’ award of Osaka University,“Dynamics Theory Including Fluctuation” (Osaka University, Japan).
2. [Press release] K. Kamiya, T. Baba, M. Boero, S. Negoro, Y. Shigeta, Nikkei Biotechnology
Onlinehttps://bio.nikkeibp.co.jp/article/news/20140419/175556/

131

Letter(1) Photochromic Switching of Diradical Character: Design of Efficient Nonlinear Opticalpubs.acs.org/JPCL
Switches [19]In conventional designs for enhancing second hyperpolarizabilities, γ, one adopted an elongationof pi-conjugation, introducing donor-acceptor substituents on the both side of molecules, and so on. On
Photochromic
Switchingof Diradical
Character:
Design ofEﬃcient
theother hand, Open-shell
singlet diradical
molecules havebeen widely investigatedbecausethey arekey
tounderstanding
thenatureofchemicalbonds.
We
have
proposedadesignprinciple
forγ, byNonlinear Optical Switches
referring a diradical character, y (0<y<1), which an index of the instability of chemical bonds. In our
Katsukiprinciple,
Okuno, Yasuteru
Shigeta,
Ryohei
Kishi, andMasayoshi
designγ becomes
large atintermediatey region.
ThisNakano*y-γ correlation has been theoreticallyconfirmed
variousmolecules
as School
H2 moleculeandScience,p-quinodimethane.
This theoretical
Department offor
Materials
Engineering
Science,such
Graduateof Engineering
Osaka University, Toyonaka,
Osaka
560-8531, Japanprediction
has subsequently been verified by the experimental results of gigantic two-photon absorption
S Supporting
cross
section, which
is proportional to the imaginary part of γ, of the polycyclic aromatic hydrocarbons*
Information
with intermediate y.
ABSTRACT:
diradical
molecules
been widely
investigatedWe haveOpen-shell
proposedsinglet
a newconcept
for havereversible
switchingofbecause they
are key to understanding
the nature ofbonds. We proposea newdiradical
characterof a moleculebychemical
photochromic
reaction.
concept for reversible switching of diradical characteran index of the instability of
Photochromic
diarylethenewithvariousopen-shell
singletchemical bondsofa molecule derivatives
by photochromic
reaction.
Photochromic
diarylethene
diradical
charactersaretheoreticallydesigned,andtheirphotochromic
derivatives with various open-shell singlet diradical characters are theoretically designed,
and their photochromic
diradical characterswitchingare
behaviors
are clariﬁed.
Theseresults
results
diradical
character switching
behaviorsclarified.
These
contributetodesigninghighlyeﬃcient
third-ordernonlinear
opticalswitchingsubstances
contribute to designing highly efficient third-order nonlinear optical
based on the correlation between the diradical character and second hyperpolarizability.
switching substances based on the correlation between the diradical
character, y, and second hyperpolarizability, γ. With this idea, we
achieve switching ratio γc/γo ~ 25 for model compounds withintermediate y for a closed-ring isomer and y=1 for open-ring isomer.
SECTION: Molecular Structure, Quantum Chemistry, and General Theory(2) Theoretical design of solvatochromism switching by photochromic reactions using
donor-acceptor disubstituted diarylethene derivatives with oxidized thiopehene rings [4]Singlet diradical compounds have been widely investigated“photochromism”. Photochromism is deﬁned as reversible

isomerization
betweenisomers, where
where atatleastone
from both theoreticaland experimental
becausePhotochromism
is defined
as a researchers
reversible
isomerization
betweentwotwoisomers,
least
21−23
directionofreversible
reactionisaphotoinduced
one.
they
have
peculiar
electronic
structures
and
are
key
to
one direction of the reversible reaction
is induced by light irradiation. Among the various
Among various photochromic compounds, diarylethene deunderstanding the nature of chemical bonds.1−10 The diradical
photochromic
compounds,
diarylethene
derivatives
undergocycloreversion
rivatives
undergo cyclization
cyclization and andcycloreversion
in 6π-electronature of a molecule is quantiﬁed by the diradical character
24−26
cyclic openreactions.and closed-ringThrough these reactions,reactionsreactions.
Since bothisomersπ-conjugationof the(y)an indexinof 6π-electrocyclic
the instability of chemicalbondsranging
11,12
lengthinamoleculecanbereversibly
changed,where
typicallyfrom0(closed-shell)
to
1
(pure
diradical),
so
that,
in
other
diarylethene derivatives are thermally stable, the photochromic reactions occur only via lightthe open-ring isomer with less extended π-conjugation iswords, 1 − y indicates an “eﬀective bond order”. Interesting
irradiation.
The various properties of the diarylethene
derivatives
such asisomer
absorption
colorless,while the closed-ringwith more spectra,
extended πphysicochemical properties of singlet diradical compounds are
refractive
indices,dielectric
constants,
redox
potentials,
and
so
on
are
quickly
andprinciple,
reversibly
conjugation is colored. Following thisvariousfound to originate in the diradical character. Among them, wediarylethene
derivatives
with modiﬁcationof aryl rings haveswitched
throughthesereactions.
We havedesigned
severaldiarylethene
have theoreticallyclariﬁedthe photochromic
correlations betweentheIn regard to thewhich
open-shelldiarylethene
been synthesized.24−26
diradical character
excitation thiophene
energies/properties,
derivatives
withandoxidizedrings andand donor-acceptor
substituents,show
thederivatives, Matsuda and Irie reported that the intramolecularthus have revealed a remarkable enhancement of the second
solvatochromism
switching by photochromic magnetic
reactions,usingin time-dependent
densityinteraction
high spin states of diarylethene
hyperpolarizability (γ), which is the microscopic origin of thirdfunctional
theory(TD-DFT)
methodwiththepolarizable
continuum
model(PCM).
It isderivatives with nitronyl nitroxide radical sources can reversiblyorder nonlinear optical (NLO) property in the intermediate
27
13−15
In
changedalong
thecyclizationandcycloreversion
reactions.
foundonly the This
open-ringisomers
exhibitthe solvatochromism, while the closed-ring
diradicalthat
character.
theoreticalprediction
has
sharp
contrasttothistraditional
π-conjugation
based
principle,
subsequentlydo
beennot
veriﬁedexperimental resultsofisomers
in bythethe examined
UV-vis.
spectral region. The mechanism of the
we here propose a reversible change scheme of diradical
gigantic two-photon absorption cross section, which issolvatochromism
behavior and its switching process
are y,clarified
from bondthe viewpoint
theof
characteri.e., the eﬀective
order, within aofrange
proportional to the imaginary part of γ, of the polycyclic
16−18charge-transfer(CT)
excitation
from
the
donor
to
the
acceptor
substituents.
We
demonstrate
closed-shell
(y
=
0)
and
pure
diradical(y=1)
statesbythearomatic hydrocarbons with intermediate y.
Although thischangeofmolecular
structurethroughthephotochromic
thatthis CT between
excitation
be controlled
by choosing
new correlationy and γcan
is expected
to open a new
F F
F F
1,14
F
F
F to γ Fswitching
reactions, and thus
apply
this y tuning method
paradigm for highly
eﬃcient
still acceptor
appropriate
pairs
ofNLO
thematerials,
donor there
andarethe
F
F
F
F
Vis.
by light irradiation.
OO
no reports on the methods for reversible switching or tuning ofOO
substituents
on
the
basis
of
the
orbitalcorrelation
O S the photochromic
S O
O Sand the SdiradicalO
By
combining
reaction
the y and γ values except for switching external strong staticUV
19
diagrambetweenthediarylethene
derivatives
andthecharacter
basedprinciple,
we
proposeanewconcept
forlightelectric ﬁeld applied to symmetric open-shell singlet systems,
D
D
A
A
20
inducedreversible
switchingofγ
valuesthroughtuningydonor-acceptor
substituents,whichisconstructedfromwhich leads to asymmetric open-shell singlet systems. The(Figure 1). There ON
can be nine classes (A−I) of OFF
systems, whichdevelopmentofsuchreversible
tuningmethod
as
well
as
of
the topologies and the orbital energies of the molecularmolecular design of practical compounds would contribute toD: donorA: acceptor
orbitalsprimarily contributing to the excitations.
opening up a new class of highly eﬃcient NLO switching.
As a typical example of such tuning methods of properties
through the change of molecular structures, we can consider© XXXX American Chemical Society

132
2418

Received: June 13, 2013
Accepted: July 11, 2013 : π conjugation

dx.doi.org/10.1021/jz401228c | J. Phys. Chem. Lett. 2013, 4, 2418−2422

Articlepubs.acs.org/JCTC(3) Density
A Density Functional
TheoryBased Protocol
to Compute
the Redox
Potential of theTransition
A
Functional
TheoryBasedProtocolto Compute
Redox
Metal Complex
the Correctionof Pseudo-Counterion:General
Theory and Applications[20]
Potential
ofwithTransition
Metal
Complex with the Correctionof PseudoOxidation andGeneral
reduction processes
one Applicationsof the most fundamental reactions in the fields ofCounterion:
Theoryareandbiology, physics, and chemistry. In this regard, it is necessary to theoretically estimate the redox

,†
†
‡,§
†
Toru
Matsui,*Yasutaka
Kitagawa,toward
Yasuteru
Shigeta,and Mitsutaka
Okumurapotentialof a given
compounddesignof compoundswith desired
redox potential. Many†computational
works employed
this ofstandardhydrogenelectrode(SHE) potential
to evaluate
the redox
Department of Chemistry,
Graduate School
Science, Osaka
University,
1-1 Machikaneyama,
Toyonaka,
Osaka 560-0043,
Japan
potential.
are many
to employ
this SHE
potential,
i.e. (1) the
SHE potential
Department However,of Materials there
Engineering
Science,problems
Graduate Schoolof Engineering
Science,
Osaka University,
1-3 Machikaneyama,
Toyonaka, Osaka
560-8531,
Japan
depends
on themodelsand the computational methods employed, (2) many experimental papers§
Core Research
for Evolutional
Science andranging
Technology(CREST),
andremoveTechnology(JST)
Agency, Kawaguchi,
reported
different
SHE potentialfrom4.05 toJapan
4.73Science
V. To
these
difficulties,
we have
332-0012
Saitama,Japan
proposed a new method to evaluate the standard hydrogen electrode potential in aqueous solution. We
S Supporting*have
added aInformation
charge correction term for transition metal complexes called “Pseudo Counter Ion
Solvation” (PCIS) model. We here evaluate the redox potential of a wide variety of transition metal
ABSTRACT:The
We meanproposeabsolutean accurateerror
schemeto evaluate
the redox
potential of redox
a widecomplexes.
(MAE)
towardexperimental
varietyoftransition
metal
complexesbyaddingacharge-dependent
correction
term
potentials of charged complexes is considerably reduced from 0.81forVa
counterion around the charged complexes, which is based on Generalized Born theory, to(maximum1.22TheV) mean
to 0.22
V (maximum
error
0.50 experimental
V). We foundthe solvationerror
energy.
absolute
error (MAE)
towardredoxaremarkableexchange-correlation
functionalon theerror
results
potentials of charged
complexes is considerably
reduced dependence
from 0.81 V (maximum
1.22V) to than
0.22 Vthe(maximumerror ones.
0.50 V).
We combination
found a remarkableexchange-correlation
ratherbasis setTheof Wachters+f(forfunctionalon the results
rather atoms)
than the basis
ones.
The combinationofmetal)
anddependence
6-31++G(d,p)(for otherwithsetthe
B3LYP
functional
Wachters+f (for metal) and 6-31++G(d,p) (for other atoms) with the B3LYP functional
gives
the least
least
MAE
0.15
V testfor complexes.
the test This
complexes.
schemeisgives theMAE
0.15 Vfor thescheme is Thisapplicableto otherapplicable
other transition
solvents,metal
andcomplexes
heavier suchtransition
metal
complexes(M1 = Cr,suchMo,solvents, andtoheavier
as M1(CO)5(pycn)Pd, Pt),=and(bpy)W),= Fe, Ru, Os)2 withthe samequality.
M2(mnt)(pycn)
Cr,M3Mo,(M(II)
= Ni,
Pd,
asW),
M(I)
(CO)2 5(M2 = Ni, (M(I)
3 (M3 M(II)(mnt)
Pt), and M(III)(bpy)3 (M(III) = Fe, Ru, Os) with the same quality.
‡(4) Unraveling the degradation of artificial amide bonds in nylon oligomer hydrolase: fromobserved by Trasatti.9 Many theoretical10−12 and experimental
1. INTRODUCTION
induced-fit to acylation processes [5]papers13−17 reported various values ranging from 4.1 to 4.8 V
Toward the design of new materials on a molecular level, it isdepending on their experimental conditions, such as thehelpfulto understandthe propertiesof a single
molecule.
Nylon-6
is a synthetic
artificial
fiber
and Themade in40’s. It was unprecedented discovery thattemperature, electrode, and so on. From the view of
redox
potential is onehydrolasesof the most that
fundamental
quantities
ofNylon-oligomer
degradethe artificial
fiber
were found in 70’.
This itis isa also
mystery
thattotheoretical/computational
chemistry,diﬃculttransition metal complexes (TMCs), which clariﬁes whether
bacteria
aquires canan easily
ability
the nylon
i.e. just
30 years.
Tobecause
elucidate
how theneeds
nylon
the SHEpotential,
this property
thethetarget molecule
taketoaneat
electronor not. so
Theearly,obtain
Gibbs
free
energy(GFE)ofaprotonintheaqueousphase.
In
oligomerhydrolase(NylB)
acquiresits
peculiar
degradation
activity
towards
non-biologicalamide
importance of measuring the redox potential of TMCs is not
order
to
avoid
such
problems,
wealso
reportedanewschemelimitedinorganic
chemistry.
redox potential
is one ofprocesses going from the induced-fit upon substratebonds,toweinspected
the Theunderlying
enzymatic
computing the SHE potential by combining experimental
thekey pieces
of informationneeded for awe
metal
cluster to theformutationalbindingto acylation.
Specificallyinvestigatedeffects of two mutants, Y170F andpK
a values of alcohol molecules and theoretical GFE with theunderstand its catalytic property. It is also meaningful to
D181G, theindicatedin former
experiments
as crucial polarizable
systems continuum
because oftheir
specific
model
(PCM)
on theamino
basis ofacid
ourinvestigate
redox potentialof signiﬁcantmetallo-proteins,
18−21previous
work
for
pK
values.
We
havecalculatedanaresidues.
Therefore,byadopting
first-principles
molecular
dynamics
complementedwithwhich play a crucial role in the electron transfer process inabsolute SHE potential of 4.52 V when we employed a goldbiomolecules.
For
example,acytochrome
c,
which
is
a
heme
metadynamics we provide a detailed insight into the underlying
acylation mechanism. Our results show
starndard calculation level as CCSD(T)/aug-cc-pVDZ. Our
compoundan ironatom,
is a mediaterof electronthat whileandincontains
the wild
type(WT)
the Tyr170
residue points
theNH
themolecules
proton-acceptor
previous study
for group
organic towards
and inorganic
consiting oftransport processes in several biologically important systems. In
site
of
an
artificial
amide
bond,
hence
ready
to
react,
in
the
Y170F
this
does
not
occur.
The
reasonistypicalelements
indicated
that
the
value
of
the
SHE
potential
order to understand the correlation between the structure andon thebycomputational
methods,
and isweunable
proposedtoa
ascribed
to the absenceof Tyr170 in
the mutant,is replaced
phenylalanine,
which
the
redox potentialof the metallo-enzymes,
it requires
accuratewhichdepends
necessity for tuning of the SHE potential. The mean absolutecomputation
schemes
fromwithﬁrst principles.
form hydrogenbond
the amide bond; thus,1−8resulting
in anerror of -1the redox potentials became 0.1 V when we used a
Although inmanyreportedoftheir
methods. potential by using a popular density functional
increase
thetheoreticians
activationhave
barriermorethan 10 kcal
mol
tuned SHE
to compute the redox potential, the error from the experimental
Nonetheless,despitethelackofhydrogenbonding
betweenthetheory (DFT) such as B3LYP.
value is quite large, such as 0.20−0.30 V in mean absolute error
Y170FThe
anddeviation
the substrate,
highestvalues
free energy
forspitethe of the success with the typical molecules, our(MAE).
from the theexperimental
originatesbarrier In
previous
scheme cannot describe TMCs with an excess charge.
mainlyfrom theistreatmenthydrogenelectrodeto suggest thatinduced-fit
similar of
to thethatstandard
of WT.
This seems
Thereremaintwo high barriers to achieve the accurate(SHE)
which process,has been treatedas a isconstantin thepotential,
induced-fit
kinetics
little andaffected by the
independent of the computational method in many theoreticalmutation.
On the basis
structural homology
papers.
The international
union ofof
pureadditional
and applied chemistry
Received: April 2, 2013
analysesrecommendson the enzymes
theV samefamily,we suggestthat May 23, 2013
(IUPAC)the valueof4.44
as a SHE
potential
Published:natural selection is responsible for the development of the© 2013 American Chemical Society
2974
dx.doi.org/10.1021/ct4002653 | J. Chem. Theory Comput. 2013, 9, 2974−2980
peculiar hydrolytic activityof Arthrobacter sp. KI72.

133

De novo design of the functional transition metal proteinsusing a coiled-coil scaffold
Yu Takano
Institute for Protein Research, Osaka University
Introduction
De novo design of proteins is becoming increasingly attractive, because it can create novel
materials that adopt a designed function at will. Additionally, it enables us to understand what isrequired for the protein function. In particular, the creation of a metal binding site bearing
unusual characteristic features within a scaffold protein would improve our understanding of thecorrelation between the coordination structures and the spectral features and facilitate design
strategies for metal binding sites. We performed quantum mechanical and molecular mechanical(QM/MM) computations for metalloprotein and found that protein environment enhances theintrinsic character of metal active sites and provides function of metalloproteins. It indicates that
it is required to investigate the electronic structures of the metal active site itself and the effectof protein environments on the active site. Our ultimate goal is to propose a guideline ofcomputational design of de novo metalloproteins as a protocol of a priori design of novel
molecules by using computics. In this project, we performed QM and QM/MM calculations on
the CuA center of cytochrome c oxidase (CcO) and nitrous oxide reductase (N2OR) to elucidate
the quantitative structure-function relationship in copper protein. Based on the computational
results, we conducted de novo designs of copper proteins and successfully created the purple
copper CuA site within a de novo scaffold coiled-coil protein. We also have investigatedmolecular interactions in the α-helices and β-sheets composed of alanine residues, using
quantum chemical (QC) methods (B97D/6-31+G(d)) and molecular mechanics (MM)(AMBER99-SB) to improve the force field for accurate description of protein behavior, whichis required for the reliable computation of de novo metalloproteins.
Computational studies of the electronic structure of the CuA site in cytochrome c oxidase
and nitrous oxide reductase
CcO and N2OR belong to purple copper proteins and possess electron transfer functions. Bothproteins receive the electron from cytochrome c at an unusual copper electron transfer center
called CuA. The CuA site contains a binuclear copper center, which is composed of two bridging
Cys residues forming a Cu2S2 core. The CuA site has two additional His residues interacting
equatorially and several weakly interacting axial groups, such as Met, His, and the main chain
carbonyl of Glu. These sites have been characterized as the binuclear copper center with mixed
valence [Cu(1.5)−Cu(1.5)] species in various spectroscopic studies. The ground state of theoxidized CuA site is strongly related to the singly occupied orbital, since the oxidized state of
the CuA site is doublet. Spectroscopic studies have suggested the σu* ground state of the CuA

134

site due to the direct CuCu interaction, facilitating a rapid electron transfer over long distanceswith low driving forces.
First of all, in order to elucidate what
factors are responsible for the stabilization ofthe σu* ground state of the CuA site, theelectronic structures of the Cu2S2 core of the
CuA site in CcO have been studied, using thedensity functional theory (M06) to elucidate
the origin of the σu* ground state of the CuA
site. Our computational results show that the
ground state of the Cu2S2 core is the πu stateeven with a shorter Cu–Cu distance, and thatan addition of electrostatic and orbital
interactions by ligand coordination stabilizes
Figure 1. Orbital diagram of the Cu2S2 core

the σu* state rather than the πu state, because
electrostatic repulsion and antibonding

orbital interaction between the dσ* orbital of the Cu–Cu dimer and the lone pairs of thecoordinating His residues rise the orbital energy of the dσu* orbital of the CuA site, as shown in
Figure 1.
Next, we have studied the coordinating effects of His, Met, and the peptide carbonyl group of
Glu of the CuA site, using the density functional theory. We constructed models to examine thecoordination effect. The models of the CuA site are shown in Figure 2. In the models, weconsidered the one-ligand removed models of the CuA site, in which each coordinating residue
was removed (the non-H161, non-E198, non-H204, and non-M207 models). The one-ligand
removed model nullifies the orbital and electrostatic effects of the removed ligand. To
investigate the electrostatic effects of the removed ligand, we also built point charge models (thepc-H161, pc-E198, pc-H204, and pc-M207 models), in which we replaced each coordinating
ligand with point charges, as illustrated in Figure 2.

Figure 2. Models of the CuA site.
Comparison between the one-ligand removed and the point charge models suggests that theorbital interactions between the Cu2S2 core and the coordinating ligands dominate   of135

the CuA site. Our computation has shown that the electrostatic effect, due to the ligation of
His161, His204, and Glu198, is more influential on the IP than the orbital effect (Figure 3).
With regard to the coordination of Met207, however, the orbital and electrostatic effects
equivalently affect the IP. These results indicate that the strong orbital and electrostatic effectsof the His198 and His204 residues both contribute to the stabilization of the σu* ground state
and the decrease in the ionization potential, as compared to the Cu2S2 core itself. The peptidegroup of Glu198 weakly coordinates to the Cu2S2 core of the CuA site and only electrostatically
influences the ionization potential of the CuA site. The coordination of Met207 provides weakorbital and electrostatic effects, which are useful for the fine-tuning of the electronic structure of
the CuA site.

Figure 3. Energy gaps between the σu* and πu states (  ) and ionization potentials (IPs)of the models of the CuA site. Black bold lines represent the core and full models. Bluedashed-dotted and red dotted lines represent the one-ligand (non-) and the point charge (pc-)
models, respectively. Black thin line is drawn on those of the full model as a reference.
We also found that three dimensional X-ray crystallographic structures of the CuA site showthat the structural variety of the Cu2S2 core of the CuA site with a short Cu–Cu distance of 2.34–
2.59 Å and a S–S
distance of 3.76–4.24
Å.

We addressed theorigin of the structuralvariety of the Cu2S2
core of the CuA site,
using

the

densityfunctional theory. Our
computation
demonstrated that we
found

the

dependence

structuraloftheenergy gap between the

Figure 4. Scatter plots of the energy gap between the σu* oxidized
and reduced states () as functions of the Cu–Cu bond length(A), the S–S bond length (B). Black lines represent the regression
lines, and R denotes the Pearson's correlations.

136

σu* and πu oxidized states (Figure 4), the ionization potentials, and total energies, though thestructural variety is insensitive to the shape and symmetry of the σu* and πu redox active
molecular orbitals (RAMOs) and the πu ground state of the Cu2S2 core of the CuA site. In
addition, the σu* oxidized state is more robust to the structural changes in ionization potentials
and total energies than the πu oxidized state (Figure 5). This robustness indicates the small
reorganization energy in the redox reaction between σu* oxidized and reduced states of the CuA
site. The optimized Cu2S2 cores have almost same structures in all the states, indicating thatsurrounding proteins are responsible for the structural variety of the Cu2S2 core of the CuA site.

Figure 5. Schematic pictures of the Cu–Cu indirect interaction via the Cu–S bonds for IP u (A)and the Cu–Cu direct interaction for IP * (B).
uCreation of a binuclear purple copper site within a de novo four-helical coiled-coil protein
The creation of a metal binding site bearing unusual characteristic features within a scaffold
protein would improve our understanding of the correlation between the coordination structures
and the spectral features and facilitate design strategies for metal binding sites. On the basis of
the blue copper site described previously, we successfully created the purple copper CuA site
within a de novo scaffold tetrameric α-helical coiled-coil protein, amino acid sequence of whichis shown in Figure 6. This protein is referred to as bi-AM2C.

Figure 6. Amino acid sequences of bi-AM2C (X = H, Y = C) for the purple copper protein.
The protein bound two copper ions and exhibited a purple color, with relatively intense
absorption bands at 488 and 530 nm in the UV−vis spectrum (Figures 7A and B). The EPR
spectrum displayed unresolved hyperfine splittings in the g region, which was similar to thenative or engineered Cus site with an A∼480/A∼530 > 1. The extended X-ray absorption structure
analyses of the protein revealed the presence of the Cu2S2 core structure, with two typicalN(His)−Cu bonds per core at 1.90 Å, two S(Cys)−Cu bonds at 2.21 Å, and the Cu−Cu bond at137

2.51 Å, which are also characteristic structures of a purple copper site. We also investigated thecoordination geometry of the active site in the model of the bi-AM2C-(Cu)2 complex. Since nocrystal structure of bi-AM2C has been reported, the model of the bi-AM2C-(Cu)2 complex wasconstructed and minimized by the conjugate gradient method (Figure 7C). The active site of thebi-AM2C-(Cu)2 complex is located in the vicinity of the second α-helix of the coiled coil. The
active site contains copper ions bridged with the deprotonated cysteinyl groups of Cys47 andCys50. The copper ions and cysteinyl sulfur atoms form an almost planar Cu2S2 core with adihedral angle of 163.2°. The dihedral angle of the Cu2S2 core of the bi-AM2C-(Cu)2 complex isclose to those of the nitrous oxide reductase from Paracoccus denitrificans (164.0°− 165.9° ).
The copper ions are strongly and equatorially coordinated with two His residues (His13 andHis81). The peptide carbonyl groups of Glu46 and Cys47 reside within 2.7 Å from the copper
ion and might axially interact with it. His16 and His84 are located over the Cu2S2 core, atdistances of 4.07 and 2.70 Å from the copper ions, respectively, implying that these His
residues might also form axial interactions with the copper ions.

Figure 7. Purple color of the solution of bi-AM2C and Cu2+ ion (A), UV-vis spectrum of bi-AM2C and Cu2+ ion (B), and computational model of bi-AM2C-(Cu)2 complex (C).

Theoretical study of the molecular interactions in secondary structures of proteins
The three-dimensional structure of a protein
determines

its

functionsandchemicalproperties. The secondary structures such as
α-helicesandβ-sheets

areimportantcomponents for the protein architecture, as
shown in Figure 8. Molecular interactions, inparticular hydrogen bonding, play significant
roles in the formation of the secondary
structures. Quantitative estimate of theseinteractions is required to understand theprincipleoftheformationofthethree-dimensional protein structure. Here, toFigure 8. Three-dimensional structure andsecondary structure of proteins

improve the force field for accurate description of protein behavior, we have investigated138

molecular interactions in the α-helices and β-sheets composed of alanine residues, using
quantum chemical (QC) methods (B97D/6-31+G(d)) and molecular mechanics (MM)(AMBER99-SB) . The characteristic interactions essential for forming the secondary structures
are discussed quantitatively.
The MM force field stabilizes the α-helix much more than the QC method. In addition, theMM force field overestimates the interaction energies of the α-helix, compared to those of theβ-sheet, implying that the improvement of the electrostatic interaction is required (Figure 9).
We also have evaluated each hydrogen bond (H-bond) energy in the α-helices and theβ-sheets by using the molecular tailoring approach (MTA), which is one of the fragment-based
methods. Within MTA, a large
system is divided into somesubsystems.

Theelectronic

properties of the subsystems arecomputationally evaluated. The
properties of the large system are
obtainedbypatching

thecorresponding properties of all thesubsystems. MTA shows that the
H-bonds
strongerin the β-sheets
than those in

are
the

α-helices due to the structural
constraint in α-helix and that the
antiparallel β-sheet can form
linear H-bonds rather than theparallel β-sheet, resulting in thestronger

H-bonds

intheantiparallel β-sheet. In addition,

Figure 9. Relationship between hydrogen-bond energies(interaction energies or relative energies) and the number ofhydrogen bonds

the H-bonds in the α-helices canbeclassified

threetypes:

N-terminal, C-terminal, and inner H-bonds, and inner H-bonds are weaker than other H-bonds
at the same H-bond distances. The differences of the H-bond energies between the parallel andantiparallel β-sheets and between the N-terminal, C-terminal, and inner H-bonds in the
α-helices indicate secondary-structure dependence on the H-bond energies.
Members of this research project
Co-Investigator (renkei-ken kyusha): Prof. Toshiki Tanaka (Nagoya Institute of Technology)
Research Collaborator: Prof. Yasuteru Shigeta (Tsukuba University)
Research Collaborator: Ms. Makoto Kita (Osaka University)
Research Collaborator: Ms. Orio Okuyama (Osaka University)
Research Collaborator: Mr. Tomoyuki Iwamoto (Osaka University)

139Publications and Invited lectures
Papers1)

K. Koizumi, Y. Shigeta, O. Okuyama, H. Nakamura, Y. Takano, "Coordination effects on theelectronic structure of the CuA site of cytochrome c oxidase", Chem. Phys. Lett. 531,
197-201 (2012).

2)

Y. Takano, Y. Shigeta, K. Koizumi, H. Nakamura, "Electronic structures of the Cu2S2 core of
the CuA site in cytochrome c oxidase and nitrous oxide reductase", Int. J. Quantum Chem.
112, 208-218 (2012).

3)

D. Shiga, Y. Funahashi, H. Masuda, A. Kikuchi, M. Noda, S. Uchiyama, K. Fukui, K.
Kanaori, K. Tajima, Y. Takano, H. Nakamura, M. Kamei, T. Tanaka, " Creation of a binuclear
purple copper site within a de novo coiled-coil protein", Biochemistry 51, 7901-7907 (2012).

4)

Y. Takano, O. Okuyama, H. Nakamura, Y. Takano, "Density functional studies of thestructural variety of the Cu2S2 core of the CuA site", Int. J. Quantum Chem. 112, 3583-3591(2012).

5)

Y. Takano, K. Yamaguchi, H. Nakamura, "Theoretical studies of effect of protein
environment on electronic structures and chemical indices of the active site of oxygenatedand deoxygenated hemerythrin", Int. J. Quantum Chem. 113, 497-503 (2013).

6)

Y. Takano, O. Okuyama, Y. Shigeta, H. Nakamura, "Density functional study of the origin of
the strongly delocalized electronic structure of the CuA site in cytochrome c oxidase",
Quantum Systems in Chemistry and Physics -Progress in Methods and Applications-,
Progress in Theoretical Chemistry and Physics Vol. 26, edited by Kiyoshi Nishikawa, Jean
Maruani, Erkki J. Brändas, Gerardo Delgado-Barrio, and Piotr Piecuch, Chapter 30, Springer
2013, pp. 513-524.
Y. Takano, M. Kita, H. Nakamura, "Quantum chemical study of conformational preferences
in intermediates and transition states of the hydrolysis of dimethyl phosphate.", J. Phys.
Conf. Ser. 454, 208-218 (2013).
M. Kita, H. Nakamura, Y. Takano, "Density functional study of the phosphodiesterhydrolysis of RNA in RNA/DNA hybrid by RNase H.", Mol. Phys. 112, 355-364 (2014).

7)

8)Invited lecture
1)

Yu Takano, "How to use PCM (Polarizable Continuum Model) for description the molecularenvironment, and application of the PCM to the protein environment of metalloprotein.", The
13rd Dai Tsukuba Physical Chemistry Seminar (December 7, 2012, Josai University)

2)

Yu Takano, "Towards de novo design of functional metalloproteins by using computer
simulation", Mie University CUTE seminar (January 15, 2013, Mie University)

3)

Yu Takano, "Relationship between molecular structure, electronic structure, and function of
metal cofactors in proteins", The 6th symposium (November, 20, 2013, Kobe University)

4)

Yu Takano, "Computational study of relationship between molecular structure, electronic
structure, and function of metal cofactors in proteins", IPR seminar (February 8, 2014, Osaka
University)

5)

Yu Takano, "Theoretical study of electronic structures of metal cofactors in proteins", The
3rd computational life science WG lecture (March 17, 2014, Tsukuba University)

6)

Yu Takano, "Electronic structures of metal cofactors in proteins -QM and QM/MM
analysis-" Kinki Chemical Society Japan lecture (May 9, 2014, RIKEN Advanced Institutefor Computational Science)

7)

Yu Takano, "Theoretical study of the molecular interactions to form secondary structure inproteins", The 14th Protein Science Society Japan annual meeting (June 26, 2014, Work Pier
Yokohama)

140

Construction of Material Design System on
Next-Generation Density Functional Theory
Yutaka Imamura
RIKEN Advanced Institute for Computational Science
1.

Introduction
Density functional theory (DFT) has been one of widely used methodologies because of

relatively accurate description and low computational cost comparable to that of Hartree-Fock(HF) method. However, the exact DFT total energy expression has not been known but has been
rigorously proposed. Hybrid functionals have become mainstream among a wide range of
exchange-correlation (XC) functionals; for instance, B3LYP, one of representative hybrid
functionals, has been applied to many systems such as molecules and nanomaterials not only by
quantum chemists but also by experimentalists. Recently, more sophisticated XC functionals suchas range-separated and local as well as orbital-specific (OS) hybrid functionals proposed by us
have been developed. The OS hybrid functionals determine portions of HF exchange interaction
by the linearity condition for orbital energies (LCOE) without resorting to numerical fitting toexperimental standard formation of enthalpies. The OS hybrid functionals have succeeded in
reproducing core and valence ionization potentials (IPs). However, the conventional scheme for
the OS hybrid functionals is not applicable to multiple LCOEs that become important for excitedstates and multiple orbital-involved chemical reactions. This study explored a new scheme todevelop new OS hybrid functionals that satisfy multiple LCOEs based on a multiply-range
separated functional [1].
2.

TheoryThis section explains how to build OS hybrid functionals that satisfy multiple LCOEs. Janak’s

theorem in Kohn-Sham DFT (KS-DFT) states that the first derivative of the total energy withrespect to the occupation number fi of the ith KS orbital is equivalent to its orbital energy:

E i .
f i(1)

Almbladh and von Barth proved the relation for the highest occupied molecular orbital (HOMO):

E
f HOMO  HOMO  IP ,(2)which indicates that the HOMO energy is equivalent to the first IP with an opposite sign. Since
the IP must be constant, the following LCOE is derived:

141


2E
 i
0.
2
f i 0 f 1 f i 0 f 1
i

(3)

i

Although Eq. (3) is exact for the HOMO, it may not necessarily hold for other orbitals; however,Eq. (3) provides a better description through the removal of the self-interaction errors.
The multiply range-separated hybrid XC functional is assumed to have the following form in
the case of N LCOEs:
N 1





SR
SR
MRi
MRi
LR
Exc  (1  SR ) EDFTx SR EHFx  (1   MRi ) EDFTx
  MRi EHFx
EHFx
 EDFTc . (4)i 1

HF/DFT
HF/DFT
HF/DFT
EX,SR, EX,MRi , and EX,LR
are the short-, middle-, and long-range HF/DFT exchange

energies, respectively, with corresponding fractions of SR ,  MRi , and  LR .

When the number of parameters of SR ,  MRi , and  LR are equal to or less than that of

LCOEs, optimization of the parameters is basically executable. In the present study,  wasdetermined using the Brent’s method, which combines the bisection and secant methods, andinverse quadratic interpolation so as to exactly satisfy LCOEs. A one-to-one correspondence
between LCOE and  was also assumed.
3.

Results and Discussion
We numerically assessed the new OS hybrid functionals by computing four types of excitedstates for CO and N2 molecules: core-valence, core-Rydberg, valence-valence, and valenceRydberg transitions using time-dependent density functional theory (TDDFT). The OS hybrid
functional with two LCOEs of HOMO and the deeper 1s orbital was adopted. XC functionals
such as BLYP, B3LYP, and LC-BLYP were examined for comparison. Table lists the excitationenergies for conventional and OS hybrid XC functionals. Deviations from experimental values
and percent deviations are listed in parentheses and square brackets. Mean absolute deviation(MADs) and mean absolute percent deviations (MAPDs) of four excitation energies fromexperimental values and overall MADs and MAPDs are also given.
The valence-valence excitation energies of CO and N2 were reproduced within 1 eV using
BLYP and B3LYP. The MADs were (0.31 and 0.37) eV and (3.51% and 4.17%) for (BLYP,
B3LYP), respectively. As for valence-Rydberg transitions, excitation energies were
underestimated especially for BLYP. The MADs and MAPDs were (1.88 and 1.01) eV and(15.72% and 8.43%) for (BLYP, B3LYP), respectively. The long-range corrected hybrid
functional LC-BLYP, which was designed to improve behavior in the asymptotic region,
accurately estimated excitation energies for valence-valence and valence-Rydberg excitations
with MADs of less than 1.0 eV.

142

Table Excitation energies (eV) calculated using conventional and OS hybrid functionals.
BLYP
B3LYP
LC-BLYP
Valence→Valence
CO molecule* 35.87 (-0.45) [-7.15] 5.90 (-0.42) [-6.69]
6.00 (-0.32) [-5.11]6.30
σ→π ( Π)* 1
8.29 (-0.22) [-2.62] 8.45 (-0.06) [-0.67]
8.63 (0.12) [1.37]
8.98
σ→π ( Π)* 3 +8.14 (-0.37) [-4.38] 7.97 (-0.54) [-6.31]
8.11 (-0.40) [-4.75]
8.24
π→π ( Σ )* 3
8.73 (-0.63) [-6.70] 8.67 (-0.69) [-7.32]
8.84 (-0.52) [-5.54]8.90
π→π ( Δ)
* 1 9.84 (-0.04) [-0.41] 9.78 (-0.10) [-1.03]
9.79 (-0.09) [-0.95]9.61
π→π ( Σ )* 1
10.08 (-0.15) [-1.47] 10.10 (-0.13) [-1.31] 10.27 (0.04) [0.41] 10.48
π→π ( Δ)
N2 molecule3+7.63 (-0.12) [-1.55] 7.23 (-0.52) [-6.72]
7.09 (-0.66) [-8.55]
6.81
πu→πg ( Σu )3
7.56 (-0.48) [-6.03] 7.68 (-0.36) [-4.47]
7.97 (-0.07) [-0.81]
8.11
σg→πg ( Πg)3
8.37 (-0.51) [-5.70] 8.11 (-0.77) [-8.63]
8.04 (-0.84) [-9.44]
7.78
πu→πg ( Δu)1
9.21 (-0.10) [-1.11] 9.38 (0.07) [0.79]
9.65 (0.34) [3.63]
9.93
σg→πg ( Πg)
3 9.74 (0.07) [0.69] 9.49 (-0.18) [-1.91]
9.24 (-0.43) [-4.43]
8.81
πu→πg ( Σu )1 9.74 (-0.18) [-1.85] 9.49 (-0.43) [-4.38]
9.24 (-0.68) [-6.84]
8.81
πu→πg ( Σu )1
10.02 (-0.25) [-2.40] 9.88 (-0.39) [-3.81]
9.84 (-0.43) [-4.16]9.87
πu→πg ( Δu)3
10.40 (-0.79) [-7.09] 10.70 (-0.49) [-4.34] 10.99 (-0.20) [-1.78] 11.60
σu→πg ( Πu)Valence→Rydberg
CO molecule
1 +9.06 (-1.72) [-15.97] 9.90 (-0.88) [-8.20] 11.10 (0.32) [2.93] 11.17σ→3sσ ( Σ )1 +9.53 (-1.87) [-16.42] 10.31 (-1.09) [-9.59] 11.64 (0.24) [2.08] 11.70σ→3pσ ( Σ )1
9.67 (-1.86) [-16.10] 10.44 (-1.09) [-9.47] 11.74 (0.21) [1.79] 11.79
σ→3pπ ( Π)N2 molecule
3 +σ→3sσ ( Σg ) 10.24 (-1.76) [-14.68] 11.08 (-0.92) [-7.66] 12.06 (0.06) [0.48] 12.41
1 +σ→3sσ ( Σg ) 10.59 (-1.61) [-13.17] 11.49 (-0.71) [-5.82] 12.64 (0.44) [3.57] 13.08
1σ→3pπ ( Πu) 10.82 (-2.08) [-16.10] 11.80 (-1.10) [-8.52] 13.04 (0.14) [1.06] 13.60
1 +σ→3pσ ( Σu ) 10.69 (-2.29) [-17.61] 11.71 (-1.27) [-9.78] 13.11 (0.13) [1.03] 13.57
Core→
CO moleculeC1s→π*
271.36 (-16.04) [-5.58] 276.23 (-11.17) [-3.89] 271.30 (-16.10) [-5.60] 285.76
O1s→π*
512.60 (-21.60) [-4.04] 520.14 (-14.06) [-2.63] 513.16 (-21.04) [-3.94] 535.46
N2 moleculeN1s→π*
382.63 (-18.37) [-4.58] 388.72 (-12.28) [-3.06] 382.73 (-18.27) [-4.56] 403.63
Core→
CO moleculeC1s→3sσ272.81 (-19.59) [-6.70] 279.41 (-12.99) [-4.44] 275.86 (-16.54) [-5.66] 292.15
C1s→3pπ273.55 (-19.75) [-6.73] 280.12 (-13.18) [-4.49] 276.83 (-16.47) [-5.62] 293.16
C1s→3pσ273.40 (-20.10) [-6.85] 280.06 (-13.44) [-4.58] 276.76 (-16.74) [-5.70] 293.24
O1s→3sσ514.08 (-24.82) [-4.61] 522.97 (-15.93) [-2.96] 516.45 (-22.45) [-4.17] 540.49
O1s→3pπ514.76 (-25.14) [-4.66] 523.79 (-16.11) [-2.98] 517.64 (-22.26) [-4.12] 541.83
N2 moleculeN1s→3sσ384.17 (-22.03) [-5.42] 391.89 (-14.31) [-3.52] 386.76 (-19.44) [-4.79] 410.24
N1s→3pπ384.63 (-22.47) [-5.52] 392.49 (-14.61) [-3.59] 387.72 (-19.38) [-4.76] 411.40
N1s→3pσ384.53 (-22.77) [-5.59] 392.50 (-14.80) [-3.63] 387.99 (-19.31) [-4.74] 411.74
MAD/MAPD (V→V)(0.31) [3.51](0.37) [4.17](0.37) [4.13]
MAD/MAPD (V→R)(1.88) [15.72](1.01) [8.43](0.22) [1.85]
MAD/MAPD (C→V)(18.67) [4.74](12.50) [3.19](18.47) [4.70]
MAD/MAPD (C→R)(22.08) [5.76](14.42) [3.77](19.07) [4.94]
MAD/MAPD (Total)(7.82) [6.86](5.16) [4.91](6.71) [3.89]

OS(-0.02)(0.47)(-0.27)(-0.46)(-0.27)(0.25)

Exptl.
[-0.39] 6.32
[5.54] 8.51[-3.17] 8.51[-4.91] 9.36[-2.75] 9.88
[2.42] 10.23(-0.94) [-12.13] 7.75
(0.07) [0.92] 8.04(-1.10) [-12.34] 8.88
(0.62) [6.64] 9.31(-0.86) [-8.87] 9.67(-1.11) [-11.16] 9.92(-0.40) [-3.90] 10.27(0.41) [3.67] 11.19(0.39)(0.30)(0.26)[3.66] 10.78[2.64] 11.4
[2.24] 11.53(0.41)(0.88)(0.70)(0.59)[3.38]
12[7.25] 12.2
[5.44] 12.9
[4.54] 12.98(-1.64)(1.26)[-0.57] 287.4[0.24] 534.2(2.63)[0.65]

401(-0.25)(-0.14)(-0.26)(1.59)(1.93)[-0.09][-0.05][-0.09][0.29][0.36]

292.4
293.3
293.5
538.9
539.9

(4.04)(4.30)(4.44)(0.52)(0.51)(1.84)(2.12)(1.04)[0.99] 406.2[1.06] 407.1[1.09] 407.3[5.63][4.17][0.49][0.50][3.55]

We turn to the core-valence and core-Rydberg transitions in CO and N2 molecules. The three
conventional functionals severely underestimated excitation energies. The MADs and MAPDs
increased in the order of B3LYP < LC-BLYP < BLYP. The values were 12.50, 18.47, and 18.67
eV for core-valence transitions, and 14.42, 19.07, and 22.08 eV for core-Rydberg transitions. For
core-valence transitions, short-range HFx is the most important; thus, the 20% HFx in B3LYP in
the core region reduced deviations. For core-Rydberg transitions, long-range HFx is also
important for the description of Rydberg orbitals. Thus, a performance difference was observed
between BLYP and LC-BLYP for core-Rydberg transitions.
Finally, we investigated the performance of the OS hybrid functional. Excitation energies are

143well reproduced for the four types of transitions, i.e., valence-valence, valence-Rydberg, corevalence, and core-Rydberg. As for core excitations, MADs and MAPDs were drastically reduced
from those of the three conventional functionals; in particular, core excitation energies of CO
were remarkably improved. As for valence excitations, reasonable MADs were obtained. The
overall MAD, 1.04 eV, and MAPD, 3.55%, were smaller than those of BLYP, B3LYP, and LCBLYP. Only the OS hybrid functionals offered reliable descriptions of all types of excitations.
4. Concluding Remarks
We proposed and numerically assessed a new scheme for building an OS hybrid functional thatsatisfies multiple LCOEs. In terms of excitation energies, the OS hybrid functional has ableddescription of three different types of orbitals, i.e., core, valence, and Rydberg, for single
calculations. This opens applications toward chemical phenomena involving not only core, butalso valence electrons.
5.

Publication list

1) Yutaka Imamura, Kensei Suzuki, Takeshi Iizuka, and Hiromi Nakai, Chem. Phys. Lett. 618,
30 (2015).
6.

Seminar1) Yutaka Imamura, "Development of Orbital-Specific Density Functional Theory", Peralta
Group Seminar at Central Michigan University, Mount Pleasant, USA, Jan. 16, 2014
2) Yutaka Imamura, "Development of Orbital-Specific Density Functional Theory", Perdew
Group Seminar at Temple University, Philadelphia, USA, Jan. 13, 2014.

144

First Principles Simulation of Nonequilibrim Transport at Nano-contact
and Design of Functional Materials
Hisao Nakamura
Nano System Research Institute, “RICS”, AIST

１ ． 	
 

Introduction

In the present research report, we summarize our recent studies of nonequilibrium transport
theory and first principles simulation of “nan-contact”. Here, we use the terminology“nan-contact” as an extended definition, which includes single/SAM molecular junctions, hetero
junction of the different semiconductor materials connected to electrodes etc. In particular, we
focus on developing a computational theory of electric/thermal current as well as interaction
between conducting electrons and ions, and we evaluate IV characteristics, local (vibrational)
heating by inelastic scatterings, current-induced conformation change, and thermoelectric
properties of nano-contact systems quantitatively. Then we analyze detail mechanism of thesenonequiribrium processes in the functional devises and make guiding principles to design
functional nano-contact devises.
We adopt mainly the framework of nonequilibrium Green’s function method combined withdensity functional theory (NEGF-DFT) to develop theoretical scheme. Our concrete target ismolecular electronics to bridge molecular synthesis/ fabrication technologies and devise physics,
design of high ZT (figure of merit) thermoelectric material, organic-inorganic hybrid
thermoelectric materials, and functional materials of nanoelecronics like nonvolatile memories.
Our aim is to establish computational electronics applicable to sub 10 nm scale device based on
quantum transport via first principles calculation.
２ ． 	
 Outline of our theoretical and computational approaches

On the transport calculation at nano-contact, electronic states in the semi-infinite electrodes
and in the contact (bridge molecule/resistance layer) have to be calculated on the equal footing.
Since the Fermi level in each electrode is shifted due to applied bias, calculation of Hartree
potential is obtained by Poisson equation with different boundary condition form that of an
equilribrium system. As stated in Sec. 1, we adopt NEGF-DFT framework. The mosttime-consuming step in the standard algorithm is self-consistent field (SCF) calculation ofelectron density (and other self-energy terms like electron-phonon interactions) since it requires
caluclation of many Green’s function matrices and accurate numerical intergration. In order toreduce heavy computational facility, we introduce “restricted SCF space” defined by thereference equilibrium state (i.e., zero-bias electronic state) and correct difference of electron
density between equilibrium and nonequilibrium conditions by updating only electron
occupation in the molecular orbitals (MOs) in the restricted SCF space. Note that this algorithm
includes the entire orbital relaxation effect by SCF. When the SCF result converges to an
unphysical state, the restricted SCF space violates smoothness (continuous change) by
iterating the SCF cycle. Hence, we can check unphysical result and/or validity of theapproximation and model directly.

145

The other important point in the present study is developing methods to simulate inelastictransport process by electron-phonon interaction and phonon thermal transport as well as
current-induced vibrational excitation. For calculation of inelastic electric current, we use therigorous formulation of the lowest order Born expansion (LOE) then introduce the following
approximations: (1) Energy dependence of the retarded (advanced) Green’s function is
calculated on the coarse-grained energy grids, and averaged over the bias window (2) subpart ofthe lesser (greater) Green’s function is integrated analytically as a function of energy and derive
analytical expression. By combining (1) and (2), computational task to evaluate electron-phonon
self-energy is much less than standard approach, which includes numerical convolution integral.
Furthermore, this conventional LOE does not require the wide-band-limit approximation. We
will apply our algorithm to study inelastic electron tunneling spectroscopy (IETS) of molecularjunctions, temperature dependence of resistance in resistance random access memory (ReRAM)
etc. In the present algorithm of LOE calculations, each phonon Green’s function is defined bynormal mode coordinate. Thermal dissipation of each intrinsic phonon mode to electrodes is
simply represented by related damping parameter. However, thermal conductance obtained bythis simplification is not as accurate as electric conductance by full NEGF-DFT. This is notsuitable to calculate ZT. Hence, separately, we implemented the program to calculate phonon
Green’s function in real space to apply thermoelectric materials. Real space phonon Green’s
function includes phonons of semi-infinite electrodes as the same with electric Green’s function,i.e., electric and thermal transport properties cab be calculated by the same level theory.

３ ． 	
 

Research Activities

3-1. Single molecular electronics by first principles transport calculation
In the ballistic electric transport at nano-contact, the transport properties such as IV
characteristics are determined by both of the intrinsic properties of the conductor (resistancelayer) and interaction between the conductor and electrodes. The former relates to “bandengineering” or “MO engineering”, and the latter is called “contact engineering” or “contact
chemistry”. A single molecular junction is the most fundamental devise and suitable to comparea theory and precise measurement. In addition, analysis of transport properties in the views of
MO engineering and contact chemistry is quite useful to design molecular device. We develop
effective Hamiltonian theory constructed by the molecular projected state Hamiltonian (MPSH)
and Green’s function by NEGF-DFT results. The complex energy of the effective Hamiltonian
spanned by each MO tells us the shifted MO energy and electronic coupling strength of
conducting MO and electrodes.
To realize single molecular electronics, mechanical stability of the junction, i.e., robustness ofanchoring of molecule to the electrode surface is required. It is usually considered thatrobustness of chemical bonds by anchor moieties relates
electric conductance positively.

Figure 1

Table 1146

However, recently, Tao’s group measured electric conductance of several molecular junctions
consisting of Au-C anchoring systematically. They found that the above relation between
mechanical robustness and conductance is sometimes violated, and not a reliable guiding
principles to synthesize molecular devise. We performed calculation of effective Hamiltonian
followed by NEGF-DFT. By using the results, we identified the conducting MO and electric
coupling strength with states in electrodes. Then we compared the coupling strength, adsorptionenergy and conductance. We found that, only when the conducting MO is the reactive MO andwhen Bloch states in the electrodes interact with reactive MO, the positive correlation statedabove is satisfied. Furthermore, the above matching is not so general. (Table 1)
3-2. Novel thermoelectric property of organometallic complex molecular materials
Efficiency of thermoelectric energy conversion is estimated by figure of merit, ZT. In order toincrease ZT, we can consider the following strategies (1) increasing Seebeck coefficient Se, (2)increasing electric conductance, (3) suppression of thermal conductance. However,simultaneous enhancement of (1) and (2) is generally difficult. Additionally, Wiedemann-Franz(WF) law tells us that enhancing electric conductance also increase electric thermal conductance.
Therefore, we have to consider validity of WF law, and possibly, design material (or devise
structure) violating WF law. When quantum dot is adopted as a device, one can expect giant
Seebeck coefficient by quantum confinement effect, interference effect of conducting MOs, andso on. In this sense, use of molecular junctions seems to be promising. However, electrictransport is sometimes tunneling in molecular conductors, in particularly, when quantum
interference effect is sufficiently large. It is well known that conductance reduces exponentiallyas a function of conductor length for tunneling transport. Since sufficient length of devise isrequired to make well-defined tangent of temperature in the devise, ZT (more strictly, power
factor) rapidly reduced in a practical devise even when thermal conductance is suppressed.
Recently, we found that long-range coherent tunneling is possible in organometallic
molecular wire theoretically. Thus, we focus on this long-range transport property and examine
design of thermoelectric devise via organometallic wire. For this purpose, we adopted
terpyridine complex of Ru connected to the electrode by S tom (Ru-complex) and analyzed
length dependence of ZT etc by calculations. Ru-complex has four nearly degenerated MOs
close to Fermi level. When we lengthen the wire (or stacking the layer) as the unit of
Ru-complex, the electric transmission coefficient spectra forms narrow overlapping resonancestructure. Since Se is determined by slope of transmission spectra as a function of energy,
narrow overlapping resonance enhances Se. Note that overlapping resonance also suggests
possibility of long-range coherent transport in thelow~middle temperature regime (~ 300 K). The above
enhancement mechanism of Se can be understand as theresult of quantum interference between four
quasi-degenerate tunneling orbitals. However, this isdifferent from giant Se by Fano resonance, which was
obtained by introducing side-chain group to a main
body organic conductor. In the view of a practicalmaterial design, the present approach has advantage
since chemical modification of the conductor is not
Figure 2
necessary and quantum interference effect is morerobust against molecular conformation change thanFano resonance.

147

Analysis of temperature dependence of Se is interesting because sign of Se relates to carrier.
As shown in Fig. 2, the sign changes by varying temperature, i.e., carrier (electron or hole)changes by varying temperature. This temperature dependence of sign of Se is characteristic
phenomenon of overlapping resonance of electric transport. On the contrary, the calculated ZT
is still much lower than the level expected as efficient thermoelectric devise in the low~middle
temperature regime (Figure 3) because electric conductance is relatively smaller than phonon
thermal conductance. To develop more practical organometallic molecular device, increasing
electric conductance (carrier concentration) by designing anchor moieties (contact chemistry)
will be promising with the strategy (3).

Figure 33-3. Inelastic transport and current-induced force at nano-contact
In sections 3-1 and 3-2, we showed studies of ballistic transport processes, where
electron-phonon interactions are omitted. In this section, we introduce our recent study of
inelastic electric current and current-induced ion migration (vibrational excitation) byelectron-phonon interactions. For this purpose, we focus on a current-induced reaction of
Melamine adsorbed on Cu(001) surface because it consists of fundamental processes to trigger
ion (atom) migration of energy-exchange by current-induced force. The force is often
considered as sum of field-driven and current-driven mean-field forces, and vibrational heating.
Although the system is simple, it can be a template to understand mechanism ofnano-fabrication, SET/REST nonvolatile memories like ReRAM, and so on.
Three conformations of melamine on Cu(001) can be switched by STM, which are labeled as
GS, C1, and C2, respectively, as shown in Fig. 4. In order to trigger reaction from theenergetically lowest state (GS) to C1, the required threshold voltage is 2.6V. This thresholdvoltage is much higher than height of reaction barrier and it is known that the reverse reaction(C1 to GS) is forbidden. On the contrary, transition between C1 and C2 states is reversible
reaction and the required voltage is in the broad range as [-1.0,1.-1.0] volt. Furthermore, thethreshold voltage to trigger the reaction is verylow.
In the present study, we focus on the three
mysteries: (1) why C1 → GS reaction isforbidden ? (2) what kind of force is driving force
for C1/C2 switching ? (3) what is physical originof the observed power law of reaction (C1 →C2) rate as a function of current ? We examine
our theoretical model and first principles
Figure 4
calculations to attack these mysteries.
Usually, the nonequilrbrium force acting on ions is classified to the field-driven force, wind148

force (current-driven force), and vibrational heating. The former two forces are summarized as
current-induced force and defined as Ehrenfest force by mean-field theory. Note thatcurrent-induced force can be defined rigorously; however, it cannot be divided into filed-driven
and wind force terms generally. Vibrational heating is non mean-field type force, i.e., kinetic
energy transfer by inelastic scatterings between conducting electron and ions.
First, we calculated current-induced force by NEGF-DFT with applying bias voltage andsearch the reaction path by nudged-elastic-band (NEB) method. By integrating current-induced
force along the reaction path, we construct nonequilibrium potential energy surface (PES).
The resulting bias-dependence of barrier height of C1/C2 transition is lower than 0.1 V evenwhen the applied bias is larger than 1.0 V. We applied the same procedure to GS/C1 andobtained similar result, i.e., change of barrier height by applying bias is very small. Hence, themain mechanism is vibrational heating.
As the next step, we calculated inelastic electron tunneling (IET) spectra for GS, C1, and C2
states, respectively. We found that one of strong peak positions of IETS of GS relates to thepromoting mode of GS→C1 transition. On the contrary, the promoting mode of C1→GS
transition is IETS inactive. This is direct evidence that C1→GS is forbidden as STM-induced
reaction. For C1/C2, we found that both of promoting modes of forward/backward reactions are
IETS active. Hence, we conclude that single mode vibrational heating model is sufficient toanalyze the current-induced mechanism and introduce rate equation approach, which is firstly
introduced as theoretical model of DIET/DIMET processes.

Figure 6

The vibrational excitation rate is evaluated by
NEGF-DFT results and parameterized to fit themodel. In Fig. 5 the reaction rate is plotted as a function of electric current for several fixed bias,
and clear power low behavior i.e., R(I) ∝ IN is obtained. Then we evaluated the power-order,N, and plotted as a function of bias voltage in Figure 6. The resulting bias dependence agrees
very well with those of experiment. The tendency of N (V) is explained by simple picture as
follows. When bias is increased, kinetic energy per one electron also increase: thus vibrational
excitation required for the reaction can be achieved by the scattering events with small numberof electrons. However, it is not straightforward that N relates to the average number of electrons
per reaction event because N is non-integer in most range and continuous function of V. Thisimplies that vibrational heating is quantum phenomenon not classical.
Figure 5149

3-4. Design of nonvolatile memory cell by first principles calculations
Finally, we show application of first principles transport calculations to design ReRAM cellconsisting of metal oxides. In the ReRAM device, the most simple cell structure consists ofmetal oxide (resistance layer) and metallic electrodes. The switching of SET/REST is controlledcontrolling by concentration of oxygen vacancy (Vo) in the resistance layer. To realize low
power cost for resistive switch, the device scale is now in sub 10 nm, which is close tomolecular electronics; thus quantum transport approach is applicable. Recently, someexperimental groups reported that that insertion of metal buffer layer improves SET/RESET(ON/OFF) ratio. Since distinct SET/RESET states are also key to power-saving read/write
processes as the memory, material design of buffer layer is highly desired. We adopted TiNelectrodes and HfO2 resistance layer. As buffer layer, we examined Ta, Hf, and Ti as well as nobuffer cell. We present schematic figure in Figure 7. When Vo is created in HfO2 layer, oxygenions (Ox) moved to the interface, i.e., the interface is oxidized. We include this oxidized effectto make ON state structure. The calculated IV curve of ON state is very close to that of OFF
state, i.e., not good performance as ReRAM. According to the calculated density of states of
HfO2 system (without electrodes), ON structure of the present model is sufficiently metallic.
Contact resistance at TiN surface and moved Ox ions frustrate electric transport through HfO2
(with Vo) conductor. IV characteristics of ReRAM cell consisting buffer layer is shown in
Figure. 8, where the metal buffer consists of only two atomic mono layers. Drastic improvementof distinct SET/REST states is found for all cases while ON/OFF ratio depends on materials.
Although the expected role of metal buffer layer was oxygen scavenger (i.e., reducing resistanceof SET state by rapid and high concentration of Vo), the present theoretical results suggest thatmetal buffer layer reduce contact resistance caused by Ox migration to the interface and thisimproves ReRAM performance. Recall that concentration of Vo in HfO2 is fixed for the all cellsof SET state, and that inserted buffer is only two atomic mono layers. The theoretical prediction
will change guiding principles to design ReRAM cell, in particular, sub 10nm scale device.

Figure 7
Figure 8

４ ． 	
 Selected publication list

1)

H. Nakamura, Y. Asai, J. Hihath, C. Bruot, and NJ. Tao, “Switch of conducting orbital bybias-induced electronic contact asymmetry in bipyrimidinyl-biphenyl diblock molecule:Mechanism to achieve pn directional molecular diode”, J. Phys. Chem. C, 115, 19931-19938(2011)

2)

K. Terada, H. Nakamura, K. Kanaizuka, M. Haga, Y. Asai, and T. Ishida, “Long Range
Electron Transport of Ruthenium-Centered Multilayer Films via Stepping-Stone Mechanism”，
ACS Nano 6，pp.1988-1999 (2012)

150

3)

R. Matsushita, M. Horikawa, Y. Naitoh, H. Nakamura, and M. Kiguchi, “Conductance and
SERS Measurement of Benzenedithiol Molecules Bridging Between Au Electrodes”, J. Phys.
Chem. C. 117, pp. 1791-1795 (2013)

4)

T. Hines, I. Diez-Perez, H. Nakamura, T. Shimazaki, Y. Asai, and N. Tao, “Controllingformation of single-molecule junctions by electrochemical reduction of diazonium terminalgroups”, J. Am. Chem. Soc.135 pp3319-3322 (2013)

5)

M. Kiguchi, Y. Takahashi, S. Fujii, M. Takase, T. Narita, M. Iyoda, M. Horikawa, Y. Naitoh,and H. Nakamura, “Additive Electron Pathway and Nonadditive Molecular Conductance byUsing a Multipodal Bridging Compound”，J. Phys. Chem. C 118，pp.5275-5283 (2014)

6)

H. Nakamura, T. Ohto, T. Ishida, and Y. Asai, “Thermoelectric Efficiency of Organometallic
Complex Wires via Quantum Resonance Effect and Long-Range Electric Transport
Property”, J. Am. Chem. Soc. 135, pp16545-16552 (2013)

7)

T. Ohto, I. Runger, K. Yamashita, H. Nakamura, and S. Sanvito, “Ab initio theory forcurrent-induced molecular switching: Melamine on Cu(001)”, Phys. Rev. B. 87, pp.
205439-1-7 (2013)

8)

K. Nishio, T. Miyazaki, and H. Nakamura, “Universal medium-range order of amorphous
metal oxide”, Phys. Rev. Lett. 111 pp155502 (2013)9)

Single Molecular Resistive Switch Obtained via Sliding Multiple Anchoring Points andVarying Effective Wire Length”M. Kiguchi, T. Ohto, K. Sugiyasu, S. Nakajima, M.
Takeuchi, and H. Nakamura, J. Am. Chem. Soc. 136, 7327-7332 (2014)10) “Additive Electron Pathway and Nonadditive Molecular Conductance by Using Multipodal
Bridging Compound”, M. Kiguchi, Y. Takahashi, S. Fujii, M. Takase, T. Narita, M. Iyoda, M.
Horikawa, Y. Naitoh, H. Nakamura, J. Phys. Chem. C., 118, 5275-5283 (2014)11) Design of ReRAM Cell Structure by Metal Buffer and Contact Engineering via
First-Principles Transport Calculation”Transport Calculation”, H. Nakamura, T.
Miyazaki, K. Nishio, H. Shima, H. Akinaga, and Y. Asai，Proceedings of IWCE 2014
(IEEE) (Paris 2014)151

Reactions analysis of plasma with self-assembled monolayer
Masanori Shinohara
Graduate School of Engineering, Nagasaki University
Abstract
We investigated an interaction between octadecyltrichlorosilane self-assembled monolayer and hydrogenplasma, with in-situ infrared absorption spectroscopy in multiple internal reflection geometry. The
molecular frame of –CH2–CH2– is etched by hydrogen plasma with the formation of CH3. The etching was
automatically stopped with the polymerization.
1．
．Introduction
Plasma processing is an inevitable tool for material processing such as semiconductor etching, surface
coatings and so on. Plasma is very complicated state, because it is a quasi-stable state and generates a lot ofkinds of radicals, ions and non-ionized neutral molecules. Then, the plasma–induced reaction is also very
complicated. In these days, much attention has been paid to the organic materials, including organic
semiconductor devices and bio-applications. These organic materials have complicated molecular
structures, compared with inorganic materials such as silicon, gallium arsenide. In the near future, plasma
processing will be required to these organic–materials processing. The reaction should be cleared forrealizing high-precision processing technology. Hence, the reaction analysis is difficult, because organic
materials and plasma are both complicated. Then, octadecyltrichlorosilane self-assembled monolayer(OTS–SAM) is adopted as the model materials for organic materials. Hydrogen plasma is adopted in thisstudy because hydrogen plasma is interesting for basic science and applied technology. In hydrogen plasmahydrogen radicals and ions are generated and they play an important role for various process. We
investigate and interaction between OTS–SAM and hydrogen plasma with in-situ infrared absorption
spectroscopy in multiple internal reflection geometry (MIR–IRAS). MIR-IRAS is powerful tool because it
can be used in-situ and real-time monitoring during plasma processing.

2. Experiment

RF power
Matching supply
network (13.56 MHz)A stainless steel chamber, maintained atless than 6.7 × 10–4 Pa was equippedwith an RF (13.56 MHz) plasma source,

Sample holder
H2

Plasmagas–feeding system and in-situ
MIR-IRAS measurement system. An
interferometer (JASCO), a HgCdTe

MIR prism as
the substrate

RF plasma
Glass tube

Thermocouple

Vacuum Pump system
IR(MCT) detector were used for
MIR-IRAS. The IR path was purged
with CO2–free dry air to reduce noise in

Fig. 1

152

IR
Concave
MirrorInterferometer

Experimental setup

MCT
detectorthe IR spectra because of H2O. The MIR prisms used in this study were made from n-type P-doped Si(100)wafers polished on both sides and had resistivity of approximately 10 Ω cm. The size of the prism was 10mm × 40 mm × 0.5 mm. After OTS–SAM was deposited on the chemical oxide covered prism, by
dropping 2.5 mM of OTS (Tokyo Chemical Industry) in toluene, the MIR prism was installed into thechamber. The prim was exposed to hydrogen plasma, generated by applying 30W of RF power at thehydrogen pressure of 6.7 Pa. The substrate was not applied to additional negative bias during plasma
exposure. Then, hydrogen ions should be annihilated near the substrate while the hydrogen radicals would
react with the SAM on the prism. The changes in chemical states were in-situ observed with MIR–IRAS.

3. Results and discussions
Fig. 2 shows the IR absorption spectra of the OTS–SAM exposed to hydrogen plasma in the C-H stretchingvibration region, compared with the as–deposited OTS–SAM. Then, the vertical axis indicates thedifference absorbance. Every spectrum shows three valleys (peaks in the negative direction) at
approximately 2850, 2915,and 2960 cm–1, and small shoulder in the negative direction at approximately
2900 cm–1. The peaks at 2850 and 2915 cm–1 correspond with CH2 components, and the peaks at 2960 cm–1
and the shoulder at 2900 cm–1 correspond with CH3. These indicates that the OTS–SAM were etched byhydrogen plasma exposure. Each peak was decreased with plasma exposure time.
In order to investigate decreasing feature of the peaks, the evolution of each maximum peak intensity wasplotted as a function of the plasma exposure time in Fig. 3, in a comparison with the as–deposited
OTS–SAM. The vertical axis indicates the residual peak intensity: Iresidual (%), which is denoted as follows;
Iresidual (%) = (Io – I decrease) / Io

(1)

where Io expresses the peak intensity acquired
1.5 min.

peak intensity in spectra acquired after plasma

5.5 min.

exposure. Iresidual indicates the residual portion

59.5 min.

Differencer absrobance

before plasma exposure and Idecrease expresses the(%) of each components on the prism. Each plot
indicates the decreasing features stop at a long–exposure time region and that the peak intensity
due to CH2 decreased more progressively than that
due to CH3. The peak intensity due to CH2
decreased into approximately 65 %. It is suggested
that each monomer become stable after

3200

approximately 6 species of CH2 per monomer isetched, considering OTS–SAM has 17 CH2
components per a monomer. The CH3 componentof the monomer should be preferentially etchedbecause it is located at the top of the monomer.
However, the CH3 component remains during

Fig. 2

3000
2800
-1
Frequency (cm )2600

IR absorption spectra of OTS-SAM

exposed to hydrogen plasma at different exposure
time in the C-H stretching vibration region,
compared with the spectrum of the as–deposited
OTS–SAM.

153

100

plasma exposure, indicating that the CH3-1component is generated by the hydrogen plasma: I(2960cm ), CH390

CH3–CH2–CH2– … –CH2–Si– + H →CH4 + –CH2–CH2– … –CH2–Si– (CH3
etching)(2)

Iresuidal (%)

exposure as follows:
80
70
60

–CH2–CH2– … –CH2–Si– + H →-1: I(2850cm ), CH2-1: I(2915cm ), CH 2

50

CH3–CH2– … –CH2–Si– (CH3 generation) (3)

40
0
10
20
30
40
50
60
Hydrogen plasama exposure time (min.)

These indicate that the after CH3 is hydrogenatedinto CH4 by hydrogen radical generated inhydrogen plasma, indicating that CH3 is etched

Fig.3

Evolution of each peak intensity as a(the model (2)). At the same moment remaining

function of hydrogen plasma exposure time

CH2 is hydrogenated into CH3 (the model (3)).
The stop of the etching cannot be explained withthe above model, which indicate the etching proceeds continuously.
Fig. 4 shows the IR absorption spectra in the low vibration region, in a comparison with the spectrum of the
as–deposited OTS–SAM. The peaks are observed at approximately at 1700 cm–1. The peak could bepossibility that the peaks are attributed to C=Obonds. However, we observed much broad peaks
due to C=O in the spectra acquired at the
OTS-SAM exposed to oxygen plasma. The peakintensity increased with the exposure time,
indicating that the polymerization would beoccurred with the formation of C=C bonds
during plasma exposure. the =CH, alkene
components would be generated by hydrogen

Difference absorbance (arb. units)

attributed to C=C bonds, although it has

59.5 min.

5.5 min.
1.5 min.

abstraction from the CH2 alkyl components of1900

the monomer, as follows;

1800–CH2–CH2– … –CH2–Si– + H →=CH–CH2– … –CH2–Si– + H2

(4)

Two =CH would coalesce to form C=C bonds inthe monomer. The polymerization would prevent
the OTS–SAM from being etched any more.

Fig.4

IR

1700
1600
-1
Frequency (cm )1500

absorption spectra of OTS-SAM

exposed to hydrogen plasma at different exposure
time in low vibration region (C=C region),compared with the spectrum of the as–deposited
OTS–SAM.

Conclusion154

We investigate an interaction between OTS–SAM and hydrogen plasma in order to understand a reaction
between organic molecules and plasmas, with MIR–IRAS. The IR absorption data showed OTS–SAM wasetched by hydrogen plasma with hydrogenation. The etching would automatically stopped with thepolymerization of the monomer during plasma exposure.

Reviewed Journal Paper
1) M. Shinohara, N. Maruno, Y. Yoshida, Y. Taniguchi, K. Ito, Y. Nakano, Y. Matsuda, H. Fujiyama,"Infrared spectroscopic study on reactions of octadecyltrichlorosilane self-assembled monolayer with
Plasmas," Jpn. J. Appl. Phys. Vol. 54 No. 1 (2015) 01AB04-1 (6 pages).
2) M. Shinohara, K. Amano, N. Maruno, Y. Yoshida, Y. Matsuda and H. Fujiyama, "Infrared Absorption
Spectroscopic Study on Reaction between Self-Assembled Monolayers and Atmospheric-Pressure Plasma,"J. Spectroscopy Vol. 2015 (2015) 417024 (7 pages).
3) M. Shinohara, Y. Taniguchi, Y. Takaki, Y. Matsuda, H. Fujiyama, "Adsorption of hydrocarbon
components generated in deuterated benzene plasma studied by in situ real-time infrared absorption
spectroscopy," Jpn. J. Appl. Phys. Vol.53 No.9 (2014) 096202 (6 pages).
4) M. Shinohara, T. Kawakami, K. Hara, S. Yagi, Y. Matsuda, H. Fujiyama, "Reactions of Surface
Hydrogen on Amorphous Carbon Films with Hydrogen Plasma," Jpn. J. Appl. Phys. Vol. 53 (2014) 010204(6 pages).
5) M. Shinohara, A. Fuakae, K. Amano, Y. Yoshida, Y. Matsuda, H. Fujiyama, "Development of an in-situ
infrared spectroscopic measurement of plasma-induced reactions in ethanol," Jpn. J. Appl. Phys. Vol. 52(2013) 11NC06 (5 pages).

Invited Tutorial Paper
1) M. Shinohara, Y. Matsuda, H. Fujiyama, "Deposition Process and Its Surface Reactions of an
Amorphous Carbon Film," The Journal of The Institute of Electrical Engineers of Japan
Vol. 135 No. 3 (2015) pp.139-141.
2) M. Shinohara, J. Kim, "Recent Trends of Plasma Engineering: –Infrared Spectroscopy of Plasma Process
and Plasma Processing in Graphene Research–," IEEJ Transactions on Fundamentals and Materials Vol.
134 No. 1 (2014) pp. 41-46.

Invited Talk
1) M. Shinohara, S. Yagi, Y. Taniguchi, N. Maruno, Y. Yoshida, Y. Matsuda, H. Fujiyama, "Infrared
spectroscopy of reactions induced by plasma," Atomic and molecular data forum (2013.10), National
Institute for Fusion Science.

155

Part III
Beyond Density-Functional Theory

Frontiers of Ab Initio Effective Models and Correlation Science
Masatoshi Imada1, Takashi Miyake2, Kazuma Nakamura3, Tamio Oguchi4,
Ryotaro Arita5, Shoji Ishibashi2, A Fujimori1, Shik Shin1
University of Tokyo1, AIST2, Kyushu Institute of Technology3, Osaka University4, RIKEN5
The main purpose of this project is to develop ab initio accurate schemes applicable toelectronic structure calculation of strongly correlated electron systems that are known to hamper
applications of conventional ab initio approaches such as the density functional theory (DFT).
The second purpose is to apply the developed methods to challenging issues in condensed
matter physics.
Among others, by utilizing a hierarchical energy structure of strongly correlated electron
systems, we have developed an ab initio downfolding scheme called multi-scale ab initio
scheme for correlated electrons (MACE) to make it possible understanding electronic propertiesof strongly correlated electron systems. In the scheme of MACE, we first calculate the global
band structures for target materials, in which the high energy electrons far away from the Fermi
level do not contain strong correlations effects and allows the conventional DFT. This part canbe performed by the local density approximation (LDA) in the DFT, or alternatively the GW
method. Then, we eliminate high-energy degrees of freedom by using the constrained
random-phase-approximation (cRPA) method and obtain the low-energy effective model. To
solve the ab initio low-energy effective models, we use various low-energy solvers such as
many-variable variational Monte Carlo method and cluster extensions of the dynamical
mean-field theory, which properly take into account both spatial and dynamical quantum
fluctuations. This scheme has made it possible to clarify electronic properties of strongly correlated
electrons accurately by low computational load. In this project, we have developed dimensional
downfolding method, a method to treat dynamical screened interaction, and implemented to treat the
spin-orbit interaction in the scheme. The applications include high-temperature superconductors
including the iron-based, cuprate and fullerene superconductors and other superconductors such asaromatic and nitride compounds. We have also applied to organic conductors,
alkali-cluster-loaded-zeolites, and systems with strong spin-orbit interaction such iridium oxides. We
have also made progress in analyzing the experimental data of photoemission experiments onmaterials such as high-Tc superconductors by the collaboration of experimentalists and theory group.
Below, some of our achievements in our project are described.

(1) Mechanism of superconductivity in iron-based superconductors [2011-1),
2012-4), 2014-4)]
In iron-based superconductors, although it is believed that electron correlations and orbital
degrees of freedom play key roles in stabilizing high-temperature superconductivity, their roles
are not fully understood yet. To clarify microscopic mechanism of superconductivity iniron-based superconductors, it is necessary to evaluate strength of interactions in an ab initio
way and it is also necessary to seriously examine the effects of electronic correlations. To
challenge these issues, we employ ab initio downfolding scheme called multi-scale ab initio
scheme for correlated electrons (MACE). We apply this method to the iron-based
superconductors [1-4]. As a result, we show that the calculated magnetic order was shown tocorrectly reproduce the experimental material dependences [2,3]. By extending these normal
state studies, we show that superconductivity emerges in the ab initio model of anelectron-doped iron-based superconductor LaFeAsO in essential agreement with theexperimental results [4]. The pairing satisfies gapped s± symmetry and the specific orbital156

(X2-Y2) is shown to play a key role in stabilizing thesuperconducting phase as well as the antiferromagnetic
phase. Then, we find a one-to-one correspondence
between superconductivity and enhanced uniform
chargefluctuations.
Similarone-to-one
correspondence is also found in the Hubbard model [5],which is one of the simplest models for cuprates.
Despite many differences between iron-based
superconductors and cuprates, our study suggests thatthe enhanced uniform charge fluctuations play a keyrole in stabilizing the superconductivity in both
Fig.1: Phase diagram of LaFeAsO
materials.
in agreement with the experimental[1] T. Miyake, K. Nakamura, R. Arita, and M. Imada, J.
phase diagram.  is the interaction
Phys. Soc. Jpn. 79, 044705 (2010).
strength and  is the doping[2] T. Misawa, K. Nakamura, and M. Imada, J. Phys.
concentration.
Soc. Jpn. 80, 023704 (2011).
[3] T. Misawa, K. Nakamura, and M. Imada, Phys. Rev. Lett. 108, 177007 (2012).
[4] T. Misawa and M. Imada, Nat. Commun. 5, 5738 (1-11) (2014).
[5] T. Misawa and M. Imada, Phys. Rev. B 90, 115137 (2014).

(2) Ab initio studies of iridium oxides [2012-2), 2014-3), 2014-3)]
Iridium oxides offer several different
aspects of the interplay between the spin
orbit interaction and the electron
correlation. we have studied there
different families of compounds as
detailed below:
Ab initio analyses of A2IrO4 (A=Sr,
Ba): Effective Hubbard-type models for Ir
5d t2g manifolds downfolded from theglobal band structure are solved based on
the dynamical mean-field theory. The
results for A=Sr and Ba correctly
reproduceparamagnetic
metalsundergoing continuous transitions to
Fig.2: Ab initio results of properties reproduced forinsulators below the N´eel temperature.
Na2IrO3: (a) Zig zagmagnetic structure. Temperature
These compounds are classified not into
dependences of (b) specific heat and (c) magnetic
Mott insulators but into Slater insulators.
susceptibility
However, the insulating gap opens by asynergy of the Neel order and significant band renormalization, which is also manifested by a
2D bad metallic behavior in the paramagnetic phase near the quantum criticality.
Topological properties of R2Ir2O7: We have theoretically shown that an emergent
two-dimensional metal embedded in the bulk insulator is realized at a magnetic domain wall ofR2Ir2O7. The domain wall has long been studied as ingredients of both old-fashioned andleading-edge spintronics. The domain wall here, as an interface of seemingly trivial
antiferromagnetic insulators, emergently realizes a functional interface preserved by zero modes
with robust two-dimensional Fermi surfaces, where pyrochlore iridium oxides proposed to hostcondensed-matter realization of Weyl fermions offer such examples at low temperatures. The

157

existence of ingap states pinned at domain walls, theoretically resembling spin/charge solitonsin polyacetylene, solves experimental puzzles observed in R2Ir2O7 with rare earth elements R.
The domain wall realizes a novel quantum confinement of electrons and embosses a net uniform
magnetization, which enables magnetic control of electronic interface transports beyond
semiconductor paradigm.
Studies on ab initio effective low-energy Hamiltonian of iridium oxide Na2IrO3: The model
has been reduced to an effective spin model on a honeycomb lattice by the strong coupling
expansion. We have shown that the ab initio model contains spin-spin anisotropic exchange
terms in addition to the extensively studied Kitaev and Heisenberg exchange interactions, andallows us to describe the experimentally observed zigzag magnetic order, interpreted as the statestabilized by the antiferromagnetic coupling of the ferromagnetic chains. Possible routes torealize quantum spin liquids from existing Na2IrO3 have been proposed.

(3) Electron-phonon interaction implemented in the low-energy solver [2014-1)]
We have developed a variational Monte Carlo (VMC) method for electron-phonon coupledsystems. we propose a variational wave function with a large number of variational parameters,
which is suitable and tractable for systems with electron-phonon coupling. In the proposed wave
function, we implement an unexplored electron-phonon correlation factor, which takes into
account the effect of the entanglement between electrons and phonons. The method has been
applied to systems with diagonal electron-phonon interactions, i.e., interactions between charge
densities and lattice displacements (phonons). As benchmarks, we compare VMC results withprevious results obtained by the exact diagonalization, the Green function Monte Carlo method
and the density matrix renormalization group for the Holstein and Holstein-Hubbard model.
From these benchmarks, we show that the present method offers an efficient way to treat
strongly coupled electron-phonon systems.

(4) Ca4Al2O6Fe2As2 superconductor [2011-2)]
It was pointed out in the early stage of iron-based superconductor research that the transition
temperature has strong correlation with the bond angle between Fe and anion atoms, .
Ca4Al2O6Fe2As2 is known for the smallest  among iron-based superconductors Our
first-principles calculations clarified that the number of the Fermi surfaces around the Gamma
point is smaller in Ca4Al2O6Fe2As2 than that in LaFeAsO. As  is hypothetically increased, thestate 0.5 eV below the Fermi level, having xy character, is pulled up. It crosses the Fermi level,
and a hole-like Fermi surface appears. As  is increased further, the orbital energy becomesequal to that of the degenerate point at 0.2 eV, and band rearrangement takes place. The present
result suggests that  affects the superconducting transition temperature through the change inthe Fermi surfaces.

(5) Aromatic compounds [2011-3)]
It was reported experimentally that aromatic compounds such as picene andcoronene become superconducting by alkali-metal doping. We have carried out
density-functional calculation of picene and coronene. We found that pristinecompounds are gapful. The conduction band consists of LUMO and LUMO+1 of theisolated molecules. In potassium-doped picene, the intralayer site is more stable than theinterlayer site.
(6) Effects of nonlocal correlation and dynamic screening [2012-8), 2012-9),
2012-10), 2013-3)]

158

The LDA+DMFT method is widely used as a standard tool for correlated materials.
The self-energy is approximated to be local in DMFT, and the Hubbard-U is assumed to
be static in the usual scheme. We have developed a LDA+DMFT scheme to treat
dynamic U, and applied the technique, combined with the constrained RPA, toBaFe2As2. The dynamic U effect enhances the electron correlation effect, and thesystem becomes strongly correlated as hole carriers increase. We have also proposed ascheme to renormalize the dynamic U effect into one-body term of the Hamiltonian. We
also studied the competition between the non-local self-energy effect and dynamic U
effect in the GW approximation. Application to SrVO3 shows that the quasiparticle
bandstructure is over renormalized when k-dependence of the self-energy is neglected.
It is partially cancelled by the static U approximation. In order to include bothk-dependence of the self-energy and dynamic U effect, we have developed ab-initio
GW+DMFT scheme and applied the method to SrVO3.
(7) Pyrochlore compounds [2012-7)]
We have implemented
relativistic DFT scheme
based on the two-component
spinor formalism in the
QMAS code, and improved
numerical convergence fortheself-consistentcalculation by changing acharge-mixing
scheme,implementing
penaltyFig.3: Magnetic structure of Pyrochlore oxides and its phasefunction
for
the
spin
momentdiagrametc. We have applied the method to a pyrochlore oxide Cd2Os2O7, and found that thematerial is an antiferromagnetic insulator in the LDA+U+SO with a reasonable value of
U. The all-in/all-out magnetic order is the most stable state, in consistent withexperimental observation. The single-ion anisotropy is comparable to the exchange
coupling, and is stronger than the Dzyaloshinskii-Moriya interaction. In Y2Mo2O7, on
the other hand, there is a peculiar competition between magnetic states. The effective
spin interactions are distinct from the simple Heisenberg form and strongly spin
anisotropic in spin space.
(8) Rare-earth permanent magnet [2013-3), 2015-2)]
N

Ti
c
Fe
a

Nd

b

Fig:4: Electron density of NdFe11TiN extended in the
direction of N triggered by nitrogenation leading to theenhanced magnetization and the increased uniaxiality.
159

Large magnetization and highcoercivity are required for strong
permanent magnets, and the latterhas positive correlation withmagnetocrystalline anisotropy. In
order to search for new permanent
magnet compounds, we havestudiedNdFe11TiN
byfirst-principles calculations using
QMAS
code.
Interstitial
nitrogenation increases electron
density between Nd and N.

Feeling Coulomb repulsion from the electron density, the Nd-f electrons are extended
in the ab directions. It induces uniaxial magnetic anisotropy. This has been confirmed
semi-quantitatively by the calculation of the crystal-field-effect parameter, A20.
Nitrogenation also enhances magnetization, whereas titanium substitution decreases
magnetization substantially. These results suggest that NdFe12N has better magnetic
properties than NdFe11TiN. Subsequent to our work, NdFe12N film has been
experimentally synthesized on top of W underlayer on MgO substrate, and it was foundto have larger magnetization and higher anisotropy field than Nd2Fe14B for wide
temperature range between room temperature and the Curie temperature.
(9) Developments of ab initio technique for deriving low-dimensional models[2010-1)]
An ab initio downfolding
method is formulated toconstruct low-dimensionalmodels. In addition to band
downfoldingbyaconstrained random phaseapproximation formulated
for 3D models, screening
away from the target layer
Fig.5: Left: Schematic diagram for effective interactions(chain) is further involved.
between electrons at r1 and r2 in the target layer, screened by
Eliminating the off-target
interlayer polarizations at r and r’. Right:
Calculateddegrees of freedom, namely,
2D-constrained RPA screened Coulomb interactions (green) ofdimensional downfolding,
LaFeAsO. Usual 3D-constraied RPA (blue) and full RPA (red)yieldsab
initioresults are also shown.
low-dimensionalmodels.
The method is applied to derive a 2D model for the layered superconductor LaFeAsO, whereinterlayer screening crucially makes the effective interaction short-ranged and reduces the onsite
Coulomb interactions by 10 –20% compared with the 3D model for the five iron-3d orbitals.

(10) Ab initio derivation of two-dimensional models of organic compounds [2012-1),
2012-6)]
With the above developed technique, we derived ab initio two-dimensional extended
Hubbard-type multiband models for EtMe3Sb[Pd(dmit)2]2 and κ-(BEDT-TTF)2Cu(NCS)2. The
HOMO antibonding band of the Pd(dmit)2 salt has a triangular structure of the transfers with a
one-dimensional anisotropy, in contrast to the nearly equilateral triangular structure predicted in
the past extended Huckel results. The ratio of the larger interchain transfer tb to the intrachaintransfer ta is around tb/ta ∼0.82. The derived screened onsite interaction U and the largest
offsite interaction V are ∼0.7 and ∼0.23 eV, respectively, for EtMe3Sb[Pd(dmit)2]2 and ∼0.8
and ∼0.2 eV for κ-(BEDT-TTF)2Cu(NCS)2. These values are large enough compared totransfers t as ∼55 meV for the Pd(dmit)2 salt and ∼65 meV for the κ-BEDT-TTF one, and theresulting large correlation strength (U−V )/t ∼ 10 indicates that the present compounds areclassified as the strongly correlated electron systems.

(11) Ab initio derivation of impurity models for iron-based superconductors

160

We also studied abinitio impurity models tounderstand
impurityeffects in iron-based
superconductors.
Effective
tight-binding
Hamiltonians for the dbands of LaFeAsO withvarious transition-metal
Fig.6: Atomic geometry and anti-bonding HOMO Wannier
impurities such as Mn, Co,
functions for organic compounds. Left: EtMe3Sb[Pd(dmit)2]2.
Ni, Zn, and Ru are
Right: κ-(BEDT-TTF)2Cu(NCS)2.
constructed.
Localelectronic
structures
around the impurity are quantitatively characterized by their onsite potential and transfer
hoppings to neighboring sites. We found that the impurities are classified into three groups
according to the derived parameters: For Mn, Co, and Ni, their impurity 3d levels measured
from the Fe 3d level are nearly, 0.3, −0.3, and −0.8 eV, respectively, while, for the Zn case, the dlevel is considerably deep as −8 eV. We also showed that, while excess carriers are tightly
trapped around the impurity site (due to the Friedel sum rule), there is a rigid shift of band
structure near the Fermi level, which has the same effect as carrier Doping.

Fig.7: Left: Isosurface contours of maximally localized Wannier functions for dxy orbital of the
impurity atom in La(Fe0.944Co0.056)AsO. Right: Comparison of electronic density of states(EDOS) for La(Fe0.944M0.056)AsO with M=Mn (red), Fe (green), Co (blue), and Ni (pink).

(12) Ab initio GW calculations for plasmon effects in the organic compound[2013-4)]
We developed an ab initio massively parallelized GW codes capable of being treated large
systems. With this code, we performed calculations to study dynamical effects on an organic
compound (TMTSF)2PF6. Calculated polarized reflectivities reproduce experimental plasmaedges at around 1.0 eV and 0.2 eV along the a and b axes, respectively. These low-energy
plasmons come out from the low-energy narrow bands energetically isolated from otherhigher-energy bands, and affect the low-energy electronic structure via the GW-type self-energy.
Because of the quasi-one-dimensional band structure, a distinct plasmaron state is observed
along the Y-G line and a large plasmon-induced electron scattering is found in the low-energy
occupied states along the X-M line.

161

Fig.8: Ab initio GW spectral functions. Red is density-functional band energies. Left: Organic
compounds (TMTSF)2PF6. Right: Transition-metal oxide SrVO3.

(13) Mechanism of high Tc superconductivity in alkali-doped fullerides [2012-11),
2014-6)]
Superconductivity in alkali-doped fullerides (A3C60) is of great interest in particular due toits high transition temperature (Tc) that is the highest among molecular solids. In the phase
diagram, the superconducting phase resides next to a Mott-insulating phase. While this situation
is similar to that of cuprates, superconductivity in A3C60 is more surprising, since the gap
function has an on-site s-wave symmetry for which one usually expects that local electron
correlations causing the Mott-Hubbard transition severely suppress its Tc., To clarify thisnon-trivial pairing mechanism of A3C60, we performed first-principles studies based onsuperconducting density functional theory (SCDFT) and multi-energy ab initio scheme forcorrelated electron systems (MACE).
SCDFT is an extension of DFT for normal states to superconducting states. There, theKohn-Sham equation is extended to the Kohn-Sham Bogoliubov-de Gennes equation fromwhich the linearized gap equation is derived. In 2005, a kernel for the gap equation in SCDFT isformulated and has been applied to many conventional superconductors. There, it has been
demonstrated that the experimental Tcs are accurately reproduced. Using the same kernel, we
performed SCDFT calculations for K3C60, Rb3C60 and Cs3C60. We found that SCDFT
systematically underestimates their Tc. This result suggests that we have to go beyond thestandard Migdal-Eliashberg theory to understand high Tc in A3C60 [1].
In MACE, we start with a derivation of an effective low-energy model for the t1u bandaround the Fermi level. Using the constrained random phase approximation (cRPA), we firstevaluated the values of interaction parameters, such as the Hubbard U and the Hund’s coupling
JH. We found that U is ~1eV, which is larger than the band width. Interestingly, U is larger forsystems having higher Tc. This trend cannot be understood in terms of the Migdal-Eliashberg
theory. We also found that the ratio JH/U is as small as 5%, which is much smaller than that oftransition metal compounds. Thus there is an interesting possibility that the Hund’s rule can beinverted by the exchange coupling (JJT) due to the Jahn-Teller effect [2].
To estimate the size of JJT and investigate the subtle competition between JH and JJT, one
needs to derive a low energy model with phonons. To this end, we formulated a new scheme,
which we call constrained density functional perturbation theory (cDFPT). There, we canestimate the size of electron-phonon coupling and phonon frequencies in the effective
Hamiltonian without including the screening effect of low-energy electrons. [3]We applied this new method to A3C60. We found that JJT is always larger than JH. In thissituation, we can expect that intra-orbital pairing is significantly enhanced. We then solved theeffective model by means of the extended dynamical mean field theory. We obtained a phase162

diagram and succeeded in reproducing the various phases observed in the experiment, including
the s-wave superconducting phase and the Mott insulating phase, at a quantitative level. [4][1] R. Akashi and R. Arita, Phys. Rev. B 88 054510 (2013)[2] Y. Nomura, K. Nakamura and R. Arita, Phys. Rev. B 85 155452 (2012)[3] Y. Nomura, K. Nakamura and R. Arita, Phys. Rev. Lett. 112 027002 (2014)[4] Y. Nomura, phD thesis, University of Tokyo (2015)(14) Development of superconducting density functional theory for plasmon
mechanism [2013-5), 2013-6)]
We extended SCDFT to take account of the dynamical structure of the screened Coulombinteraction and electron-hole asymmetry in the electronic structure. Through an application to
fcc lithium under high pressures, we demonstrate that the new kernel in the gap equation
improves the agreement between the calculated and experimentally observed Tc. [1][1] R. Akashi and R. Arita, Phys. Rev. B 88, 014514 (1-12) (2013), Phys. Rev. Lett. 111, 057006(1-5) (2013).

(15) Development of HiLAPW code and its applications to Rashba surface systems
and topological insulators [2013-8), 2014-8)]
Aims of our group in this project are twofold: a development of new methods to enhance thecapability of our density-functional-theory code HiLAPW and applications of the code to avariety of novel materials. One of the distinguished achievements in the methodologicaldevelopment is the proposal of an efficient and accurate formula for stress tensor calculations
within the all-electron full-potential linearized augmented plane-wave (FLAPW) method. We
have shown that the adoption of the Soler-Williams type basis in the FLAPW formalism results
in a much simpler and robust expression of the stress tensor.
Applications of the HiLAPW code have been made mostly for novel materials andphenomena such as Rashba surface systems and topological insulators. The most impact result
achieved is to clarify that the origin of weak Rashba-like band structure observed in Bi(111) thinfilms by an angle-resolved photoemission spectroscopy (ARPES) experiment is
one-dimensional (1D) edge states of triangular bi-layer islands on the surface. Calculated band
dispersions and spin-polarizations are consistent with the measured ARPES results. Anotherpronounced result can be seen in the electronic structure calculation for Au wires on Si(557)
surface. It is shown that Rashba 1D metallic bands are formed not only from Au-6s orbitals but
also Au-5d and neighboring Si-3p orbitals, leading to large spin-orbit origin out-of-plane spinpolarization due to asymmetric electron density around the Au atoms by hybridization oforbitals with different parity. Peculiar electronic structure found in Bi overlayer on athree-dimensional topological insulator TlBiSe2 has been successfully explained as a proximity
effect due to spin-dependent hybridization between Bi layers and TlBiSe2 surface.

(16) Single-component organic conductors [2014-12)]
Conventional organic metals consist of more than two kinds of molecules. Their metallic natureis brought by charge transfer between different molecules. The discovery of the firstsingle-component molecular metal Ni(tmdt)2 (tmdt = trimethylenetetrathiafulvalenedithiolate)[1] has opened a new paradigm. Subsequently, various related compounds have beensynthesized. They form a new class of materials named “single-component molecular metals(SCMM)”.
We have studied electronic structures of several SCMM's by means of first-principles
calculations [2]. First, we investigated the central metal dependence of the character of163

electronic states around HOMO (or SOMO) and LUMO for isolated molecules. It has beenfound that the energy level of the pdσ(-) state shfts systematically depending on the central
metal. We have also calculated electronic structures of their solid forms and revealed that band
dispersion in the vicinity of the Fermi level for each solid reflects the electronic states of thecorresponding isolated molecule. It should be noted that the relative energy level of the pdσ(-)
state is one of predominant factors to control the electronic properties of the solid form.
[1] H. Tanaka et al., Science 291, 285 (2001).
[2] S. Ishibashi and K. Terakura, Crystals 2, 1210 (2012).

(17) Exotic ferroelectricity in tetrathiafulvalene-p-chloranil [2014-7)]
For the organic ferroelectric tetrathiafulvalene-p-chloranil (TTF-CA), theoretical calculations
based on the Berry phase technique predicted large values of spontaneous polarization (8~10μC/cm2) [1,2] though experimental confirmation was difficult because of leakage current.
Recently, Kobayashi et al. successfully obtained a value of 6.3 μC/cm2 [3]. In addition, theyfound that the polarization is more than 20 times larger compared with that of the point charge
model and their directions are opposite [3]. We investigate details of the electronic structure andthe origin of exotic ferroelectricity in TTF-CA in terms of effective charges andmaximally-localized Wannier orbitals (MLWOs) from first-principles calculations.
In the crystal unit cell, there are two TTF molecules and two CA molecules forming twoheterogeneous columns along the a-axis. There is a partial charge transfer between the
TTF-HOMO and the CA-LUMO forming four electronic bands below and above the band gap[1]. Calculations were performed on the 90 K paraelectric structure (described as λ=0) and the
40 K ferroelectric structure (λ=1) [4] and their interpolations (λ=0.1, 0.2, … , 0.9). Moleculareffective charges are defined as sums of Born effective charges for the constituent atoms. We
have found that the molecular effective-charge-tensor components associated with thepolarization show unusually large variations with λ and that two topmost occupied bands are
responsible for these behaviors. We constructed MLWOs from the four bands in the vicinity ofthe band gap as well as from the two topmost occupied bands. The MLWOs from the four bands
have TTF-HOMO-like or CA-LUMO-like shapes while those from the two bands look likelinear combinations of the TTF-HOMO at the center and the CA-LUMOs on both sides. From
analyses using these MLWOs, we propose a physically transparent picture to understand themechanism of covalency-induced electronic polarization [5].
[1] S. Ishibashi and K. Terakura, Physica B (Amsterdam) 405, S338 (2010).
[2] G. Giovannetti et al., Phys. Rev. Lett. 103, 266401 (2009).
[3] K. Kobayashi et al., Phys. Rev. Lett. 108, 237601 (2012).
[4] M. Le Cointe et al., Phys. Rev. B 51, 3374 (1995).
[5] S. Ishibashi and K. Terakura, J. Phys. Soc. Jpn. 83, 073702 (2014).

(18) Electron correlation in the Fermi-liquid system SrVO3 and the Hund’s metal
SrMoO3 [2014-9)]
A prototypical correlated system with d1 electronic configuration, SrVO3, has been studied by
ARPES using high-quality single-crystalline films epitaxially grown on SrTiO3 substrates. Low(~60 meV) and high energy (~0.3 eV) kinks were observed in band dispersions, which we
attribute to electron-phonon interaction and electron correlation, respectively. Through the
Kramers-Kronig transformation of photoemission spectra in a self-consistent cycle, we obtained
the electron self-energy over a wide energy range including the incoherent (lower
Hubbard-band) feature. The d2 electron system SrMoO3 has also been studied by hard x-ray
photoemission spectroscopy. In contrast to SrVO3, the spectra did not show a clear signature of164

electron correlation in spite of the enhanced electronic specific heat. These apparently
conflicting observations were consistently explained within the “Hund’s metal” scenario andwere corroborated by DMFT calculations on the d2 electronic configuration.

(19) Atom substitution effects in Fe-based superconductors [2013-9)]
Effects of transition-metal atom substitution for Fe atoms in Fe-based superconductors havebeen studied by ARPES measurements of Ba(Fe1-xMx)2As2 (M = Mn, Co, Ni, Cu, Zn). On theelectron doping side (M = Co, Ni, Cu, Zn), the Fermi surface volume was found to be graduallydeviated from prediction by the rigid-band model and concomitantly deep 3d states were formed.
For M = Zn, the antiferromagnetic band structure of the parent compound was perfectlyconserved, indicating that no electron doping occurred at all. We attribute this to the formationof a fully occupied Zn 3d band well below EF and hence the stable valence of Zn2+.As for thehole-doped side (M = Mn), too, hole doping did not occur, which we attribute to the stablehalf-filled Mn 3d shell, namely, the stable valence of Mn2+.

(20) Fermi surfaces and superconducting gap anisotropy
superconductors [2012-16), 2014-10), 2014-12), 2014-13)]inFe-basedIn order to elucidate the origin of the nodal superconducting behavior of BaFe2(As1-xPx)2, wehave studied the Fermi surfaces and the superconducting gaps of this compound by ARPES. We
did not find line nodes on the hole Fermi surfaces but a significant gap anisotropy on theelectron Fermi surfaces. As for SrFe2(As1-xPx)2, which has a shorter c-axis parameter than the Bacompound, one of the three hole Fermi surface became more three-dimensional, and thesuperconducting gap showed different behaviors.
In iron-pnictide superconductivity, the interband interaction between the hole and electron
Fermi surfaces (FSs) is believed to play an important role. However, KFe2As2 has threezone-centered hole FSs and no electron FS but still exhibits superconductivity. Our
ultrahigh-resolution laser angle-resolved photoemission spectroscopy unveils that KFe2As2 is a
nodal s-wave superconductor with highly unusual FS-selective multi-gap structure: a nodelessgap on the inner FS, an unconventional gap with “octet-line nodes” on the middle FS, and analmost-zero gap on the outer FS. This gap structure may arise from the frustration between
competing pairing interactions on the hole FSs causing the eightfold sign reversal. Our results
suggest that the A1g superconducting symmetry is universal in iron-pnictides, in spite of thevariety of gap functions.
We have also investigated the superconducting (SC)-gap anisotropy for several Ba-doped
KFe2As2 samples using laser-based angle-resolved photoemission spectroscopy.We show that
the SC-gap anisotropy and node positions drastically change with a small amount of Ba doping.
Our results totally exclude a possibility of d-wave symmetry and strongly suggest that both spinand orbital fluctuations are important for the pairing interaction in the Ba-doped KFe2As2.
We performed a laser angle-resolved photoemission spectroscopy (ARPES) study on awide
doping range of the Ba1−xKxFe2As2 (BaK) iron-based superconductor. We observed a robust
low-binding energy (BE) kink structure (kink1) in the dispersion which is doping dependent
whereby its energy peaks at the optimally doped level (x ∼ 0.4) and decreases towards theunderdoped and overdoped sides. We attribute this kink to electron-mode coupling in good
agreement with the inelastic neutron scattering (INS) and scanning tunneling microscopy (STM)
results on the same compound where a similar bosonic mode associated with spin excitations
was observed. The relation between the mode energy (Ω) and the SC transition temperature (Tc)
deduced from our laser ARPES data follow the universal relation deduced from INS and STM.
In addition, we could resolve another kink at higher BE (kink2) showing less doping and165

temperature dependence compared to kink1 and which thus may be of different origin.

Selected Publication list
20101) K. Nakamura, Y. Yoshimoto, Y. Nohara, M. Imada, "Ab initio Low-Dimensional Physics Opened
Up by Dimensional Downfolding: Application to LaFeAsO", J. Phys. Soc. Jpn. 79 (2010)
123708(1-4).
2) M. Imada, T. Miyake, "Electronic Structure Calculation by First Principles for Strongly CorrelatedElectron Systems" , J. Phys. Soc. Jpn. 79 (2010) 112001(1-42).
3) Takashi Miyake, Taichi Kosugi, Shoji Ishibashi and Kiyoyuki Terakura, “Electronic Structure ofNovel Superconductor Ca4Al2O6Fe2As2” J. Phys. Soc. Jpn. 79, 123713 (1-4) (2010).

2011
1) Takahiro Misawa, Kazuma Nakamura, Masatoshi Imada, "Magnetic Properties of Ab initio Modelfor Iron-Based Superconductors LaFeAsO",J. Phys. Soc. Jpn. 80 (2011) 023704(1-4).
2) Taichi Kosugi, Takashi Miyake, and Shoji Ishibashi, “First-principles Electronic Structure ofSuperconductor Ca4Al2O6Fe2P2: Comparison with LaFePO and Ca4Al2O6Fe2As2”, J. Phys. Soc. Jpn.
81, 014701 (1-7) (2012).
3) T. Kosugi, T. Miyake, S. Ishibashi, R. Arita and H. Aoki, “Ab initio electronic structure of solid
coronene: Differences from and commonalities to picene”, Phys. Rev. B 84, 020507(R) (1-4) (2011).
4) Yu-ichiro Matsushita, Kazuma Nakamura, Atsushi Oshiyama, “Comparative study of hybrid
functionals applied to structural and electronic properties of semiconductors and insulators”, Phys.
Rev. B 84, 075205 (1-13) (2011).
5) Yoshiro Nohara, Kazuma Nakamura, Ryotaro Arita, “Ab initio Derivation of Correlated
Superatom Model for Potassium Loaded Zeolite A”, J. Phys. Soc. Jpn. 80, 124705 (1-7) (2011).
6) S. Konbu, K. Nakamura, H. Ikeda an R. Arita, “Fermi-Suface Evolution by Transition-Metal
Substitution in the Iron-based Superconductor LaFeAsO”, J. Phys. Soc. Jpn. 80, 123701 (1-4)(2011).
7) Kazuma Nakamura, Ryotaro Arita, Hiroaki Ikeda, “First-principles calculation of transition-metal
impurities in LaFeAsO”, Phys. Rev. B 83, 144512 (1-9) (2011).
8) T. Yoshida, I. Nishi, S. Ideta, A. Fujimori, M. Kubota, K. Ono, S. Kasahara, T. Shibauchi, T.
Terashima, Y. Matsuda, H. Ikeda, and R. Arita, “Two- and three-dimensional Fermi surfaces andtheir nesting properties in superconducting BaFe2(As1-xPx)2”, Phys. Rev. Lett. 106, 117001(1-4)(2011).

2012
1) Hiroshi Shinaoka, Takahiro Misawa, Kazuma Nakamura, Masatoshi Imada, "Mott Transition andPhase Diagram of κ-(BEDT-TTF)2Cu(NCS)2Studied by Two-Dimensional Model Derived from Ab
initio Method", J. Phys. Soc. Jpn. 81 (2012) 034701(1-12).
2) R. Arita, J. Kunes, A.V. Kozhevnikov, A.G. Eguiluz, M. Imada, "Ab initio Studies on the Interplay
between Spin-Orbit Interaction and Coulomb Correlation in Sr2IrO4 and Ba2IrO4", Phys. Rev. Lett.
108 (2012) 086403(1-5).
3) Shiro Sakai, Giorgio Sangiovanni, Marcello Civelli, Yukitoshi Motome, Karsten Held, Masatoshi
Imada, "Cluster-size dependence in cellular dynamical mean-field theory", Phys. Rev. B 85 (2012)
035102(1-10).
4) Takahiro Misawa, Kazuma Nakamura, and Masatoshi Imada, "Ab Initio Evidence for Strong
Correlation Associated with Mott Proximity in Iron-Based Superconductors", Phys. Rev. Lett 108,
(2012) 177007(1-5).
5) Yusuke Nomura, Merzuk Kaltak, Kazuma Nakamura, Ciro Taranto, Shiro Sakai, Alessandro
Toschi, Ryotaro Arita, Karsten Held, Georg Kresse, and Masatoshi Imada, "Effective on-site

166interaction for dynamical mean-field theory", Phys. Rev. B 86 (2012) 085117(1-8).
6) Kazuma Nakamura, Yoshihide, Yoshimoto, Masatoshi, Imada, "Ab initio two-dimensional
multiband low-energy models of EtMe3Sb[Pd(dmit)2]2 and κ-(BEDT-TTF)2Cu(NCS)2 withcomparisons to single-band models", Phys. Rev. B 86 (2012) 205117(1-9)7) H. Shinaoka, T. Miyake and S. Ishibashi, "Noncollinear magnetism and spin-orbit coupling in 5d
pyrochlore oxide Cd2Os2O7", Phys. Rev. Lett. 108, 247204 (1-5) (2012).
8) M. Casula, Ph. Werner, F. Aryasetiawan, T. Miyake, A. Millis, L. Vaugier, and S. Biermann,"Low-energy models for correlated materials: bandwidth renormalization from Coulombic
screening", Phys. Rev. Lett. 109, 126408 (1-5) (2012).
9) Jan M. Tomczak, Michele Casula, Takashi Miyake, F. Aryasetiawan and S. Biermann, "Combined
GW and dynamical mean field theory: Dynamical screening effects in transition metal oxides", Euro.
Phys. Lett. 100, 67001 (1-6) (2012).
10) Philipp Werner, Michele Casula, Takashi Miyake, Ferdi Aryasetiawan, Andrew J. Millis, andSilke Biermann, "Satellites and large doping- and temperature-dependence of electronic properties inhole-doped BaFe2As2", Nature Phys. 8, 331-337 (2012).
11) Yusuke Nomura, Kazuma Nakamura and Ryotaro Arita, “Ab initio derivation of electronic
low-energy models for C60 and aromatic compounds“, Phys. Rev. B 85, 155452(1-11) (2012)12) S. Ishibashi and K. Terakura, "Electronic Structure of Cu(tmdt)2 Studied with First-Principles
Calculations", Crystals, 2, 1210-1221 (2012).
13) A. Takayama, T. Sato, S. Souma, T. Oguchi, and T. Takahashi, “Tunable spin polarization in
bismuth ultrathin film on Si(111)”, Nano Lett. 12, 1776-1779 (2012).
14) S. Aizaki, T. Yoshida, K. Yoshimatsu, M. Takizawa, M. Minohara, S. Ideta, A. Fujimori, K.
Gupta, P. Mahadevan, K. Horiba, H. Kumigashira, and M. Oshima, "Self-energy on the low- tohigh-energy electronic structure of correlated metal SrVO3", Phys. Rev. Lett. 109, 056401(1-5)(2012).
15) W. Malaeb, T. Shimojima, Y. Ishida, K. Okazaki, Y. Ota, K. Ohgushi, K. Kihou, T. Saito, C. H.
Lee,S. Ishida, M. Nakajima, S. Uchida, H. Fukazawa, Y. Kohori, A. Iyo, H.Eisaki, C.-T. Chen,S.
Watanabe,H. Ikeda, S. Shin, “Abrupt change in the energy gap of superconducting Ba1-x Kx Fe2As2
single crystals with hole doping”, Phys Rev. B.86,(2012)165117
16) K. Okazaki, Y. Ota, Y. Kotani, W. Malaeb, Y. Ishida,T. Shimojima, T. Kiss, S. Watanabe, C.-T.
Chen, K. Kihou,C. H. Lee, A. Iyo, H. Eisaki, T. Saito, H. Fukazawa,Y. Kohori, K. Hashimoto, T.
Shibauchi, Y. Matsuda, H. Ikeda,H. Miyahara, R. Arita, A. Chainani, S.Shin, “Octet-line node
structure of superconducting order parameter in KFe2As2”, Science 337,(2012) 1314.
20131) M. Hirayama, T. Miyake and M. Imada, "Derivation of Static Low-Energy Effective Models by
ab initio Downfolding Method without Double Counting of Coulomb Correlations: Application to
SrVO3, FeSe and FeTe", Phys. Rev. B 87 (2013) 195144(1-22).
2) T. Miyake, C. Martins, R. Sakuma and F. Aryasetiawan, "Effects of k-dependent self-energy in theelectronic structure of correlated materials", Phys. Rev. B 87, 115110 (1-7) (2013).
3) Takashi Miyake, Kiyoyuki Terakura, Yosuke Harashima, Hiori Kino and Shoji Ishibashi,“First-principles study of magnetocrystalline anisotropy and magnetization in NdFe12, NdFe11Ti and
NdFe11TiN”, J. Phys. Soc. Jpn. 83, 043702 (1-4) (2014).
4) Kazuma Nakamura, Shiro Sakai, Ryotaro Arita, Kazuhiko Kuroki, “GW calculation of plasmon
excitations in the quasi-one-dimensional organic compound (TMTSF)2PF6”, Phys. Rev. B, 88,125128 (1-5) (2013).
5) Ryosuke Akashi and Ryotaro Arita, “Density functional theory for superconductors withparticle-hole asymmetric electronic structure”, Phys. Rev. B 88, 014514 (1-12) (2013).
6) Ryosuke Akashi and Ryotaro Arita, “Development of density functional theory for167

plasmon-assisted superconducting state: Application to Lithium under high pressures”, Phys. Rev.
Lett. 111, 057006 (1-5) (2013).
7) Ryosuke Akashi and Ryotaro Arita, “Nonempirical study of superconductivity in alkali-doped
fullerides based on density functional theory for superconductors”, Phys. Rev. B 88, 054510 (1-5)(2013).
8) N. Nagasako and T. Oguchi, “Stress Formulation in the All-Electron Full-Potential Linearized
Augmented Plane Wave Method: II. Accuracy Check in the Generalized Gradient Approximation”, J.
Phys. Soc. Jpn. 82, 044802(1-10) (2013).
9) S. Ideta, T. Yoshida, I. Nishi, A. Fujimori, Y. Kotani, K. Ono, Y. Nakashima, S. Yamaichi, T.
Sasagawa, M. Nakajima, K. Kihou, Y. Tomioka, C.H. Lee, A. Iyo, H. Eisaki, T. Ito, S. Uchida, and R.
Arita, "Dependence of carrier doping on the impurity potential in transition-metal-substituted
FeAs-based superconductors", Phys. Rev. Lett. 110, 107007(1-5) (2013).
10) H. Suzuki, T. Yoshida, S. Ideta, G. Shibata, K. Ishigami, T. Kadono, A. Fujimori, M. Hashimoto,D. H. Lu, Z.-X. Shen, K. Ono, E. Sakai, H. Kumigashira, M. Matsuo, and T. Sasagawa, “Absence ofsuperconductivity in the “hole-doped” Fe pnictide Ba(Fe1-xMnx)2As2: Photoemission and x-ray
absorption spectroscopy studies”, Phys. Rev. B 88, 100501R (1-5) (2013).

20141) Takahiro Ohgoe, Masatoshi Imada, "Variational Monte Carlo Method for Electron-Phonon
Coupled Systems", Phys. Rev. B 89, 195139 (1-10) (2014).
2) Takahiro Misawa, Masatoshi Imada, "Origin of High-Tc Superconductivity in Doped Hubbard
Models and Their Extensions: Roles of Uniform Charge Fluctuations", Phys. Rev. B 90, 115137(1-16) (2014).
3) Youhei Yamaji, Masatoshi Imada, "Metallic Interface Emerging at Magnetic Domain Wall of
Antiferromagnetic Insulator: Fate of Extinct Weyl Electrons", Phys. Rev. X 4, 021035 (1-27) (2014).
4) Youhei Yamaji, Yusuke Nomura, Moyuru Kurita, Ryotaro Arita, Masatoshi Imada"First-Principles Study of the Honeycomb-Lattice Iridates Na2IrO3 in the Presence of Strong
Spin-Orbit Interaction and Electron Correlations", Phys. Rev. Lett. 113, 107201 (1-5) 82014).
5) Takahiro Misawa, Masatoshi Imada, "Superconductivity and its mechanism in an ab initio modelfor electron-doped LaFeAsO", Nat. Commun. 5, 5738 (1-11) (2014).
6) Yusuke Nomura, Kazuma Nakamura, Ryotaro Arita, “Effect of Electron-Phonon Interactions on
Orbital Fluctuations in Iron-Based Superconductors", Phys. Rev. Lett. 112, 027002 (1-5) (2014).
7) Shoji Ishibashi and Kiyoyuki Terakura, “Exotic Ferroelectricity in Tetrathiafulvalene-p-Chloranil:
Anomalous Effective Charges and a Picture in the Framework of Maximally Localized Wannier
Orbitals”, J. Phys. Soc. Jpn. 83, 073702 (1-4) (2014).
8) T. Oguchi, “Quasi-one-dimensional nature of the Rashba states of Au wires on Si(557) surface”, J.
Electron Spectrosc. Relat. Phenom. (1-5) (2014), http://dx.doi.org/10.1016/j.elspec.2014.09.004 inpress9) H. Wadati, J. Mravlje, K. Yoshimatsu, H. Kumigashira, M. Oshima, T. Sugiyama, E. Ikenaga, A.
Fujimori, A. Georges, A. Radetinac, K. S. Takahashi, M. Kawasaki, and Y. Tokura, “Photoemission
and DMFT study of electronic correlations in SrMoO3 Effects of Hund’s rule coupling and possible
plasmonic sideband”, Phys. Rev. B 90, 205131(1-8) (2014).
10) T. Yoshida, S. Ideta, T. Shimojima, W. Malaeb, H. Suzuki, I. Nishi, A. Fujimori, S. Shin, Y.
Nakashima, H. Anzai, M. Arita, A. Ino, H. Namatame, M. Taniguchi, K. Ono, S. Kasahara, T.
Shibauchi, T. Terashima, Y. Matsuda, M. Nakajima, S. Uchida, Y. Tomioka, T. Ito, K. Kihou, C.H.
Lee, A. Iyo, H. Eisaki, H. Ikeda, and R. Arita, “Anisotropy of the superconducting gap in theiron-based superconductor BaFe2(As1-xPx)2”, Sci. Rep. 4, 7292(1-6) (2014).
11) K. Okazaki1, Y. Ito, Y. Ota, Y. Kotani, T. Shimojima,T. Kiss, S. Watanabe, C.-T. Chen,
S. Niitaka, T. Hanaguri, H. Takagi, A. Chainani,S. Shin Superconductivity in an electron band just168

above the Fermi level: possible route to BCS-BEC superconductivity” Scientific
Reports.,4:4109(2014)1-6
12) Y. Ota, K. Okazaki, Y. Kotani, T. Shimojima, W. Malaeb, S. Watanabe, C.-T. Chen, K. Kihou, C.
H. Lee, A. Iyo,H. Eisaki, T. Saito, H. Fukazawa, Y. Kohori, S. Shin, “Evidence for excluding thepossibility of d-wave superconducting-gap symmetry in Ba-doped KFe2As2”, Phys Rev.
B.89,081103(2014).
13) T. Shimojima, T. Sonobe, W. Malaeb, K. Shinada, A. Chainani, S. Shin, T. Yoshida, S. Ideta, A.
Fujimori, H. Kumigashira, K. Ono, Y. Nakashima, H. Anzai, M. Arita, A. Ino, H.Namatame, M.
Taniguchi, M. Nakajima, S. Uchida, Y. Tomioka, T. Ito, K. Kihou, C. H. Lee, A. Iyo, H. Eisaki, K.
Ohgushi, S. Kasahara, T. Terashima, H. Ikeda, T. Shibauchi, Y. Matsuda, K. Ishizaka, “Pseudogap
formation above the superconducting dome in iron pnictides”, Phys Rev. B.89,045101(2014)

2015
1) Motoaki Hirayama, Ryo Okugawa, Shoji Ishibashi, Shuichi Murakami and T. Miyake, “Dirac
Point in Trigonal tellurium and selenium”, JPS Conf. Proc. 5, 011024 (1-6) (2015).
2) Yosuke Harashima, Kiyoyuki Terakura, Hiori Kino, Shoji Ishibashi and Takashi Miyake,“First-Principles Study of Structural and Magnetic Properties of R(Fe,Ti)12 and R(Fe,Ti)12N (R=Nd,
Sm, Y)”, JPS Conf. Proc. 5, 011021 (1-8) (2015).
3) A. Takayama, T. Sato, S. Souma, T. Oguchi, and T. Takahashi, “One-dimensional edge stateswith giant spin splitting in a bismuth thin film”, Phys. Rev. Lett. 114, 066402(1-5) (2015).
4) T. Shoman, A. Takayama, T. Sato, S. Souma, T. Takahashi, T. Oguchi, K. Segawa, and Y. Ando,“Topological proximity effect in a topological insulator hybrid”, Nature Commun. 6, 6547(1-6)(2015).

Personal list of number of publications and invited talks
Masatoshi Imada: [Published papers in refereed journals] 31,[Invited talks in international conferences] 26, [Invited talks in domestic conferences] 7
Takashi Miyake: [Published papers in refereed journals] 23,[Invited talks in international conferences] 5, [Invited talks in domestic conferences] 7
Kazuma Nakamura: [Published papers in refereed journals] 17,[Invited talks in international conferences] 7, [Invited talks in domestic conferences] 10
Ryotaro Arita: [Published papers in refereed journals] 20,[Invited talks in international conferences] 25, [Invited talks in domestic conferences] 1
Tamio Oguchi: [Published papers in refereed journals] 42,[Invited talks in international conferences] 7, [Invited talks in domestic conferences] 2
Shoji Ishibashi: [Published papers in refereed journals] 14,[Invited talks in international conferences] 2, [Invited talks in domestic conferences] 13
Atsushi Fujimori: [Published papers in refereed journals] 12,[Invited talks in international conferences] 10, [Invited talks in domestic conferences] 9
Shik Shin: [Published papers in refereed journals] 61, [Invited talks in international conferences] 20
Total: [Published papers in refereed journals] 220,
[Invited talks in international conferences] 102

169

Many-Body Theory from First Principles
Y. Takada1, K. Shirai2, R. Maezono3, H. Maebashi1, M. Sakurai1
The University of Tokyo1, Osaka University2, JAIST3
1. Introduction
By employing the Green's-function techniques, the quantum diffusion Monte Carlo (DMC)
simulations, several types of variational approaches, and the local-density approximation (LDA)or its refinements such as GGA to the density functional theory (DFT), we have studied various
aspects of quantum many-body problems in condensed matter physics, based primarily on thefirst-principles Hamiltonian HFP to investigate the following two issues: (i) Some important
physical concepts are so far established only by the analysis of model Hamiltonians. We assess
their relevance in HFP by mainly using DMC, whereby we may find new physics byunderstanding the concepts more deeply. (ii) In the framework of DFT, all the many-bodyeffects should originate from the universal energy functional, indicating that they should appear
even in the homogeneous electron gas, in either its ground or excited states. With thisrecognition, we try to discover new concepts and/or quantum phases in the homogeneouselectron gas by use of the Green’s-function method not only in the many-body perturbation
approach but also in the nonperturbative one like the GW scheme which can be applied to both
Fermi and Tomonaga-Luttinger liquids. A reliable method for calculating superconducting
transition temperature Tc from first principles is developed along this line of research.
2. Summary
Here we mention a couple of topics as concrete problems in the first issue: (i) We have madeDMC calculations to analyze the Kondo spin-singlet resonance state in the system of a proton
embedded in the electron gas to find a paradigm shift in the metallic screening to a point charge
due to the competition between the short-range spin-dependent interaction at the proton site andthe long-range Coulomb interaction among metallic electrons, the latter of which is absent in the
impurity Anderson model but present in HFP. The exciton and biexciton physics is also
investigated by DMC in the electron-hole bilayer system to establish a rich phase diagram.
As for the second issue, we have succeeded in the improvement on the GW scheme byinventing a good functional form for the three-point vertex function , a key quantity in the
self-consistent calculation of the electron self-energy in metals, to satisfy the conservation
laws of not only the local electron number but also the total momentum. With use of thisscheme, we have found an indication of a new exotic “light-fermion” phase in the 3D
low-density electron gas. In the spin-charge separated 1D Luttinger liquid, we have discovered
the concept of “pseudoelectron” by GW in combination with the Bethe Ansatz method.
Superconductivity in boron and carbon systems as well as electron-doped SrTiO3 isinvestigated not only by theoretical calculations but also by collaboration with experimentalists.
More detailed explanations on the above topics, along with some other interesting subjects,
are given in the next section.
3. Accomplishments[1] Paradigm Shift in Metallic Screening to a Point Charge: Sharp Transition from Charge toSpin-Singlet Resonance State in the Proton Embedded Electron Gas (Takada, Maezono, andYoshizawa)
According to Debye and Hückel in 1923, a point charge +Ze in a metal is screened by theaccumulation of metallic electrons (charge resonance as described by the linear response theory).

170

This concept of metallic screening is prevailing for a century, but if Z is not small, we need toconsider the nonlinear effects in the screening, including the contribution from spin resonance.
The contribution will be enhanced, if Z is a positive odd integer, such as Z=1 (case of a proton),in which a spin-polarized bound state might appear around the charged impurity site.
With the above idea in mind, we have investigated the problem of hydrogen impurity inmetals, which attracts long attention from a technological point of view like hydrogen storage insolids. Its electronic state has been investigated in terms of a proton embedded in the electrongas, namely, an interacting many-electron system in a compensating uniform positive
background, mostly by LDA to DFT, according to which we may summarize the situation as
follows: At high metallic electron densities, it is well described by a bare proton H+ screened bymetallic electrons (usual charge resonance), while at low densities two electrons are localized at
the proton site to form a closed-shell negative ion H- protected from surrounding metallic
electrons by the Pauli exclusion principle. However, no details are known so far about thetransition from H+ to H- in the intermediate-density region.
As schematically shown in Fig. 1, we
have obtained its complete picture, inparticular, a sharp transition from H+
screening charge resonance (CR) to
Kondo-like spin-singlet resonance (SSR),
the emergence of which is confirmed by
the presence of an anomalous Friedel
oscillation characteristic to the Kondo
singlet state through DMC calculations
with total electron number N up to 170.
This picture enriches the paradigm formetallic screening to a point charge inthe sense that, depending on Z and rs,
defined by rs=(3/4 n)1/3aB-1 with n theelectron density and aB the Bohr radius,
the SSR with a very long Kondo
screening length takes the place of the Fig. 1: Phase diagram for the sharp sequential transitions
CR with a short Thomas-Fermi screening among (a) charge resonance, (b) singlet-spin resonance,
length. We also note that hydrogen is and (c) closed-shell H- ion confinement states in themost stably embedded in the electron gas proton-embedded electron gas with N the total numberof electrons and rs the electron density parameter toin the form of the SSR, implying thatspecify the homogeneous electron gas.
hydrogen is expected to reside at a sitecharacterized by the local density of rs ~ 4 in an inhomogeneous metal.
Incidentally, the accurate data obtained by DMC for the charge density distribution aroundthe proton n(r) as a function of rs are found to contribute much to the improvement on theexchange-correlation energy functional in the framework of GGA, a key quantity in the
Kohn-Sham scheme in DFT.
[2] Excitons and Biexcitons in Symmetric Electron-Hole Bilayers (Maezono)
Symmetric electron-hole bilayer systems have been studied at zero temperature using DMC.
A flexible trial wave function is used that can describe fluid, excitonic, and biexcitonic phases.
We have calculated the condensate fractions and pair correlation functions for a large number ofdensities rs and layer separations d and obtained the phase diagram as shown in Fig. 2. At small
d we find a one-component fluid phase, an excitonic fluid phase, and a biexcitonic fluid phase,171

and the transitions among them appear to be continuous. At d = 0, excitons appear to survive
down to about rs = 0.5 a.u., and biexcitons form at rs > 2.5 a.u. A snapshot of the state isshown in each phase in Fig. 3.

Fig. 2: Schematic picture of the phase diagram expected for 2D electron-holegas. Vertical (horizontal) axis means the inter-layer (mean inter-particle)
distance given in Bohr unit. With fixing rs to be 4.0, one gets such phasetransition that from plasma phase, to exciton phase, and finally to biexitonic
phase, as our results confirm.

Fig. 3: QMC snapshots capturing 2-component plasma, excitonic, and biexcitonic phases
at the particle density, rs = 4 bohr. Each phase appears as the spacing between layers, d,decreases from three toward zero.
[3] “Light Fermion” Problem in the Low-Density Electron Gas (Takada and Maebashi)
The electron-gas model plays a very useful role in the discussion of the many-bodyproperties of conduction electrons in metals. This model becomes even more important in
low-density systems in which a0pF is much smaller than unity (a0: the lattice constant and pF:
the Fermi wave number), because the first-principles Hamiltonian HFP in metals is reduced tothis model in this limit, indicating that the universal behavior in the low-density metals can be
captured by the investigation of the electron gas at low densities.
This model is completely specified by a single density parameter rs. In usual metals inwhich rs is in the range 1 ~ 5, this model can be well treated by the appropriate combinationof ring diagrams, ladder ones, and their exchange partners, but the situation becomes complex
and difficult for rs larger than 5.25 at which the electronic compressibility diverges andsubsequently the dielectric catastrophe occurs in the sense that the static dielectric function in
the long-wave-length region is negative. In close connection of this dielectric catastrophe, wehave already discussed an anomalous behavior of the interatomic distance in the alkali fluid172metals in the supercritical region, namely, for rs between 5 and 8. We have also reported thecalculated results on several physical quantities satisfying various sum rules, including the
momentum distribution function n(p) and the one-electron spectral function A(p, ) in thesame rs region with employing the nonperturbative scheme of the GW method in which avery important improvement is made for the functional form of the three-point vertex function, so that the self-consistent calculation for the effective mass at the Fermi level m* is madefeasible for 5 < rs < 8, as shown in Fig. 4.

Fig. 4: Effective mass at the Fermi level in unitsof the mass of a free electron. For rs<5, m* in the
GW scheme agree well with the accurate one
obtained by the effective potential expansion(EPX) method, but it decreases rapidly with rs for
rs > 5.

Fig. 5: Momentum distribution functionn(p) for the very low-density electron gas.
At rs ~ 20, n(p) for p < pF exhibits the very
flat behavior, indicating the emergence ofsome new quantum phase.

Recently, we have applied this scheme to the even lower-density electron gas to find that m*seems to vanish at rs~20, a new critical point associated with the problem of “light fermion”,
concomitantly with the onset of strange behaviour in n(p) which is markedly different from thatfor rs < 8, as shown in Fig. 5. We believe that physics behind these singular properties is theproximity to the instability of spontaneous electron-hole pair-formation excitations, whereby
there are no (or very few) screening charges working for the electrons near the Fermi level.
Note that m* in the Hartree-Fock approximation in which the bare long-range Coulombinteraction is used in the calculation of the self-energy, becomes zero at the Fermi level,
suggesting that the unscreened long-range Coulomb interaction induces a state with m*~0.
[4] Concept of “Pseudoelectron”: Generic Features of an Electron Injected into the Luttinger
Liquid (Maebashi and Takada)
The concept of spin-charge separation plays a central role in describing low-energy physics
near Fermi points in a 1D interacting electron gas, a typical example of the spin-1/2 Luttinger
liquid (LL). This concept may be confirmed in real materials by the recent high-resolution
angular resolved photoemission spectroscopy (ARPES) in which the one-electron spectral
function A(p, ) can be directly measured in the wide range of momentum p and energy . Then,if p is not restricted to the region near pF, the linear spectrum approximation, usually adopted in
the LL theory, is not sufficient in appropriately obtaining A(p, ). In fact, the effect of thenonlinear spectrum on A(p, ) has been intensively studied in recent years. According to thosestudies on integrable systems, A(p, ) has singularities for arbitrary p in proportion to173

| - (p)|- (p) with =s and c, where s(p) and c(p) are energies of spin and charge collective
excitations, respectively. In the usual LL theory, the exponent (p) is independent of p, but thenonlinearity in the electron dispersion makes it depend on p. The power of the thresholdsingularity in A(p, ) is determined by s(p) and its actual value has been given from thefinite-size spectrum obtained by the Bethe-ansatz method. For nonintegrable systems, thisthreshold singularity remains intact, but the singularity at = c(p) is smeared into a broad peak.
In those preceding works, on the belief
that the electron nature will not sustain in
the spin-charge separated system, only the
singularities at= s(p) and c(p) are
discussed. For p>>pF, however, the effect ofinteractions becomes so weak that we would
naively expect that the nature of an injected
electron to measure A(p, ) manifests itself
as a main peak in A(p, ). Then we may ask:
Does an electron-like excitation mode
actually exist in the 1D interacting systems
for p>>pF? If yes, a related and more
intriguing question is: How does theelectron-like mode reconcile with thephysics of spin-charge separation for p~pF?
In pursuit of answers to those questions,
we have carefully studied the one-electron Fig. 6. Structural change of the pseudoelectron peakGreen's function G(p,t) in momentum space in the one-electron spectral function A(p, ) for theand time and found that for p~pF, its Luttinger liquid (Yang-Gaudin model). Inset: The
long-time asymptotic form is composed of entire structure of A(p, ) near pF.
three independent modes of power-law decay. Two of them correspond to well-known spinonand (anti)holon excitations, but the rest describes the mode of an electron-like particle(“pseudoelectron”) which may be regarded as an electron dressed with a “cloud” of low-lying
spin and charge collective excitations. This pseudoelectron does not appear as a main structurein A(p, ) for p~pF and never leads to a finite jump in n(p). As p goes away from pF, thepseudoelectron structure gets broader, but with the further increase of p, it becomes less broadand eventually for p>>pF, it evolves as a main and divergent peak in A(p, ) by swallowing theantiholon mode. Concomitantly, its dispersion relation approaches the one of a free electron,
allowing us to regard the pseudoelectron as a free electron, but actually it is not quite, nor theLandau's quasiparticle, basically because this excitation is accompanied by power-law decay.
Those results clarify the generic feature of A(p, ) in a 1D metal and answer the aforementioned
two questions, as illustrated in Fig. 6[5] Survey of High-Tc Materials in Hard Semiconducting Boron Crystals (Shirai)
Since this century began, there was a big progress in the superconducting material research.
Superconductivity was discovered among semiconductors, which was previously considered as
only a theoretical interest. As a breakthrough, superconductivity was discovered in a boron
crystal at high pressures. Since then, discovery of superconductivity followed in many
semiconductors and now researchers are convinced that even phonon-mediated superconducting
mechanism can yield high-Tc superconductors, namely, above 40K. In this line of progress,
boron crystals occupy a special position. These crystals are mechanically hard materials,
suggesting strong electron-phonon interactions. Their light masses are also desirable for high-Tc

174superconductors. In fact, there are many theoretical predictions to demonstrate high Tc for boron
and related compounds, including hypothetical ones (Table I). Then the main concern ofexperimentalists is how to prepare these structures or heavily doped samples.
The mission of this theoretical study is to devise suitable methods of synthesizing boron andits compounds in order to achieve high Tc. To this end, the DFT calculation of the phase diagram
is of central importance, proposing ideas for material synthesis to experimentalists. This report
includes the experimental results in accordance with our proposals. Lastly, we emphasize
another role of this study as stimulating a search for new mechanisms of superconductivity in
low-carrier-density systems.
CrystalB (fcc)B ( -Ga)B (bct)-B
B12(CBC)
B-doped dia.
BC5
LixBC

N(Ef)
[/eV]
0.15
0.02
0.009
0.24
0.03
0.12
0.23

< >
[meV]
107
124
97
65.8
105
67.4
58

0.39-0.53
0.38
1.02
0.093
0.81
0.39
0.89
1.5

0.09-0.13
0.12
0.17
0.1
0.10
0.1
0.09

Tc (K)

References

5-15
6
> 50
<0.001
36.7
4.4
45
> 40

Papaconstantopoulos, 2002
Ma, 2004
Bose, 2005
Dekura, unpublishedCalandra, 2004
Xiang, 2004
Calandra, 2008
Rosner, 2002

Table I. Prediction of Tc for boron and boron-related compounds

Strategy of high Tc superconductors
In this study, we place the following three strategies as the basis of searching high-Tc
superconductors: (i) Use of high pressure. Almost all materials become metals under highpressure. Hence, high-pressure method is the most reliable method for obtaining
superconductivity. (ii) Heavy doping. Currently, superconducting semiconductors are mainly
prepared by doping method in more conventional processes. (iii) Use of compounds as analternate method for doping. Heavy doing is very difficult when the amount of doping exceeds
ten at.%. We expect appropriate form of compounds as playing a similar role as MgB2.
Theoretical and experimental achievements(a) Superconductivity under high pressure
When superconductivity was first discoveredfor -rhombohedral ( -R) boron at Tc~6K, thetransition occurred at a very high pressure(~160GPa). At that time, there was no phase
diagram for boron and we did not know thestructure at high pressures. Accordingly, ourfirst mission was to predict phase diagram ofboron. After completing this calculation, we
found that -rhombohedral ( -R) boron isstable at high pressures (see, Fig. 7). By
collaborating with experimentalists, we madea plan to search superconductivity of -Rboron at high pressures. The merits ofstudying -R boron are its controllability ofdefect states and its simple structure, which isFig. 7: Prediction of phase diagram for boron.
advantageous for theoretical work.
After several-year survey, Shimizu et al.
succeeded in observing superconductivity for -R boron at high pressures of ~160GPa.
Although Tc of ~6K is not so high, this discovery yielded significant contribution to175

superconductivity research. We showed that the metallic transition occurs at around 130GPa,
and surprisingly the original structure of -R boron is retained up to 200GPa. This is unusual.
Usually, for example, for Si, the crystal first undergoes phase transition to metallic structure(hexagonal), and then exhibits superconductivity. For the case of boron, superconductivity
occurs even with retaining the original structure. The mechanism of metallization for this case isband overlap. Band bowing of the conduction bottom is the cause of this overlap.
(b) Superconductivity by doping method
Li doping for -R boron is a promising candidate. However, in spite of twenty-year efforts ofexperimentalists, no success has been obtained. The problem lies at difficulty in doping for -Rboron. For -R boron, on the contrary, Li doping is possible, but no metallic behavior isobserved. Our study for doping based on phase-diagram calculation explains why the results are
not as we expected. For -R boron an intrinsic feature of geometrical frustration prevents the
crystal from undergoing metallic transition. For -R boron, there is no such difficulty. Instead,
its strong covalency prevents us from achieving heavy doping. At normal conditions, wepredicted the solubility limit of Li at almost 0.1 at.%. This doping level is marginal for -Rboron to exhibit superconductivity. Very recently, Kimura’s group succeeded in obtaining
Li-doped -R boron at around this level, and showed superconductivity (Tc~5K). This isconsistent with our prediction.
(c) Compounds superconductivity
The above approaches brought about superconductivity
for -R boron, but Tc is not so high as predicted. The main
problem lies at the currently obtained carrier concentrations.
For high-pressure experiment, the conduction and valencebands touch only slightly. For Li-doped -R boron, doping
level of Li is only 0.1 at.%. We need as high doping level as
10 at.%. This limit could be lifted by using appropriatecompounds. Theoretically, B13C2 is ideal for this purpose.
Fig. 8: Fermi surface ofThis compound is predicted as metal without doping, andLi-doped -R boron.
the predicted Tc is about 37K. Unfortunately there is thus far
no sign of superconductivity, and even of metallic behavior. The discrepancy between this fact
and theory is a long-standing issue for this compound. We have solved this problem in terms of
the effect of intrinsic defects of special type. Without controlling these defects metallic behavior
cannot be achieved. A proposal for defect control is under consideration.
d) Prediction of Tc
For -R boron under conditions of doping or high pressure, the carrier concentrations are as
low as 1021cm-3. Our prediction for Tc by the DFT calculation is exceedingly low, less than 1mK,
while experiment somehow achieved ~5K. This big discrepancy says that the present
predictability of Tc for low-carrier concentrations is not reliable. In particular, the co-existing ofelectrons and holes complicates the problem. Solving this is still a challenge for theory.
Summary and outlook
Our predictions for metallic behavior of boron compounds have led experimentalists to soundway for finding superconductivity. The currently obtained Tc is less than 10K, which is, however,by no means the intrinsic limit; it is just due to the preparation conditions presently feasible.
Our study is still being continuing and the on-going subjects are:1) Hydrogenation of -tetragonal boron. One idea of solving defect states is passivation of
defects by hydrogen incorporation. Recently, hydrogenation for -tetragonal boron has beensucceeded by Ekimov’s group. It is a promising candidate for high-Tc superconductors.

1762) Control of boron carbide. The problem of B13C2 is frustration. High pressure synthesis has
potential to resolve this. Recently, Manghnani has succeeded in compressing B13C2 by morethan 10%. This has potential to have metallic behavior.
3) Li doping to -R boron. Currently, the solubility is around 0.1 at.%. However, by using
high-pressure technique, we predict to achieve several at.% and accordingly high Tc.
[6] Superconductivity in Pseudoferroelectric Crystals: Case of n-doped SrTiO3 (Sakurai and
Takada)Superconductivity near the ferroelectric quantum critical point is an intriguing issue of
research and from this perspective, strontium titanate (STO: SrTiO3) and its derivatives such as
CaxSr1-xTiO3 attract attention in recent years. STO is a widely used perovskite oxide with a band
gap of 3.2 eV and is close to a displacive-type ferroelectric transition. When doped with
substituting Nb for Ti or removing oxygen, the sample shows metallic behavior. Below 0.5 K, it
exhibits superconductivity where the carrier density dependence of the critical temperature Tc(n)has a dome shape, as is the case in high-Tc cuprates. In 2013, Behnia’s group observed
superconductivity even at n=5.5×1017cm-3 in oxygen-deficient samples. They also discovered
another Tc dome in the doping range lower than previously achieved in Nb-doped sample.
Based on the microscopic Hamiltonian H containing the single-band pairing interaction in the
ferroelectric displacive soft phonon mechanism in the long-range dielectric formalism, we havemade an ab initio calculation of Tc in the Kirzhnits-Maksimov-Kohmskii scheme for thesuperconducting gap equation with determining the Coulomb pseudopotential * from firstprinciples. In considering H,
the one-electron dispersion isassumed to be parabolic with aneffective mass m*. With thevalues of parameters in H takenfrom experiments, the Tc dome
observed in Nb-doped samples(i.e., in higher doping range) isreproduced well as shown in
Fig. 9. We also find that a trend
in Tc for oxygen-deficient
sample (i.e., lower doping) is
captured by using a smaller m*,which agrees with mesurements,
Fig. 9: Calculated Tc as a function of the carrier density n forand a smaller phonon frequency,
Nb-doped STO (black) and for reduced STO (green),
indicating the approach to a compared to the measurements done by Behnia’s group.
ferroelectric transition.
[7] Superconductivity in Graphite Intercalation Compounds: Case of BaC6 (Takada and Sakurai)
Very recently, Tanigaki’s group succeeded in observing superconductivity in Ba intercalated
graphite. The observed Tc~65mK is much lower than the value of 0.23K in the Eliashberg theory.
In terms of Takada’s standard model for superconductivity in graphite intercalation compounds(GIC) in which the 3D interlayer band with a spherical Fermi surface superconducts, Tc is also
calculated to be about 0.2K. In order to investigate the reason for this discrepancy between
theory and experiment, the band-structure calculation is done to find that the Fermi surface forthe interlayer band in BaC6 is not spherical but truncated, as seen in Fig. 10, due to the smaller177

Fig. 10: Left: Superconducting transition temperature Tc observed in GIC plotted
as a function of the adjacent graphite layer distance d. Right: Fermi surfaces forthe 3D interlayer bands in CaC6, SrC6, and BaC6.

Brillouin zone for the system of large d. By including this effect of truncation and also that ofcore polarization of Ba, which is very important in the polar-coupling mechanism in ourstandard model for GIC superconductors, we have successfully reproduced the observed Tc.
[8] Non-Additivity in Metallic Tri-Wire Binding (Maezono)
We have investigated the non-additive contribution to the binding energy of three metallic
wires modeled by 1D homogeneous electron gases. The three-wire contribution is evaluated in
the equilateral triangle geometry by subtracting the bi-wire interaction energies from the totalenergy of the tri-wire configuration. As shown in Fig. 11, the three-wire contribution scales
according to the power law d E ~ d -a (d being the wire separation) with the exponent (rs)being smaller than 3 and slightly increasing with rs from 2.46 at rs = 1 to 2.91 at rs = 10, wherers is the density parameter of the 1D electron gas. We find that the contribution falls off quite
slowly, implying that it could be physically important.
Biwire/rs=3.0

u2(hartree/wire)

0.001

0.0001

N=055
N=111
N=Infinity
NeilPRL, N=35
NeilPRL, N=55
NeilPRL, N=101
ChiSq fit for N=Infinity (alpha=-2.541)

1e-05

Triwire/rs=3.0
0.001

0.0001u2(hartree/wire)

0.01

1e-05

1e-06

1e-06

1e-07

N=055
N=111
N=Infinity
ChiSq fit for N=Infinity (alpha=-2.670)

1e-07

10
Distance (bohr)

10
Distance (bohr)

Fig. 11; Asymptotic behavior of the bi-wire interactions u2 (left panel) and the non-additive
contribution u3 (right panel) at rs=3.0[9] Molecular Crystal Polymorphism (Maezono)
The prediction of molecular crystal polymorphism is one of the most challenging topics for
current first principles electronic structure calculations. We have revisited our previous DMC
simulation of p-DIB (para-Diiodobenzene) molecular crystal polymorphism to see how finite
size errors affect the prediction of the polymorphism. We performed a significantly larger DMC
calculation with a 1×3×3 simulation cell and a DFT nodal surface obtained from the PBE

178

functional in the GGA to DFT. It was found that the resulting polymorph stability is still
consistent with experiment, while standard DFT approaches failed (see, Fig. 12).

Fig. 12: Two possible polymorphs of p-DIB (para-Diiodobenzene). Conventional DFT cannot
predict the correct stable structure, α, but our QMC has been confirmed to predict it.

[10] Superconductivity in a Correlated E e Jahn-Teller System (Takada and Maebashi)
The competition of electron-phonon (e-ph) and electron-electron (e-e) interactions in themechanism of superconductivity is an old issue in strongly correlated systems and it has been
investigated mostly in a single-orbital system, like the Hubbard-Holstein model in which thee-ph interaction enhances charge fluctuations, inducing an s-wave superconductivity in thevicinity of CDW, whereas the e-e interaction works oppositely, leading to a d-wave
superconductivity near SDW.
Here we add a further complication to this correlated and strongly phonon-coupled system byincluding the orbital degree of freedom. More specifically, we consider a 2D square lattice witheach site made of an E⊗e Jahn-Teller (JT) center. At each center, we also consider the e-einteraction in an appropriate way to make this JT crystal as a prototype of thecharge-spin-orbital complexes with the Hamiltonian H=H0+He-e+He-ph, where H0 is thenoninteracting part composed of the electron hopping term characterized by thenearest-neighbor and next-nearest-neighbor hopping integrals, t and t’, respectively, withkeeping the orbital symmetry and the degenerate-phonon term with the phonon energy 0. The
orbital degree of freedom will be described by pseudospin for analogy to spin degree of freedom
and the pseudospin symmetry is conserved throughout the crystal in this choice of H0. Other
terms, He-e and He-ph, consist of local-site terms written with the intra-orbital Coulombinteraction U, the Hund’s-rule coupling J, and the JT coupling g.
Due to the SU(2) symmetry in spin space and the conserved symmetry in pseudospin space,
the Cooper pairing state can be specified by three quantum numbers; S the total spin of the pair,
L the total pseudospin, and Ly its y component, making it possible to write the anomalous
self-energy as ΔSLLy(k), where k is a combined notation of crystal momentum k and fermion
Matsubara frequency. Because of the rotational symmetry around the orbital-y axis, Ly=±1 states
are degenerate and thus we treat only either Ly=0 or 1 here. The group theory determines thetransformation property of ΔSLLy(k) in k space; it transforms in accordance with Γ, one of theirreducible representation of the point group C4v (A1, A2, B1, B2, or E). The Pauli exclusion
principle dictates that ΔSLLy(k) must be antisymmetric under two-electron interchange, indicatingthat Γ must be E for (S,L) equal to either (0, 0) or (1, 1); otherwise Γ must be either A1, A2, B1,
or B2. With including this transformation property in Γ, we can easily write down the Eliashberg
equation for ΔSLLy(k) at T=Tc with the pairing interaction VSLLy(q) containing the charge, spin, andorbital susceptibilities c(q), s(q) and o(q), all of which are evaluated in the RPA with use of179

the irreducible susceptibility 0(q).
In Fig. 13, the phase diagram at T=0.02t is plottedin U-g plane for the typical case of t’=0.125t, U=8t,
J=t, and 0=0.10t at half filling. Two boundaries,
denoted by LI and LII, indicates the lines where χo(q)and χs(q) diverge, respectively. In the close vicinityof these boundaries, those fluctuations are enhanced
strongly enough to make the system enter into
various superconducting phases, each labeled by
Fig. 13: Phase diagram in U-g plane at(Γ;S,L,Ly). Among them, we find (E;0,0,0) a novel half filling for U/8=J=t, t’=0.125t, andchiral p-wave pairing state px(k)±ipy(k) characterized Ω0=0.10t at T=0.02t. Units of strengths
by spin-singlet, orbital-singlet, and odd-parity in are so defined as UM=32/9 0(Q,0) and20
momentum space. This is a state very specific to the gM /Ω0=1/ (Q,0), where Q [=( )] isthemomentummaximizing bothdegenerate multi-orbital system and is induced byo(q,0) and s(q,0).
the cooperative effects of orbital and spin
fluctuations that are enhanced by e-ph and e-e interactions, respectively.
The conservation of the pseudospin symmetry is assumed in this study, but it is not always
the case. A tentative analysis indicates that perturbation breaking this conservation is expected
to enhance Tc for the iron pnictides, while it reduces Tc very much for the vanadium oxides.
4. Research Members
Principal Investigator:
Co-Investigators (Kenkyū-Buntansha):
Co-Investigators (Renkei-Kenkyūsha):
Research Collaborators:

Yasutami Takada (ISSP, U. Tokyo)
Koun Shirai (Osaka U.)
Ryo Maezono (JAIST)
Susumu Saito (Tokyo Inst. Tech.)Junji Haruyama (Aoyama-Gakuin U.)
Hideaki Maebashi (ISSP, U. Tokyo)
Masahiro Sakurai (ISSP, U. Tokyo)
Kanako Yoshizawa (ISSP, U. Tokyo)

5. Publications and Invited Talks
Original Papers (58 papers in total)
1)

K. Hongo and T. Iitaka, M. Watson, A. Aspuru-Guzik, and R. Maezono, “Finite-size effects
in diffusion Monte Carlo simulations of para-diiodobenzene”, J. Chem. Theory Comput. inpress (2015).

2)

K. Shirai, K. Sakuma, and N. Uemura, “Theoretical study of the structure of boron carbide
B12C2”, Phys. Rev. B 90, 064109:1-10 (2014).

3)

H. Maebashi and Y. Takada, “Structural evolution of the one-dimensional spectral function
from the low- to the high-energy limit”, Phys. Rev. B 89, 201109(R):1-4 (2014).

4)

A.J. Misquitta, R. Maezono, N.D. Drummond, A.J. Stone, and R.J. Needs, “Anomalous
non-additive dispersion interactions in systems of three one-dimensional wires”, Phys. Rev.
B 89, 045140:1-9 (2014).

5)

R. Maezono, P.L. Rios, T. Ogawa, and R.J. Needs, “Excitons and biexcitons in symmetricelectron-hole bilayers”, Phys. Rev. Lett. 110, 216407:1-5 (2013).

6)

K. Shirai and N. Uemura, “Why does a metal get an insulator? -- Consequences of unfilled bands
on boron crystals –”, Solid State Sciences 14, 1609-1616 (2012).

7)

C. Hori, H. Maebashi, and Y. Takada, “Superconductivity in a Correlated E⊗e Jahn–Teller

180

System”, Supercond Nov Magn. 25, 1369-1373 (2012).

8)

H. Maebashi and Y. Takada, “Analysis of exact vertex function for improving on the GW
scheme for first-principles calculation of electron self-energy”, Phys. Rev. B 84, 245134:
1-13 (2011)

9)

H. Dekura, K. Shirai, A. Yanase, “Efficient method for Li doping ofPhys. Rev. B 84, 094117: 1-13 (2011).

-rhombohedral boron”,

10) H. Zheng and Y. Takada, “Importance of counter-rotating coupling in the superfluid to Mott
insulator quantum phase transition of light in the Jaynes-Cummings lattice”, Phys. Rev. A 84,
043819: 1-8 (2011).

Books and Chapters in Books (4 English articles and 2 Japanese articles in total)
1) J. Haruyama, “Carbon-based superconductors: Toward high-Tc superconductivity” (Pan
Stanford Publishing, Singapore), editing total 302 pages (2015).
2) Y. Takada, “Theory of superconductivity in graphite intercalation compounds”, inComprehensive Semiconductor Science and technology, Vol.1, ed. by P. Bhattacharya, R.
Fornari, and H. Kamimura (Elsevier) pp. 410-426 (2011).
Invited Talks (41 talks in total)
1)

2)

3)

K. Shirai, K. Sakuma, and N. Uemura, “Defect states of boron carbide B13C2”, 18th
International symposium on boron, borides and related materials (Honolulu, USA, 31
August- 5 September 2014).
K. Hongo and R. Maezono, “Quantum Monte Carlo study of finite size effects inpara-diiodobenzene molecular crystals”, XVIIIth International workshop on quantum systemin chemistry, physics and biology（Paraty, Rio de Janeiro, Brazil, 1 December 2013）
R. Maezono, “Studies of electron-hole systems using DMC”, Quantum Monte Carlo in the
Apuan Alps VIII (Vallico Sotto, Tuscany, Italy, 27 July 2013).

4)

Y. Takada, “Standard model for superconductivity in graphite intercalation compounds:
Prediction of optimum Tc”, AIMR workshop on superconductivity and magnetism associatedwith geometry and dimensionality from organics to inorganics (Sendai, 17 May, 2013).

5)

K. Shirai, “Electronic structures of boron crystals”, 37th Int. conf. and exposition on
advanced ceramics and composites (Daytona Beach, Florida, USA, Jan. 27 -Feb. 1, 2013).

6)

Y. Takada, “Superconductivity in a correlated E⊗e Jahn–Teller system”, Superstripes 2011:
Quantum phenomena in complex matter (Rome, Italy, 11-15 July, 2011).

Organizers of International Conferences/Workshops (4 in total)
1) K. Shirai, The CECAM workshop “Modeling the Physical Properties of Clustering Crystals”,
Lausanne, Switzerland, at the Ecole Polytechnique Fédérale de Lausanne (EPFL) from 4-6
November 2013 (Co-Chair).
2) Y. Takada, 7th ISSP International Workshop and Symposium “Emergent Quantum Phases inCondensed Matter –From topological to first principles approaches”, ISSP, U. Tokyo,
Kashiwa, 3-21 June 2013 (Co-Chair).
3) K. Shirai, Japan-France Joint Seminar 2012 “Physics and Control of Clustering Solids”, 5 -7
Nov. 2012, Awaji Yumebutai, Awaji Island, Hyogo, Japan (Chair).
4) R. Maezono, JAIST International Winter school 2012 “Quantum Monte Carlo Electronic
Structure Calculation”, 19-24 February 2012, JAIST, Nomi, Japan (Chair).

181

Computational Design and Realization of Spintronics Materials
K. Sato1, T. Oda2 T. Nozaki3 and M. Ogura4
1
Division of Materials and Manufacturing Science, Graduate School of Engineering,Osaka University,
2
Faculty of Mathematics and Physics, Institute of Science and Engineering,
Kanazawa University,
3
Spintronics Research Center, National Institute of Advanced Industrial Science andTechnology (AIST),
4Department of Physics, Graduate School of Science, Osaka University,
1.

Introduction
In this research project, to make a breakthrough in realizing spintronics as a practicalelectronics, we carried out collaborative research between computational design for spintronics
and experimental verification. Concerning to the design for semiconductor spintronics, it has
been desired to fabricate dilute magnetic semiconductors (DMS) with high Curie temperature(TC). The main obstacle to realize high-TC DMS is low solubility of transition metal (TM)impurities in semiconductors. In order to overcome this difficulty, Sato proposed three possible
directions of materials design (Sec. 2). Firstly, ‘co-doping’ method was proposed to control
solubility of TM, and applied to the typical DMS GaMnAs. Secondly, it was shown that the
spinodal decomposition in DMS could be used to organize nano-structures. Each nano-structure
contains TM with high concentration, thus high-TC is expected. MgO-based DMS was pickedup as typical example. Thirdly, new materials with high solubility of TM impurities were
explored. LiZnAs- and GeTe-DMS were found to be good candidates for realizing high-TC
DMS. In addition to the application of first-principles method to materials design as given
above, it is also very important to develop computational method of electronic structure. Oguradeveloped screened-KKR method for band structure calculations to realize order-N scheme (Sec.
3). The options to calculate magneto-optical properties and electric transport properties within
the Keldysh formalism were also implemented.
Oda studied the topics on the search of metallic spintronic material (Sec. 4). In 2012, Oda
started also studying a new topic under a collaborative research with the group of thenon-scheduled project on “Development and application of the van der Waals density functional”(group of Ikutaro Hamada), in order to increase in sophistication about the method of electronic
structure computations. In the latter collaboration, the method of van der Waals density
functional (vdW-DF) was implemented in the code which has the option of imposing electricfield (EF). As a result of the collaboration, a scheme which is applicable to magnetic materials
was developed, and successfully applied some systems of magnetic molecules. Nozaki
performed experimental demonstration concerning to the computational design for metallic
spintronics, especially for the voltage control of magnetic anisotropy (Sec. 5).
In Sec. 6 a list of collaborators is given, and in Sec. 7 publications and invited talks related tothis project are summarized.
2.

Computational materials design for semiconductor spintronics

2.1. ‘co-doping’ method to control solubility of TM impurities in DMS
According to the first-principles prediction of Curie temperature of DMS, high concentration
doping of TM impurities is required to achieve high-TC. Due to the low solubility of Mn in

182

Temperature [K]Temperature [K]Temperature [K]GaAs, GaMnAs usually shows phase separation into GaAs and MnAs. This is why
non-equilibrium crystal growth technique is needed in fabricating DMS. Phase stability can bedetected by calculating mixing energy ∆𝐸, which is defined as ∆𝐸 = 𝐸 𝐺𝑎!!! 𝑀𝑛! 𝐴𝑠 −1 − 𝑥 ×𝐸 𝐺𝑎𝐴𝑠 − 𝑥×𝐸(𝑀𝑛𝐴𝑠), where 𝐸 is the total energy of the system. Homogeneous
GaMnAs, in which Mn distribute randomly at Ga sites, can be described by using the
Korringa-Kohn-Rostoker coherent potential approximation (KKR-CPA) method. By definition,
positive (negative) ∆𝐸 indicates phase separation (homogeneous mixing). Free energy of thesystem can be estimated by adding entropy term to the mixing energy and the temperaturedependence of the free energy gives phase diagram of the system. In Fig. 1-(a), calculated phase
diagram of GaMnAs is shown. In the calculation we did not suppose any ordered phaseappeared. As shown in the figure, very large solubility(a)1000
gap is predicted in GaMnAs. In particular, spinodal
regionis wide, and 𝑥 = 0.2 is already in the spinodal
800
region at 𝑇 = 500 (K). This reasonably explains600
difficulty of crystal growth of homogeneous GaMnAs. Li
400
Li: 0%
co-doping at the interstitial site changes the situation200
binodal line
significantly as shown in Figs. 1-(b) and (c). Due to thespinodal line
0
lowering of ∆𝐸, solubility gap and spinodal region are
1000 (b)reduced very much and high concentration doping of Mn
800
becomes possible, e.g., even at thermal equilibrium at
600
𝑇 = 500 (K), Mn can be doped up to 25% without phaseseparation. Similar co-doping effect is observed in
400
GeCrTeco-doped with I.
200
Li: 5%
Since the co-dopant Li behaves as a donor in GaMnAs,
0
the hole carriers are compensated. Therefore, it is1000 (c)necessary to remove Li after the crystal growth. In order800
to show the possibility of low temperature annealing, we
600
calculate diffusion barrier of interstitial Li in GaMnAs
400
and by performing kinetic Monte Carlo simulations we
200
estimated effective diffusion constant of interstitial Li in
Li: 10%GaMnAs. It was found that binding energy between
0
0

0.2

0.4
0.6
Mn concentration

0.8

Fig. 1: Calculated phase
diagram of Li-doped GaMnAs.
Interstitial Li concentration is(a) 0%, (b) 5% and (c) 10%.

1

interstitial Li and substitutional Mn is rather small
compared to interstitial Mn and substitutional Mn,
therefore interstitial Li can diffuse rather long distance (~1µm) during reasonable annealing time (~24 hours) withreasonable annealing temperature (~500 K) even with very
high concentration of Mn (~30 %).

2.2. Self-organization of nano-structures in DMS
In standard DMS systems, such as GaMnAs, InMnAs and so on, magnetic TM impurities are
doped in non-magnetic semiconductors. Recently, ferromagnetic DMS systems without doping
magnetic impurities attract scientific attention as d0 ferromagnetism. Typical examples are Sior Ge-doped K2S, C- or N-doped CaO and SrO. We found that MgO could be ferromagnetic bydoping N at O site or by introducing Mg vacancies. MgO-based DMS is interesting due to its
sustainability and compatibility with existing spintronics devices. There are experimental
verifications concerning to the d0 ferromagnetism of MgO-based DMS. In contrast to thepredicted low TC, there are some experimental observation of room temperature ferromgnetism183

in 13% N-doped MgO and MgO with a few % Mg-vacancy.
We believe that this discrepancy between theoretical predictions and experimental
observations is due to the spinodal decomposition in these systems. According to thecalculations of effective pair interactions between N
impurities in MgO, there are attractive effective interactions
between N impurities. The effective pair interactions are also
calculated to be attractive between Mg-vacancies. For the
calculation of pair interactions, the generalized perturbation
method formulated by Ducastelle and Gautier was employed.
Due to these attractive interactions, nano-structure ofself-organized and high concentration of N or Mg-vacancy isrealized locally. Particularly, columnar structures appeare
under the layer-by-layer crystal growth condition (Fig. 2).
Since the attractive interaction between Mg-vacancies are
significant only for 2nd neighbors, the columnar
Fig. 2: Self-organization of Mg
nano-structures shown in the figure are simple cubic array of
vacancies in MgO. The location
Mg-vacancies. We claim that this nano-structure formationof Mg-vacancies are indicatedalso explains the conductivity, tunnel barrier and quantumby blue points.
oscillations of MgO-based magnetic tunnel junctions.
2.3. Search for new ferromagnetic DMS systems
There are several semiconductor systems which show large solubility of TM impurities. For
example, GeTe, which is one of the typical IV-VI semiconductors, is known to accommodate
Mn up to 50 % in thermal equilibrium. It is also known that GeTe has intrinsically p-type due tothe Ge vacancies. Thus, Mn-doped p-type GeTe is promising as high-TC DMS. Actually, TC =190 K was observed in Mn-doped GeTe. In order to see how large TC can be expected, we
calculated TC of GeMnTe as a function of concentration of Mn and Ge-vacancy. The electronic
structure of GeMnTe with Ge-vacancies was calculated by using the KKR-CPA and magnetic
exchange interactions between Mn were calculated by using the Liechtenstein’s formula. TC can
be calculated based on the mean field approximation (MFA), random phase approximation(RPA) and Monte Carlo simulation (MCS). Among them the MCS gives exact TC within the
numerical accuracy. According to the calculated DOS by the KKR-CPA, the GeMnTe system

Fig. 3-(a): Calculated effective exchangeinteractions between Mn in p-type GeTe as afunctionof
distanceforvariousconcentrations of Ge vacancy. Mn
concentration is fixed to 10 %.

Fig. 3-(b): Calculated Curie temperature of
Mn-doped p-type GeTe. Ge vacancy
concentration is 20 %. MFA (black crosses),
RPA (red pluses) and MCS (blue squres are
employed for the calculations.

184

shows very similar electronic structure to GaMnAs, i.e., Mn-d states are located at the middle ofhost valence bands. Because of the strong hybridization, the states at the top of the valencebands, which are mainly Te-p states, show considerable amplitude of Mn-d states. The
calculated exchange interactions are shown in Fig. 3-(a). Mn does not bring any carriers in
GeTe, thus the system is insulating and the exchange interactions are negative(anti-ferromagnetic) due to the super-exchange interaction between Mn. The hole carriers
originated from Ge-vacancies activate ferromagnetic interaction via the p-d exchangemechanism, and the interaction become positive. As shown in Fig. 3-(b), calculated TC shows
maximum (~250 K) at 40% of Mn concentration with 20 % Ge-vacancy. This TC is higher than
the record in GaMnAs but lower than room temperature. We also calculated electronic structure
and magnetism of Mn-doped Ge-Sb-Te ternary compound, which is known as phase changematerial, by using order-N KKR. For the calculations, we used KKRnano package developed by
Juelich group. Local environmental effects in exchange interactions were investigated.
As another candidate of DMS where TM impurities can be doped up to high concentration,
we propose LiZnAs compounds. This compound is a kind of derivative of GaAs, i.e., Ga3+ ion is
replaced with Li+ and Zn2+. Zn ion occupies cation site in Zinc Blende structure and Li ion
locates at interstitial site. Since Mn2+ is iso-electric to Zn2+, we can expect high solubility. Thiswas confirmed by the calculation of the formation energy. Since Mn2+ is iso-electric to Zn2+, wehave to dope charge carriers to induce ferromagnetic interactions between Mn. One of theadvantage of LiZnAs is that we can control charge carriers by changing Li concentration. By
reducing (increasing) Li concentration, we can make LiZnAs p-type (n-type). As increasing theconcentration of carriers, TC calculated by the MFA becomes positive (ferromagnetic). It was
shown that both p-type and n-type doping could induce ferromagnetism. This is unique featureof the present system, because ferromagnetic n-type DMS is not common. According toaccurate MCS shown in Fig. 4, TC reaches
100K with 15% Mn and 30% excess Li. Thisis higher than the TC = 34 K of existing n-type
ferromagnetic InFeAs. The carrier doping
also affects phase stability of Mn-doped
LiZnAs. The calculated mixing energy of
LiZn1-xMnxAs indicates the phase separation
into LiZnAs and LiMnAs. It was found thatthe mixing energy was reduced as increasingint
and decreasing Li concentration from
Fig. 4: Calculated TC of Li(Zn1-x, Mn x)As+Li y
stoichiometry. Therefore, the tuning of Li
by using the MCS as a function of Mn
concentration contributes to two aspects ofconcentration x for various interstitial Li
the fabrication of DMS, i.e., increasing TC
concentration y.
and suppressing phase separation.
In addition to the development of computational materials design for semiconductor
spitnronics, Sato and Fukushima studied conventional calculation procedure of Hubbard U
parameter within the constrained-DFT scheme. In this scheme, U is calculated as 𝑈 =𝐸 𝑁 + 1 + 𝐸 𝑁 − 1 − 2𝐸(𝑁), where E(N) is the total energy of N electron system. In thecase of Mn in GaN, U was calculated to be 0.94 eV. By including the spread of the wave
function, U was corrected as 3.8 eV which agrees reasonably with the previously proposedvalue U = 4 eV.

185

3.

Development of KKR-CPA code and order-N KKR method

Ogura developed the KKR-CPA package to calculate magneto optical properties such as
magnetic circular dichroism, magnetic Kerr effects and so on. The method is based on the Kubo
formula applied to the optical conductivity calculation. This method was applied to typical
DMS systems such as CdMnTe and GaMnAs. It was re-confirmed that the ferromagnetism wasstrongly related to the existence of hole carriers in the valence bands.
Another important property of semiconductor spintronics materials is the electric
conductivity, especially for magnetic multi-layered systems. For the simulation for spintronics
devices, we have to treat large systems, therefore order-N method is indispensable. In the KKR
method, we have a freedom to choose reference system. Normal choice is free space. Instead,
we can use hypothetical array of repulsive potentials. Due to the exponential decay of thestructure constants, we only have to include neighboring scattering sites in the Green’s function.
Due to the tri-diagonal shape of the Green’s function, the calculation load becomes order-N. We
applied this method to the p-n junction of GaAs and calculated electric conductivity under thefinite bias. For p-type (n-type) region, GaBeAs and GaSiAs were supposed. At both sides ofjunctions, Al leads were assumed. Keldysh Green’s function method within the KKR
framework was also developed in order to calculate the electronic structure under the finite bias
self-consistently. This formalism opens the way to calculate spin transfer torque.
4.

Computational materials design for metallic spintronics

Concerned with the design of metallic spintronic materials, Oda studied on the magnetic stateof magnetic thin films under the electric field (EF), with using the fully relativistic
two-component pseudopotential first-principles electronic structure method based on the density
functional theory (DFT). The program code developed in the project was based on thepreviously-developing house-made code. During the financed period, the new options ofimposing EF were added and upgraded. As a result, though the results related with the material
design are described later, efficiency of the program code was verified by successful
computations. Moreover, thanks to the discussions with the members of the experimental groupfor metallic spintronic materials the study of this project was efficiently prompted andsuccessfully realized a fruitful research result.
As a target of magnetic thin films, the magnetic anisotropy energy (MAE) which is extracted
from the direction dependence of the total energies of the system was studied; particularly forthe metallic thin film (vacuum/M/Fe/M(001), M=Pt, Pd), the magnetic junction film
(MgO/Fe/M(001), M=Au.Pt), and double interface thin film (MgO/Fe/MgO) were investigated.
In the metallic thin film, the semi-quantitative agreement with the available experimental data
was obtained and the validity of computational method was confirmed. In the magnetic junction
film, the EF effects of MAE on the systems of Pt substrate are larger than those of Au substrate.
In the double interface thin film, both the large effect and non-linear behavior with respect tothe EF of MAE were obtained, building up a first step to understanding the mechanism on
voltage (bias)-effect in the experimental measurement. The guiding principles obtained in the
project can be very useful to the design on EF effect for the metallic spintronic materials.
The research results of the EF effect on MAE are summarized to the following seven points.
1. In the two kinds of the junction films (MgO/Fe/M(001), M=Au, Pt), the magnetic
anisotropy and its EF effect were investigated. We found that in the Pt system the EF effectbecome several times larger than those of the Fe system without the Pt layer.
2. Evaluating the MAEs and their variation with respect to the EF in the metallic magnetic thin

186

3.

4.

5.

6.

7.

films (vacuum/M/Fe/M(001), M=Pt, Pd), we successfully explained the quantitative
properties in the EF effect observed in experiments. Moreover, introducing a new quantityof MAE density for analyzing the EF effect of magnetic anisotropy, we successfully
obtained the knowledge on the real space distribution contributed to the MAE.
We indicated that the MAEs and their EF effect can be changed by inserting themonoatomic layer of the elements (Au, Pt, Pd) at the interface between the metallic
magnetic layer and the insulating layer, and successfully discussed the critical EF value atwhich the magnetic anisotropy transition occurs.
Discussing the problem of segregation effect for Au element by evaluating the MAE and its
EF effect in the junction thin film, we obtained the very good agreement in conformity withthe experimental result. Based on these results and the fact of the stable surface energy of
Au layer, we obtained the probable guess that the segregation of Au frequently appears on
the Fe layer when using the Au substrate in the experiment.
We obtained the discussions about the role of Co element at the interface of MgO/Fe byinvestigating the structural and electronic properties and the MAE in the junction film
MgO/Fe(1-x)Co(x), etc. It was clarified that the Co element suppresses the stability of
perpendicular magnetization, however, enhances the EF effect on MAE. From these results,
the effectiveness of Co control in the magnetic material Fe(1-x)Co(x) was not clear.
Using the code of magnetostatic dipole-dipole interaction, which was developed during the
project period, we found that the shape magnetic anisotropy induced by several Fe
monoatomic layers was closely canceled out by the perpendicular magnetic anisotropy
originated from the spin-orbit interaction. This theoretical fact was found to agree well withmany
experimental
facts.
The
switching of magnetic anisotropy
which is induced by EF wastheoretically supported.
We investigated the MAE and its EF
effect in the double interface
MgO/Fe/MgO(001) and obtained thenon-linear property in the EF variationof MAE. The MAE data calculated,the variation rate with respect to theFig. 5: MAE with respect to EF in the double
EF, were in good agreement with theinterface system MgO/Fe/MgO.
experimental data.

Here, as an example, details of the 7th research result are described. In Fig. 5, the MAEs areshown with respect to the EF. The important results are summarized to two points: obtaining thenon-linear dependence of MAE and a good agreement with the experimental result on the EF
variation rate of MAE. Property of the non-linear dependence was found to correlate with thenumber of electrons on the Fe atom at the interface which the EF was imposed on. In Fig. 6, weshow the partial density of states (PDOS) projected to the 3d orbitals on the Fe atom at theinterface, at the EF which minimized the MAE. We obtained the localized electronic states of
Fe 3d orbitals just above the Fermi level. They were found to extend to the directions where thecovalent bond was not formed at the interface, and also found to correspond well to the interface
resonance state (IRS) observed in experiment.
Concerned with sophistication in the first-principles molecular dynamics with the option ofEF, various options in the boundary condition of EF were successfully introduced. Concernedwith development in the computational code, combining the MPI parallel computation with the187

OpenMP
parallelcomputation(implementingahybridparallelcomputation), we successfully obtained a
speed-up in the execution. In order to utilize
GP-GPU in application calculations infuture, we also investigated the expected
speed-up of the code.
Concerned with the research results indevelopment,
implementation,andverification of the van der Waals density
functional (vdW-DF) method and in theapplication to magnetic system, the resulting
data in the non-magnetic materials wereconfirmed to coincide with the previous datareported in past and the new functional of
vdW-DF was proposed for magnetic
materials. In the latter achievement, theFig. 6: Partial density of states (PDOS) projected
application to practical magnetic materials
to 3d orbitals on the Fe atom at the interface. The
was reported first time over the world. In thevertical line specifies the Fermi level.
vdW-DF method, the options of atomic
forces and cell stresses were introduced. For the verification calculations of argon, graphite,selenium, and solid carbon dioxide (dry-ice), we obtained good results. Concerned withmagnetic systems, we also obtained systematically good results in the calculations of the pair ofoxygen molecules and the solid oxygen. The new functional for vdW spin-polarized density
functional method, which was developed and investigated for magnetic materials during thisproject, was not applied to so many systems. Therefore, it is necessary to increase the number ofapplications for development and verification of the functional. As a future problem of interface
system, it may be interesting to clarify the effect of EF in the realistic materials where the vdW
interaction is important.
Here, details of the results related with the application to magnetic material of the vdW-DF
are described. The structural data of solid oxygen at ambient pressure is shown in Table 1. The
results of LDA and GGA differ largely from the respective experimental data, however, these of
vdW-DFs much improves the structural data. It is important that the extension to
spin-polarized materials of vdW-DF is applied to both the study of solid oxygen under highpressure and the application of magnetic systems other than oxygen system to order to verify theeffectiveness of vdW-DF.
Table 1. Crystal structure data, molecular binding energy, and magnetic energy of the solid oxygen atambient pressure.
Δ𝐸 !"

	
  

Δ𝐸 !"#abcβVolume	
  

(Å)

(Å)

(Å)

(°)

(Å /mole)(meV/mole)

LDA

3.29

3.28

4.05

113.9

19.93

522

GGA(PBE)

4.59

3.93

5.05

122.1

38.54

41

95

vdW-DF

4.68

3.68

4.70

125.2

33.04

221

118

vdW-DF-GC

4.92

3.56

4.29

128.3

33.93

213

87

vdW-DF2

3.83

3.85

4.30

118.6

27.75

225

304

vdW-DF2-GC

3.91

3.88

4.36

119.9

28.56

209

251

Exp.

5.403

3.429

5.086

132.3

34.85

188

3

	
  

(meV/mole)5.

Experimental demonstration of voltage-induced perpendicular magnetic anisotropy

5.1. Materials search for voltage control of magnetic anisotropy
Spintronic devices is expected as a promising green IT due to its low stand-by power basedon the non-volatility of ferromagnetism. However, one of the technical challenges is the
reduction in operating power. For manipulating spin states, we need to use electric-current
application and it consumes high energy due to Ohmic dissipation. Therefore, voltage-control ofmagnetic properties will be a key technology for future spintronics to realize an ideal green IT
with low stand-by and operating power.
One promising approach is the voltage-control of magnetic anisotropy (VCMA) in an
ultrathin ferromagnetic metal layer. We first demonstrated this effect in all solid device
consisting of Au / ultrathin Fe / MgO junction in 2009. VCMA effect can be induced by various
mechanisms, such as charge screening induced spin-imbalance and modification in band
structure, voltage control of interfacial oxidation state, Rashba spin-orbit coupling, ferroelectric
switching of chemical bonding or strain and so on. In particular, carrier-mediated effect at theinterface of ultrathin ferromagnetic metal and MgO has high potential for applications, however,
we need further improvement in the amplitude of voltage effect.
To enhance the voltage effect we focused on the materials research for the buffer materials.
We prepared single crystal junction structure of buffer material X (Pd or Ag)/ ultrathin Fe /MgO / Polyimide / ITO on single crystal MgO(001) substrate using molecular beam epitaxy.
Magnetic property of the ultrathin Fe layer was investigated by magneto-optical Kerr effectunder the bias voltage application between the buffer layer and top ITO electrode. For the caseof Pd buffer, estimated surface anisotropy energy Ki,0 and the slope of the surface anisotropy
energy change were 470 mJ/m2 and 100 fJ/Vm, respectively. These are comparable to thatobserved in Au/ultrathin Fe/MgO junction. On the other hand, for the Ag buffer prepared atroom temperature exhibits high Ki,0 of about 980 mJ/m2 as shown in Fig. 7-(a). An example ofthe bias voltage effect on magnetic hysteresis curve is displayed in Fig. 7-(b) for the Fe
thickness of 0.7 nm. Clear changes in the perpendicular anisotropy was observed and the slopeof the anisotropy change reached 195 fJ/Vm. The VCMA effect should be controlled at the
Fe/MgO interface, however, we found that the buffer material also has strong influence
probably through the segregation or inter diffusion during the deposition or annealing process.
1000
2

Eperpt tFe(µJ/m )Kerr ellipticity (a.u.)

(a)

800
600
400
200
0
-200
-400
0.0

0.2

0.4

0.6
t (nm)

0.8(b)-200 V
200 V-1000 -800 -600 -400 -200 0

1.0

200 400 600 800 1000

Magnetic field (Oe)Fe

Fig. 7: (a) Surface anisotropy energy as a function of Fe thickness in Ag / ultrathin Fe / MgO structure,and (b) example of VCMA effect observed in the junction with tFe=0.7 nm.

189

5.2.

Impact of under-layer materials on voltage-induced magnetic anisotropy change in
CoFeB/MgO junctions
After the first demonstration of VCMA effect in the junction structure with buffer / ultrathin
ferromagnet / MgO / Polyimide / ITO, we realized this effect in a magnetic tunnel junction
structure. It is now one of the standard structures to investigate the VCMA effect through the
TMR effect, however, experimental results, such as the amplitude of the VCMA change or evenits sign, are often scattered between the research groups and theoretical predictions. In this study,
we investigated the VCMA change in sputter-deposited-CoFeB/MgO junctions with different
buffer layers of Ru and Ta.
Buffer/Ta(5)/Ru(0 and 5 nm)/Co16Fe64B20(1.4 nm)/MgO(2 nm)/Co16Fe64B20(10 nm) were
deposited on thermally oxidized Si substrate by using DC and RF magnetron sputtering. Then,the films were micro-fabricated into magnetic tunnel junctions (MTJs) using electron-beamlithography and an Ar ion milling. The samples with Ta and Ru under-layers were annealed at
300°C and 200°C, respectively, to realize perpendicular spontaneous magnetizations inthin-CoFeB layers. We investigated the VCMA from TMR curves under in-plane magnetic
fields. Sign of the bias voltage is defined with respect to the top thick-CoFeB electrode.
Figs. 8-(a) and -(b) shows the normalized in-plane magnetization curve determined from MR
curves under positive and negative bias voltages. The polarities of voltage-induced
perpendicular magnetic anisotropy change are opposite between MTJs with Ta and Ru
under-layers. This feature was also confirmed through the voltage-driven FMR measurement.
As discussed above, VCMA effect should originate from the CoFeB/MgO interface, however,
we observed clear changes in the VCMA even with the sign change. Possible origins aredifferences in the crystalline structure or intermixing condition at the CoFeB/MgO interface ordifference in the spin-orbit strength in the underlayer may also affect on the electronic structures
around the Fermi level in the CoFeB. We need further investigation to make these points clear.

(a)

(b)

Fig. 8: Magnetic field dependence of the normalized in-plane component of the magnetization
estimated from TMR curves under different bias voltage conditions in CoFeB/MgO junctions grown on(a) Ta and (b) Ru under-layers.

190

curves.

191	
 Voltage control of magnetic anisotropy in a magnetic tunnel junction with MgO double
barriers
An important technical issue of VCMA effect is to realize the large anisotropy change withkeeping high thermal stability. Because of the interface effect, we need to use an ultrathin layerof the order of a few monolayers to observe the VCMA as discussed above. On the other hand,thermal stability of nano-sized magnetic bit depends on its volume, therefore, reduction in the
thickness degrades the thermal stability. A magnetic tunnel junction (MTJ) with double MgObarriers is promising structure to solve this problem. Since the perpendicular anisotropy comesfrom the Fe/MgO interface, surface anisotropy can be doubled by using the MgO/Fe/MgO
structure. This structure has been studied for the spin-torque based devices, but there was noreport about the VCMA.
Fig. 9-(a) shows the detailed sample structure of double barrier MTJ prepared in this study.
Here, middle FeB thin layer is the voltage-driven layer, and bottom thick Fe layer is a reference
layer to detect the magnetization direction of FeB layer. If two MgO barriers are completely
symmetric, first order term of the voltage effect could be cancelled by two interfaces, so top
side MgO barrier was designed to be thinner than the bottom side one in order to introduce theasymmetry. Therefore, we can consider that the bias voltage is applied only at the bottom side
MgO/FeB interface. However, the top MgO barrier plays an important role to give highperpendicular anisotropy to the FeB layer. Voltage effect on the perpendicular magnetic
anisotropy was summarized in Fig. 9-(b).
Perpendicular magnetic anisotropy energy, Eperp(a)was evaluated from the bias voltage dependence of
TMR curves with saturation magnetization value
obtained from VSM measurement. The surface
anisotropy energy, EperptFeB under zero bias voltage
was estimated to be about 300 µJ/m2. This value isabout 6 times larger than that obtained in ourprevious study (Au/FeCo/MgO structure) andabout 1.5 times observed in MgO/CoFeB/Ta	 structure, thanks to the two FeB/MgO interfaces.
400
In the positive bias direction, where the depletion(b)of electrons is induced at the bottom MgO/FeB
380
interface, linear enhancement of the surface
360
anisotropy energy was observed with the slope of
110 fJ/Vm. This is about 2 time larger than that340
observed in CoFeB/MgO/CoFeB/Ta MTJ. These320
results suggest that we can achieve large VCMA
effect with keeping high thermal stability in the300
double barrier MTJs.
-2000 -1500 -1000 -500 0 500 1000 1500 2000
Bias voltage (mV)And another interesting feature observed in thissample is that the perpendicular anisotropy
increases even under the negative bias direction.
Fig. 9: (a) Sample structure ofThis feature was explained theoretically as an
voltage-driven
doublebarrier
influence of charged interface by Oda. If we can
MgO-MTJ and (b) summary ofcontrol this nonlinearity intentionally by
voltage-induced surface anisotropy
structural design, it has high potential to extend
energy change estimated from TMR
the availability of VCMA.
Eperp tFeB (µJ/m2)

5.3.

6.

Collaborators
S. Kuroda (University of Tsukuba), H. Katayama-Yoshida (Osaka University), H. Asahi(Osaka University), Y. Suzuki (Osaka University), H. Akai (The University of Tokyo), M.
Geshi (Osaka University), T. Fukushima (Osaka University), M. Seike (Osaka University,
Sysmex), H. Fujii (SPring-8), N. D. Vu (Osaka University), V. M. T. D. Tran (UCB), S. Doi(The University of Tokyo)

7.

Publications and Invited talks
Publications
1)

K. Sato, L. Bergqvist, J. Kudrnovsky, P. H. Dederichs, O. Eriksson, I. Turek, B. Sanyal, G.
Bouzerar, H. Katayama-Yoshida, V. A. Dinh, T. Fukushima, H. Kizaki, R. Zeller,“First-principles theory of dilute magnetic semiconductors”, Rev. Mod. Phys. 82 (2010)
1633-1690.

2)

L. Bergqvist, K. Sato, H. Katayama-Yoshida and P. H. Dederichs, “Computational Materials
design for high-TC (Ga, Mn)As with Li-codoping”, Phys. Rev. B 83 (2011) 165201 (6 pages).

3)

K. Sato and H. Katayama-Yoshida, “Electronic structure and magnetism of IV–VI compound
based magnetic semiconductors”, J. Non-crystal. Sol., 358 (2012) 2377-2380.

4)

M. Seike, V. A. Dinh, T. Fukushima, K. Sato and H. Katayama Yoshida, “Self-Organized
Nanostructures and High Blocking Temperatures in MgO-based d0 Ferromagnets”, Jpn. J.
Appl. Phys. 51 (2012) 050201 (3 pages).

5)

M. Seike, T. Fukushima, K. Sato and Katayama-Yoshida, “Design of self-organizednanostructures to achieve high blocking temperatures in MgO-based d0 ferromagnets”,
Journal of the Korean Physical Society, 62 (2013) 1807-1811.

6)

T. Fukushima, H. Katayama-Yoshida, K. Sato, G. Bihlmayer, Ph. Mavropoulos, D. Bauer,
Ru. Zeller and P. H. Dederichs, “Hubbard U calculations for dilute magnetic
semiconductors”, J. of Phys.: Cond. Matt., 26 (2014) 274202 (6 pages).

7)

M. Ogura and H. Akai, “First-principles calculation of magnetic circular dichroism spectra ofmagnetic semiconductors”, Phys. Rev. B 82 (2010) 184426 (9 pages).

8)

M. Ogura, H. Akai and J. Kanamori, “Enhancement of Magnetism of Fe by Cr and V”,
Journal of the Physical Society of Japan 80 (2011) 104711 (6 pages).

9)

M. Ogura and H. Akai, “First-principles KKR-CPA calculation of the magnetic and transport
properties of La1-xXxMnO3 (X = Ca, Sr)”, Journal of Physics: Condensed Matter 24 (2012)
455501 (6 pages).

10) N. H. Long, M. Ogura, and H. Akai, “Effects of spin-wave excitations in half-metallic
materials”, Physical Review B 85 (2012) 224437 (6 pages).
11) D. Yoshikawa, M. Obata, Y. Taguchi, S. Haraguchi, and T. Oda, “Possible origin of
non-linear magnetic anisotropy variation in electric field effect in a double interface system”,
Appl. Phys. Express 7 (2015) 113005 (1-4).
12) M. Obata, M. Nakamura, I. Hamada, and T. Oda, “Improving the Description of
Nonmagnetic and Magnetic Molecular Crystals via the van der Waals Density Functional”, J.
Phys. Soc. Jpn. 84 (2015) 024715(1-9).
13) M. Obata, M. Nakamura, I. Hamada, and T. Oda, “Implementation of van der Waals density
functional approach to the spin polarized system: interaction potential between oxygen
molecules”, J. Phys. Soc. Jpn. 82 (2013) 093701(1-5).
14) M. Tsujikawa, S. Haraguchi, T. Oda, “Effect of atomic monolayer insertions on electricfield-induced rotation of magnetic easy axis”, J. Appl. Phys. 111 2012) 083910 (1-4).
15) S. Haraguchi, M. Tsujikawa, J. Gotou and T. Oda, “Electric-field effects on magnetic
anisotropy in Pd/Fe/Pd(001) surface”, J. Phys. D: Appl. Phys. 44 (2011) 064005 (8pages).

19216) M. Tsujikawa, S. Haraguchi, T. Oda et al., “A Comparative ab initio study on electric-fielddependence of magnetic anisotropy in MgO/Fe/Pt and MgO/Fe/Au films”, J. Appl. Phys. 109(2011) 07C107(1-3).
17) T. Nozaki, Y. Shiota, S. Miwa, S. Murakami, F. Bonell, S. Ishibashi, H. Kubota, K.
Yakushiji, T. Saruya, A. Fukushima, S. Yuasa, T. Shinjo, and Y. Suzuki, “Electric-field
induced ferromagnetic resonance excitation in an ultrathin ferromagnetic metal layer”,
Nature Physics 8 (2012) 491-496.
18) Y. T. Takahashi, Y. Shiota, S. Miwa, F. Bonell, N. Mizuochi, T. Shinjo, and Y. Suzuki,“Fabrication of Fe/MgO/Gd magnetic tunnel junctions”, IEEE Transaction on Magnetics 49(2013) 4417-4420 .
19) T. Nozaki, K. Yakushiji, S. Tamaru, M. Sekine, R. Matsumoto, M. Konoto, H. Kubota, A.
Fukushima, and S. Yuasa, “Voltage-Induced Magnetic Anisotropy Changes in an Ultrathin
FeB Layer ”, Appl. Phys. Exp. 6 (2013) 073005 (3 pages).
20) Y. Shiota, F. Bonell, S. Miwa, N. Mizuochi, T. Shinjo and Y. Suzuki, “Opposite signs ofvoltage-induced perpendicular magnetic anisotropy change in CoFeB/MgO junctions withdifferent underlayers”, Appl. Phys. Lett. 103 (2013) 082410 (3 pages).
Total 47 publications

Invited Talks
1) K. Sato, “Spinodal decomposition and magnetic properties of dilute magnetic
semiconductors”, European Materials Research Society (EMRS) fall meeting, Warsaw,(Warsaw, Poland, 13-17 Sep., 2010).
2) M. Ogura, “First-principles calculation of the magneto-optical effects of magnetic
semiconductors”, International Conference on Core Research and Engineering Science ofAdvanced Materials (Osaka, Japan, 30 May – 4 Jun., 2010).
3) T. Oda, “Toward a Computer Modeling in Magnetic Anisotropy and its
Electric-Field-Control for Nano-Structures”, European Materials Research Society (EMRS)
fall meeting, (Warsaw, Poland, 13-17 Sep., 2010).
4) T. Nozaki, “Voltage-control of perpendicular magnetic anisotropy in fully epitaxial magnetic
tunnel junctions”, SPIE 2010 NanoScience+Engineering (San Diego, 1-5 Aug., 2010).
5) T. Oda, “Toward a computer modeling in magnetic anisotropy and its electric-field-control
for nano-structures”, International Workshop on Computational Science and Application innanoscience and nanotechnology, (Hanoi, Vietnam, 31 Oct., 2011).
6) T. Nozaki, “Voltage-induced magnetic anisotropy change in ultrathin Fe(Co)/MgO
junctions”, 2011 MRS Spring Meeting and Exhibit (San Francisco, USA, Apr. 26, 2011).
7) K. Sato, “Computational Design of Oxide-based Spintronics Materials”, Asian Workshop on
First-Principles Electronic Structure Calculation (ASIAN-15), (Taipei, Taiwan, 5-7 Nov.,
2012).
8) K. Sato, “Computational Nano-materials Design and Realization for Semiconductor
Spintronics: Control of Defect and Spinodal Nano-Decomposition”, Gordon Research
Conference on Defects in Semiconductors (Biddeford, USA, 12-17 Aug., 2012).
9) T. Nozaki, “Voltage control of spin dynamics and spin-filtering effect in fully epitaxial
magnetic tunnel junctions”, International Colloquium on Magnetic Films and Surfaces(Shanghai, Sep. 24-28, 2012).
10) T. Nozaki, “Electric-field induced ferromagnetic resonance in magnetic tunnel junctions”,
58th Magnetism and Magnetic Materials Conference, Denver, Colorado, USA, 8 Nov. 2013.
11) T. Oda, “ Recent development in the non-collinear magnetic molecular dynamics ” ,International Symposium on Computational Science (ISCS2014) (Bandung, Indonesia, 20
May, 2014).
Total 38 invited talks

193

MBE growth and magnetic properties of diluted magnetic semiconductors based on
II-VI and IV-VI compounds
Ke Zhang, Satoshi Ishitsuka, Takeru Domon, Ryutaro Sakurai, Ryota Akiyama, Ken
Kanazawa, Shinji Kuroda
Institute of Materials Science, University of TsukubaWith an aim of searching for high-temperature ferromagnetism in semiconductors and of
elucidating the mechanism of ferromagnetism, we have studied various materials of diluted magnetic
semidonductors (DMSs) in which transition-metal (TM) elements are incorporated in II-VI or IV-VI
compounds. We grew thin films of these DMSs by molecular beam epitaxy (MBE) and investigatedstructural and magnetic properties of the grown films. Our studies on the respective materials aredescribed below.
1. Suppression of ferromagnetism due to co-doping of acceptor impurity in (Zn,Cr)Te(Zn,Cr)Te has been regarded as a candidate of room-temperature ferromagnetic semiconductors[1].
It was also reported that the co-doping of donor or acceptor impurities in (Zn,Cr)Te has a significant
effect on its magnetic properties; the ferromagnetism is enhanced by the co-doping of donor impurity
iodine (I) [2] while it is suppressed by the co-doping of acceptor impurity nitrogen (N) [3]. In thisstudy, we have investigated in a quantitative way how the magnetic properties and the electronic stateof Cr change due to the N doping in order to clarify their correlation and to uncover to the origin of the
suppression of ferromagnetism[4].
We prepared a series of N-doped Zn1-xCrxTe thin films grown by MBE with a systematic variationof Cr composition in the range of Cr compositions of x = 0.01 – 0.1 and N concentration [N] in therange of 1018 – 1020 cm-3. We measured the magnetization of the grown thin films under theapplication of magnetic field perpendicular to the film plane. We also performed X-ray absorption finestructure (XAFS) measurement at Cr K-edge to get the information of the electronic state of Cr.
The magnetization measurement reveals that the ferromagnetism disappears at the amount of [N]corresponding to an almost constant ratio of [N]/[Cr] = 0.08~0.1. Figure 1 plots the three characteristic
temperatures representing the critical behaviors of ferromagnetic transition as a function of [N] for analmost fixed Cr composition in the range of x = 0.06 ~ 0.09. As shown in the figure, all thesetemperatures decrease gradually with [N] at first, but suddenly drop to zero at [N] = 1×1020 cm-3,
corresponding to the ratio [N]/[Cr] ~ 0.08. For the other values of Cr composition x = 0.01 and 0.03,
the ferromagnetism disappears at the amount of [N] corresponding to the ratio [N]/[Cr] = 0.08 ~ 0.1.
On the other hand, the X-ray near edge fine structure (XANES) at Cr K-edge exhibits an abrupt

Figure 1: The three characteristic
temperatures
representing
criticalbehaviors of magnetization, the Curie
temperature TC, the blocking temperature
TB, and the paramagnetic Curie-Weisstemperature P, are plotted as a functionof [N] for an almost fixed Cr
compositions x = 0.06 ~ 0.09. The scaleof the ratio [N]/[Cr] is also shown below.

194change in the features of the shoulder peak at the amount of [N] corresponding to the ratio [N]/[Cr] =0.07 ~ 0.08. This correlation between the changes in magnetism and XANES suggests that the
suppression of ferromagnetism can be attributed to the change of the Cr electronic state due to theacceptor doping.
2. MBE growth and magnetic properties of (Zn,Fe)Te thin films
DMSs in which Fe is incorporated in II-VI compounds have been long studied and reported to
exhibit van-Vleck type paramagnetism[5]. However, experimental studies on Fe-incorporated telluride
was limited to those containing only a small Fe composition less than 1%[6]. In this study, we haveattempted to grow thin films (Zn,Fe)Te with a higher Fe content by MBE and have investigated thestructural and magnetic properties[7].
We prepared a series of Zn1-xFexTe thin films with Fe compositions of x = 0 ~ 0.2 grown by MBE
in a systematic variation of the ratio between Zn and Te fluxes and the substrate temperature during
the growth. We examined the crystal structure of the grown films by x-ray diffraction (XRD) andtransmission electron microscope (TEM) and investigated the magnetic properties.
As a result, it is found that the structural and magnetic properties are different according as thefilms were grown either in the excess of Te flux (Te-rich) or in the excess of Zn flux (Zn-rich). In the
XRD -2 scan, additional diffraction peaks assigned as FeTe of the tetragonal structure are detectedin the films grown in the Te-rich condition, while no other peaks from extrinsic precipitates appear in
the films grown in the Zn-rich condition. In the magnetization measurement, the films grown in the
Te-rich condition exhibit paramagnetism up to x~0.08 while those grown in the Zn-rich condition
exhibit ferromagnetic behaviors such as hysteresis in the magnetization curve for x > 0.03. The
ferromagnetic transition temperature TC deduced from Arrott plot analysis reaches 320K. The origin of
the ferromagnetic behaviors observed in the films grown in the Zn-rich condition can be attributed to
the formation extrinsic precipitates or Fe-aggregated regions which are structurally coherent to thehost matrix.
3. Quaternary DMS compounds containing two kinds of transition metals
In the studies on DMSs so far, ternary compounds containing only one kind of magnetic element
have mainly been investigated, while quaternary compounds containing two kinds of magnetic
element have rarely been reported. In quaternary DMSs, however, a robust magnetic ordering might
possibly be realized due to the interaction between different kinds of magnetic element. In particular,
in a special combination of TM elements, such as Cr and Fe in II-VI compounds, it was theoretically
predicted[8] that the two kinds of TM elements are coupled antiferromagnetically and a half-metallic
electronic state is realized. In this study, we have investigated magnetic properties of a quaternary
DMS in which Cr and Fe are incorporated in ZnTe.
We prepared a series of thin films of Zn1-x-yCrxFeyTe with a fixed Cr composition x ~ 0.06 andFigure 2: The coercive force HC andsaturation magnetization MS at 2K areplotted against Fe content y for
Zn1-x-yCrxFeyTe thin films with a fixed Cr
content x ~ 0.06.

195varied Fe composition y in the range of y = 0 ~ 0.02 grown by MBE. The magnetization measurement
reveals that ferromagnetic behaviors observed in (Zn,Cr)Te is enhanced by the incorporation of Fe.
Figure 2 plots the coercive course HC, the saturation magnetization MS at 2K as a function of Fe
composition y for the fixed Cr composition x ~ 0.06. With the increase of Fe composition, the coercive
force HC increases, while the saturation magnetization MS decreases. These results are seemingly
consistent with the theoretical prediction of antiferromagnetic coupling between Cr and Fe.
4. MBE growth and magnetic properties of (Sn,Mn)Te thin films
DMSs based on IV-VI compounds have been expected to exhibit ferromagnetism at a hightemperature due to the carrier-induced mechanism[9,10]. Among various IV-VI compounds, SnTe has
also been attracting attention as a typical material of topological crystalline insulator[11]. Then, it isinteresting how the properties of topological surface state is changed by the incorporation of magnetic
impurities, which are expected to break the time-reversal symmetry, requisite for the protection of the
topological surface state. In this study, we have investigated the magnetic properties of (Sn,Mn)Te thinfilms grown by MBE. We grew thin films of (Sn,Mn)Te on a BaF2 (111) substrate using a compoundsource of SnTe and an elemental source of Mn. By optimizing the MBE growth conditions, we havesucceeded to obtain Sn1-xMnxTe epitaxial films grown only in the (111) orientation without a mixture
with regions grown in other orientations up to a Mn composition around x = 0.06. In the magnetization
measurement, only paramagnetic behaviors are observed in the magnetization curve down to 2K. The
absence of ferromagnetic behaviors may be due to relatively low values of Mn composition and holeconcentration in the grown films[12]. We are now attempting to achieve a higher Mn composition
without a formation of extrinsic precipitates and a mixture with regions grown in other orientations.
References[1] H. Saito, V. Zayets, S. Yamagata, K. Ando, Phys. Rev. Lett. 90, 207202 (2003).
[2] S. Kuroda, N. Nishizawa, K. Takita, M. Mitome, Y. Bando, K. Osuch, T. Dietl, Nat. Mater. 6, 440(2007).
[3] N. Ozaki, I. Okabayashi, T. Kumekawa, N. Nishizawa, S. Marcet, S. Kuroda, K. Takita, Appl.
Phys. Lett. 87, 192116 (2005).
[4] K. Zhang, R. Akiyama, K. Kanazawa, S. Kuroda, H. Ofuchi, phys. stat. sol. (c) 7-8, 1324 (2014).
[5] A. Twardowski, J. Appl. Phys. 67, 5108 (1990).
[6] W. Mac, M. Herbich, N. T. Khoi, A. Twardowski, Y. Shapira, M. Demianiuk, Phys. Rev. B 53,
9532 (1996).
[7] S. Ishitsuka S. Ishitsuka, T. Domon, R. Akiyama, K. Kanazawa, S. Kuroda, physica status solidi(c) 7-8, 1320-1323 (2014).
[8] H. Akai, M. Ogura, Phys. Rev. Lett. 97, 026401 (2006).
[9] Y. Fukuma, H. Asada, N. Moritake, T. Irisa, T. Koyanagi, Appl. Phys. Lett. 91, 092501 (2007).
[10] Y. Fukuma, H. Asada, S. Miyawaki, T. Koyanagi, S. Senba, K. Goto, H. Sato, Appl. Phys. Lett. 93,252502 (2008).
[11] T. H. Hsieh, H. Lin, J. Liu, W. Duan A. Bansil, L. Fu, Nat. Comm. 3, 982 (2012).
[12] A. J. Nadolny et al., J. Magn. Magn. Mater. 248, 134 (2002).
List of publications
1) K. Kanazawa, S. Yoshida, H. Shigekawa, S. Kuroda, "Cross-sectional STM study of impurity
states in diluted magnetic semiconductor (Zn,Cr)Te", AIP Conf. Proc., vol.1566, 331-332 (2013).
2) H. Kobayashi, K. Yamawaki, Y. Nishio, K. Kanazawa, S. Kuroda, M. Mitome, Y. Bando,"Structural analysis of Cr aggregation in ferromagnetic semiconductor (Zn,Cr)Te", AIP Conf.
Proc., vol.1566, 341-342 (2013).
3) K. Zhang, R. Akiyama, K. Kanazawa, S. Kuroda, H. Ofuchi, “Effect of acceptor co-doping on
magnetism and electronic states in ferromagnetic semiconductor (Zn,Cr)Te”, phys. stat. sol. (c)196

7-8, 1312-1315 (2014).
4) S. Ishitsuka, T. Domon, R. Akiyama, K. Kanazawa, S. Kuroda, “Structural and magnetic
characterization of (Zn,Fe)Te thin films grown by MBE”, phys. stat. sol.
5) (c) 7-8, 1320-1323 (2014).
6) R. Akiyama, H. Oikawa, K. Yamawaki, S. Kuroda, “Electric-field modulation of ferromagnetismin hexagonal chromium telluride thin film”, phys. stat. sol. (c) 7-8, 1324-1327 (2014).
7) R. Akiyama, K. Fujisawa, R. Sakurai, S. Kuroda, “Weak antilocalization in (111) thin films of a
topological crystalline insulator SnTe”, J. Phys.: Conf. Ser. 568, 052001 (2014).
8) K. Kanazawa, T. Nishimura, S. Yoshida, H. Shigekawa, S. Kuroda, “Real space probe ofshort-range interaction between Cr in a ferromagnetic semiconductor ZnCrTe”, Nanoscale 6,
14667-14673 (2014).
9) K. Kanazawa, K. Yamawaki, N. Sekita, Y. Nishio, S. Kuroda, M. Mitome, Y. Bando, “Structuraland magnetic properties of hexagonal Cr1-Te films grown on CdTe(001) by molecular beam
epitaxy”, J. Cryst. Growth 415, 31-35 (2015).
List of invited talks
1) S. Kuroda, “Quaternary DMS containing two kinds of TM elements: Ferromagnetism due tointeraction between different TM elements”, Energy Materials Nanotechnology Meeting(EMN2013) (Dec. 7-10, 2013, Orlando, USA).
2) S. Kuroda, “Quaternary magnetic semiconductors containing two kinds of transition metalelements”, International Workshop of Computational Nano-Materials Design on Green Energy(JSPS Core-to-Core Program (A) Advanced Research Networks) (Jun. 1-3, 2014, Osaka Univ.,
Japan).

197

Surface plasmons and magneto-optics in metal/magnetic quantum wells
Hiroaki Matsui 1
Faculty of Engineering, the University of Tokyo 1
1. Introduction
It has been known that optical and magnetic properties in oxide semiconductor materials haveprovided interesting physical aspects such as excitonic emissions, magnetic-optics andphoto-catalysis. In this work, we focus on surface plasmons that have been applied for optical
nanodevices. Surface plasmon resonances combined with light and magnetism are expected to
be promising for new optical technology. Therefore, it is important to understand opticaltransitions in oxide semiconductors and their interactions with surface plasmons under lightirradiations. Recently, surface plasmons excited on metallic surfaces have received muchattention for investigations concerning optical functionalities on metal/semiconductor hybrid
heterostructures. Strong electric fields induced around metallic surfaces play an important rolefor enhancements of optical excitations in semiconductor layers. Optical dynamics of energy
transfer determine optical properties of semiconductors. In this study, we further develop opticalinteractions between magnetism and surface plasmons. Therefore, we will be required tounderstand light coupling of excitonic systems in semiconductors with surface plasmons.
2.1 Polarization filtering: theoretical and experimental approachesHigh polarization filters in the UV range are expected to be promising for optical sensing andlight detections. Nonpolar ZnO has self-polarization derived from asymmetric atomarrangement, which is much effective to produce polarization filter devices. Figure 1 showsenergy levels and splitting of the valence band (V.B.) in nonpolar ZnO as a function of in-planelattice strains ( yy and zz). These 2D results were calculated from the k⋅p theory perturbation.
E31 = E3 - E1 (meV)

E31 = E3 – E2 (meV)

(a)

(b)

55

30

yy (%)

E31

E32

C.B.

35
40

50
45
45

40

50

35
30

55

(c)

E1
E2
V.B.
E3

zz (%)zz (%)

Fig. 1. In-plane lattice strains ( yy, zz) and energy splitting E31 (a) and E32 (b) of thevalence band (V.B.). (c) schematic picture of energy levels of V.B.

198

on energy transition related to the E1 and E3 in the V.B,
leading to high polarization degree. Figure 2 showspolarization degree as a function of photon energy in
the ZnO layers. The ZnO layer with in-plane
compressive strains ( yy = -0.1%,

zz= -0.42%)

exhibited high polarization degree of 19.8 ascompared to ZnO layers ((degree)the ZnO layers provided high energy splitting based

20

Polarization degree,

The introduction of in-plane compressive strains into

10

15

5

zz = -0.62%). The

theoretical datas were consistent with experimentaloTg = 450oC
Tg = 730oC

T = R.T.

0
3.1

3.2

3.3

3.4

3.5

Photon energy (eV)= 8.2) without in-plane

compressive strain ( yy = +0.42,

i = 45

Fig. 2. Polarization degree as a function ofphoton energy in ZnO layers fabricatedunder different growth conditions.

results for realizing polarization filtering on ZnO.
2.2 Optical dynamics of metal/quantum well heterostructures
Dynamic processes of light energy

uncoated QW
Ag-coated QW

areimportanttoobtainperformance of optical applications
such

as

emitting

devicesandPL

PL intensity (a.u.)

wells

Extinction (a.u.)transfer from metal to quantum(d)photo-catalysis. In this work, we
1.5

employed a single quantum well
(SQW) based on ZnO in order tomonitor

opticaldynamics,

andexamined recombination lifetimes of

2

2.5

3

Photon energy (eV)

3.5

Fig. 3. (a) A cross-section TEM image of Ag/ZnO SQWheterostructure. (b) A TEM image in the vicinity of Ag NPs. (c) A
cross-section TEM image at an interface between Ag NPs and
SQW. (d) Absorption and PL spectra PL of Ag NPs and SQW.

excitons in a SQW by time-resolved
photoluminescence. Optical interactions between lights and surface plasmons were studied.
A ZnO/Cd0.08Zn0.92O SQW with a 4. 8nm well width was grown by pulsed laser ablation(PLD). A well width (LW) in the SQW was 4.8 nm. Ag nanoparticles (NPs) were also formed on
the SQW by PLD. Figure 4 shows a cross-section TEM image of an Ag/ZnO SQW structure(Fig. 3a). Ag NPs arranged as a single monolayer, and exhibited plasmon resonances in thevisible range at around 2.5 eV (Fig. 3b). Spatial separation between Ag NPs and SQW was
about 5 nm (Fig. 3c). Excitonic PL from the SQW was similar to the plasmon peak of Ag NPs(Fig. 1d). Figure 4(a) shows temperature dependence of PL quenching in the Ag-coated SQW.
The PL modulation was observed in low temperatures below 90 K (Fig. 4a). The PL intensity
showed weak temperature dependence with an S curve, indicating formations of localized
excitons (Fig. 4b). Localization energy was 8.5 meV. Figure 5d shows TRPL decay curves of PL

199

2.4

2.6

PL intensity (a.u.)

-8

(c)
2.8

Photon energy (eV)

(b)

2.78
2.76
= 8.5 meV
E (T )

2.74
0

E (0)

T

100

T2

Temperature (K)012Time (ns)3

Fig. 4. (a) Temperature dependence of PL
quenching. Inset indicates PL spectra of
Ag-coated (red) and un-coated (black) SQWs.
(b) Temperature dependence of PL peak energy
from the SQW. (c) TRPL (lifetime) spectra of
Ag-coated (red) and un-coated (black) SQW.

T = 10 K

W/O Ag

2

k BT

200

T = 75 K

PL intensity (a.u.)(a)-4

Intensity (a.u.)

Peak energy (eV) PL quenching ratio

0

W Ag

300

0

1
2
Time (ns)3intensity in the un-coated SQW at 10 K, which could be fitted using two types of lifetimes ( 1and 2). 1 and 2 were 0.27 and 2.1 ns. In contrast, the Ag-coated SQW showed 1 = 0.24 and 2= 1.7 ns. This demonstrated optical coupling between the plasmon energy of Ag NPs andexcitons in the SQW. Their dynamics were cleared through this experiment.
2.3 surface plasmons and magneto-optic
Surface plasmons can be combined with magneto-optics(magnetic spins). For example, it has been known that
Au/Co superlattices show large magneto-optical response,

Optical density(a)which are related to interactions between surface plasmons

50 nm – 150 nm

0.3

0.5

and magnetic properties. Therefore, it is expected tomagneto-optical

coupling

betweensurface

plasmons and magnetism.
We fabricated metal nanodot structures using top-down
techniques, which showed plasmon resonances in the range
from ultra-violet (UV) to visible (Fig. 5a). The plasmon
resonance was dependent on nanodot size (volume).
Furthermore, we evaluated degree of Zeeman splittingfrom Zn0.90Co0.10O layers with the metallic nanodots.
Zeeman splitting only enhanced in low temperatures below
50 K (Fig. 5b), which showed the possibility ofplasmon-induced magneto-optical enhancements in thisresearch project. Hereafter, it will be required tounderstand optical coupling of surface plasmons withmagneto-optics.

200

0.9

0.8

Zeeman splitting (meV)

produce

0.7

Wavelength ( m)

0.6
0.4
0.2

(b)
0

0

20

40

60

80

Temperature (K)100Fig. 5. (a) Surface plasmon spectra of Pd
nanodot structures (dot diameter: 50 - 150nm). (b) Zeeman splitting energy
estimated from MCD spectra without(black) and with (red) metal nanodot.

3. Summary
In this work, we demonstrated optical interactions between surface plasmons, light andmagnetism. In Se. 2.1, we presented high polarization filter devices based on ZnO fromtheoretical and experimental approaches. Furthermore, optical dynamics were investigated on
the plasmon-exciton interactions of ZnO-based quantum wells combined with metallic
nanostructures in SE. 2.2. Finally, we studied plasmon-induced magneto-optical modulation
based on Zn1-xCoxO layers (Se. 2.3).
4. Research representative
Hiroaki Matsui (Assistant Professor, the University of Tokyo)
5. Resultant outcomes
1) H. Matsui, A. Ikehata and H. Tabata, “Surface plasmon sensors on ZnO:Ga layer surfaces:
Electric field distributions and absorption-sensitive enhancements”, Appl. Phys. Lett. 106,
019905 (2015).
2) H. Matsui, N. Hasuike, H. Harima and H. Tabata, “Engineering of optical polarization based onelectronic band structures on A-plane ZnO layers under biaxial strains”, J. Appl. Phys. 116,
113505 (2014).

3) A. Portela , T. Yano , C. Santschi , H. Matsui , T. Hayashi , M. Hara , O. J.F. Martin and H.
Tabata, “Spectral tunability of realistic plasmonic nanoantennas”, Appl. Phys. Lett. 105,
091105 (2014).
4) H. Matsui, W. Badalawa, T. Hasebe, S. Furuta, W. Nomura, T. Yatsui, M. Ohtsu and H.
Tabata, “Coupling of Er light emissions to plasmon modes on In2O3: Sn nanoparticle sheetsin the near-infrared range”, Appl. Phys. Lett. 105, 041903 (2014).
5) H. Matsui, W. Badalawa, A. Ikehata, and H. Tabata, “Oxide surface plasmon resonance for a
new sensing platform in the near-infrared range” Advanced Opt. Materials 1, 397 (2013).
6) H. Matsui and H. Tabata, “Lattice, band and spin engineering on Zn1-xCoxO” J. Appl. Phys.
113, 183523 (2013).

201

Development of nonequilibrium dynamical mean-field theory
and its application to low-dimensional strongly correlated
systems
Naoto Tsuji
Department of Physics, University of Tokyo
In this project, we have developed the nonequilibrium dynamical mean-field theory (DMFT), and applied the method to nonequilibrium phenomena in strongly correlated systems. In particular, we proposed
to extend the nonequilibrium DMFT to cluster formalisms, which take account of non-local correlations in
the time evolution of strongly correlated systems. The nonequilibrium dynamical cluster theory was applied to the Hubbard model, where we found a characteristic momentum-dependent relaxation dynamics.
We have also studied nonequilibrium dynamics of electron-phonon systems and superconductors.

1 Development of nonequilibrium DMFT
The nonequilibrium DMFT is a selfconsistent formalism of calculating time
evolution of quantum many-body systems
that maps the corresponding lattice modelto an impurity model embedded in an effective dynamical mean field (Fig. 1). The
advantage of this approach is that (i) it cantreat the thermodynamic (infinite systemsize) limit, (ii) the result becomes exact in
the large dimensional limit of lattice models, and (iii) it can cover long-time evolution until the system thermalizes. Ourgroup has contributed to the development of
the nonequilibrium DMFT from the earlystage, and implemented impurity solvers
such as weak-coupling perturbation expansions [6]. Now the nonequilibrium DMFT
has been established as a powerful method
to analyze various types of models including symmetry-broken phases [8]. Summa- Figure 1: Schematic illustration of the nonequilibriumrizing recent progress, we wrote a review ar- DMFT algorithm [5].
ticle on the nonequilibrium DMFT [5].

2 Cluster extensions of nonequilibrium DMFT
The limitation of the nonequilibrium DMFT lies in the local approximation of the self-energy, which becomes better as the spatial dimension increases. However, when one consider low-dimensional systems(e.g., d ≤ 2), the eﬀect of non-local spatial fluctuations becomes important.
To include those eﬀects, we proposed a cluster extension of the nonequilibrium DMFT (namely, thenonequilibrium dynamical cluster theory) [4]. This maps a lattice model to a cluster model instead ofa single-site impurity model, which is a nonequilibrium generalization of existing equilibrium dynamical
1

202

cl
Ḡlat
K (t, t ) = G K [ K ](t, t )

k̃
K

ky

kx
lat
(t, t ) =K+ k̃cl
K (t, t )Figure 2: Schematic illustration of the nonequilibrium dynamical cluster approximation [4]. The latticemodel is mapped to a cluster model by coarse-graining the momentum space.

cluster theories. There are mainly two types of mapping: the cellular dynamical mean-field theory (CDMFT,
real-space based) and dynamical cluster approximation (DCA, momentum-space based). We adopted thelatter (Fig. 2) since it keeps the lattice translational symmetry.
We applied the nonequilibrium DCA to the interaction quench problem for the one- and two-dimensional
Hubbard models. As a simple cluster solver, we used the iterative perturbation theory. In 1D, we benchmarked the method by comparing the results with the time-dependent density matrix renormalization group.
It turned out that results for local or nearly local quantities (that can be defined within the cluster) converge
very rapidly with respect to the cluster size Nc . On the other hand, the results are greatly improved fromthose of the nonequilibrium DMFT (i.e., Nc = 1 case), which predicts too fast thermalization. This meansthat non-local correlation eﬀects are quite important even for (nearly) local quantities.
In 2D, local quantities calculated by the nonequilibrium DCA agree well with those obtained fromthe nonequilibrium DMFT, and Nc dependence is relatively weak compared to the 1D case. The nonlocal eﬀects become critical when highly non-local quantities such as the momentum distribution are concerned. While the nonequilibrium DMFT always gives a momentum-independent relaxation, the nonequilibrium DCA shows that the system relaxes quite inhomogeneously in momentum space: the momentum distribution at the Fermi surface relaxes to the thermal one faster near k = (±π, 0), (0, ±π) thannear k = (±π/2, ±π/2). This can be explained by the momentum-dependent lifetime of quasiparticles
τ(k)−1 ∝ ImΣR (k, ω). In fact, it agrees with the relaxation time extracted from the nonequilibrium DCA
results. In the present case, the 2D Hubbard model at half filling has a van Hove singularity, due to which
the system behaves as a marginal Fermi liquid (ImΣR (k, ω) ∝ ω around ω = εF ).

3 Applications to electron-phonon systems
The role of the electron-phonon interaction for nonequilibrium dynamics of superconductors has not been
fully understood yet. We focused on the (Hubbard-)Holstein model, one of the representative models ofelectron-phonon systems, and studied its equilibrium ordered phases using DMFT [2][7]. As an impurity
solver, we extended the continuous-time quantum Monte Carlo method to be able to treat ordered phases,
including superconductivity, antiferromagnetism, and charge density wave, on an equal footing.
The DMFT calculation showed that the Holstein model on a bipartite lattice exhibited the supersolid
phase (i.e., coexistence of superconductivity and charge density wave) at the intermediate electron-phonon
2203coupling regime [2]. The supersolid phase is diﬀerent from a hysteretic region near first order phase transition, and is stable against phase separation. Accompanied by the emergence of the supersolid phase, aquantum critical point (QCP) appears between the superconducting and supersolid phases. At the QCP,
charge fluctuation diverges, and the superfluid density (or London penetration depth) shows kink-like singular dependence on the filling. We further studied various aspects of the newly found supersolid phase of
the Holstein model.
We also investigated the dynamics and relaxation process of the Holstein model using the nonequilibrium DMFT with the self-consistent Migdal approximation as an impurity solver [1]. It was revealed
that the dominant thermalization process crossovers from electron to phonon degrees of freedom as one
increases the electron-phonon coupling strength. On the weaker coupling side, the coherent phonon oscillation decays faster than the relaxation of the electron momentum distribution. On the stronger couplingside, the phonon oscillation is long-lived, and the electron momentum distribution eﬀectively thermalizes
at each time with the nonequilibrium phonon background. This kind of “two-step relaxations” (i.e., electrons relax faster and phonons relax later) occurs even without an electron-electron interaction on top of theelectron-phonon interaction.

4 Applications to superconducting systems
We extended the nonequilibrium DMFT to the superconducting phase, and applied it to the quench problem
for the attractive Hubbard model (the same results are equally applied to the antiferromagnetic phase of therepulsive Hubbard model due to the duality between the repulsive and attractive models at half filling) [8]. It
was found that the system is trapped to a nonthermal quasi-stationary state for a while after excitation. Thisquasi-stationary state (called the nonthermal fixed point) maintains a long-range superconducting order up
to certain time scale even when the excitation energy, if transformed to heat, amounts to temperature higher
than the thermal critical temperature. As one varies the excitation energy, the stationary state vanishes, andthe system starts to directly approach the thermal state. At this transition point (which is diﬀerent fromthe thermal critical point), the relaxation time to the nonthermal fixed point diverges, and a characteristic
critical behavior is observed.
The method was further applied to the superconducting phase of the attractive Hubbard model driven
by a continuous ac electric field. The results indicated that the ac driving field with frequency Ω generates
a coherent oscillation of the superconducting order parameter with frequency 2Ω. This is due to the nonlinear coupling (A2 Ψ) between the amplitude of the order parameter Ψ and the electric field A. Moreover,
the amplitude of this 2Ω oscillation of the order parameter is maximized when 2Ω coincides with the superconducting gap 2∆. This was explained by the resonance between the external driving and the Higgs
amplitude mode inherent in superconductors whose eigenfrequency in the weak-coupling regime is 2∆.
This so-called Higgs-mode resonance phenomenon was recently observed in a terahertz laser experimentusing a conventional low-temperature superconductor [3].

5 Cooperation researchers, Collaborators
Cooperation researchers:• Hideo Aoki (Department of Physics, University of Tokyo)• Takashi Oka (Department of Applied Physics, University of Tokyo)
Collaborators:• Philipp Werner (University of Fribourg)• Martin Eckstein (University of Hamburg)• Peter Barmettler (University of Geneva)
3204• Yuta Murakami (University of Tokyo)

6 Invited talks (12 talks in total)(1) N. Tsuji, ”Higgs mode in conventional and unconventional superconductors”, A workshop on ”Nonequilibrium phase transitions in diverse physical systems” (9 December 2014, Tokyo, Japan).
(2) Ryo Shimano, Ryusuke Matsunaga, Yuki Hamada, Arata Sugioka, Hiroyuki Fujita, Kazumasa Makise,
Yoshinori Uzawa, Hirotaka Terai, Zhen Wang, Naoto Tsuji, and Hideo Aoki, ”Higgs Mode and Terahertz Nonlinear Optics in Superconductors”, 19th International Conference on Ultrafast Phenomena(UP2014, 10 July 2014, Okinawa, Japan).
(3) N. Tsuji, ”Higgs mode and Anderson pseudospin resonance in superconductors”, Higgs modes incondensed matter and quantum gases (24 June 2014, Kyoto, Japan).
(4) N. Tsuji, ”Anderson pseudospin resonance with Higgs mode in superconductors”, New Horizon ofStrongly Correlated Physics (NHSCP2014, 3 July 2014, Kashiwa, Japan).
(5) N. Tsuji, ”Nonthermal fixed point in the antiferromagnetic Hubbard model”, Non-equilibrium dynamics of correlated electron-systems (19 December 2013, Krvavec, Slovenia).
(6) N. Tsuji, ”Prethermalization and nonthermal fixed point in the Hubbard model”, Interdisciplinary
mini-workshop on nonequilibrium physics (8 December 2013, Kyoto, Japan).

7 Published papers (11 papers in total)[1] Y. Murakami, P. Werner, N. Tsuji, and H. Aoki, ”Interaction quench in the Holstein model: Thermalization crossover from electron- to phonon-dominated relaxation”, Phys. Rev. B 91, 045128(2015).
[2] Y. Murakami, P. Werner, N. Tsuji, and H. Aoki, ”Supersolid phase accompanied by a quantum criticalpoint in the intermediate coupling regime of the Holstein model”, Phys. Rev. Lett. 113, 266404(2014).
[3] R. Matsunaga, N. Tsuji, H. Fujita, A. Sugioka, K. Makise, Y. Uzawa, H. Terai, Z. Wang, H. Aoki,
and R. Shimano, ”Light-induced collective pseudospin precession resonating with Higgs mode in asuperconductor”, Science 345, 1145 (2014).
[4] N. Tsuji, P. Barmettler, H. Aoki, and P. Werner, ”Nonequilibrium dynamical cluster theory”, Phys.
Rev. B 90, 075117 (2014).
[5] H. Aoki, N. Tsuji, M. Eckstein, M. Kollar, T. Oka, and P. Werner, ”Nonequilibrium dynamical meanfield theory and its applications”, Rev. Mod. Phys. 86, 779 (2014).
[6] N. Tsuji and P. Werner, ”Nonequilibrium dynamical mean-field theory based on weak-coupling perturbation expansions: Application to dynamical symmetry breaking in the Hubbard model”, Phys.
Rev. B 88, 165115 (2013).
[7] Y. Murakami, P. Werner, N. Tsuji, and H. Aoki, ”Ordered phases in the Holstein-Hubbard model:Interplay of strong Coulomb interaction and electron-phonon coupling”, Phys. Rev. B 88, 125126(2013).
[8] N. Tsuji, M. Eckstein, and P. Werner, ”Nonthermal antiferromagnetic order and nonequilibrium criticality in the Hubbard model”, Phys. Rev. Lett. 110, 136404 (2013).

4205

Effect of electron-phonon couplings on electronic structuresand material design
Takashi Koretsune1, Susumu Saito2
RIKEN Center for Emergent Matter Science (CEMS)1
Tokyo Institute of Technology2
1. Introduction
In recent years, first-principles calculations based on the density functional theory (DFT)
have become essential tools to investigate the electronic structures of various materials.
Moreover, advanced methods to discuss corrections for the DFT results such as GW
approximation has been developed intensively. In this study, we focus on another correction for
the DFT results, that is, the effect of electron-phonon couplings. First, we have developed two
different codes based on the frozen phonon method and the density functional perturbation
theory (DFPT) and confirmed that these two approaches give consistent results and well
reproduce experiments. By employing these methods, we have discussed the temperature andisotope dependence of band structures, and possibility of material design by utilizing theelectron-phonon couplings and isotope effects. We believe our study is of great importance forthe understandings of the effect of electron-phonon couplings from first-principles calculations.
2. Results
1) Isotope effect on the band structure of diamond and graphene
It has been known that the band gap of diamond is reduced due to electron-phonon couplings
even at T=0 and the reduction has large temperature dependence. This means that the band gap
also has isotope dependence. Even a superlattice structure made of 12C and 13C has beensynthesized to utilize the isotope effect. To discuss electronic structures in such nanostructures
made of 12C and 13C, it is of great importance to discuss the difference of the band gap, band
offset and so on in 12C diamond and 13C diamond. For this end, we have synthesized highly pure
impurity-free diamond using chemical vapor deposition (CVD) method for several isotope
compositions and have discussed the isotope dependence of the band gap experimentally andtheoretically.
First, we determined the isotope composition in obtained CVD diamond by Raman peak
positions. From the width of the Raman peak, we also found that the obtained diamond is quiteclean and impurity and defect free. Figure 1 shows the Cathode luminescence (CL) spectra of
diamond with the isotope composition of 12C1-x13Cx. As can be seen, the peak positions havelarge isotope dependence. These peaks correspond to the indirect band gap of diamond. Thus,
considering the isotope dependence of the phonon mode with including the randomness, we
obtained the following expression for the band gap:

206

Fig. 2. Temperature dependence of indirect
band-gap shift due to second-order terms ofelectron-phonon

couplings

in

12

C

diamondFig. 1. Cathode luminescence spectra

calculated using density functional perturbation

for CVD diamond with several isotope

theory (red line). Blue line represents the shift duecomposition, 12C1-x13Cx.

to thermal expansions.

Eg = 5497.66 + 14.37 xf + 0.99 xf2 meV.
Here, xf is the ratio of 13C in diamond. This indicates that the difference of the band gap
between 12C and 13C diamond is 15.4 meV [11].
On the other hand, we also estimated theoretically the isotope effect by calculating the second
order terms of electron-phonon couplings, that is, self-energy term and Debye-Waller term
within the density functional perturbation theory. Figure 2 shows the temperature dependence of
the indirect band gap in 12C diamond due to these two terms together with the thermal expansion
effect, which comes from higher order terms in electron-phonon couplings. This temperaturedependence well agrees with the experiments. Using this result, we can estimate that thedifference of band gap between 12C and 13C diamond is 12 meV at T=0. Furthermore, the band
offsets at the conduction bottom and the valence top are found to be about 7 meV and 5 meVrespectively.
In case of graphene, using the same method, we found that the work function becomesdifferent in 12C and 13C due to electron-phonon couplings. This suggests that the junction of 12C
and 13C graphene would be a pn-junction without applying agate voltage. We also discussed the possibility of band gap
opening using the periodic patterning of carbon isotope.
2) Phonon properties in an adamantane monolayer on aAu(111) surface
Adamantane is the smallest diamondoid, which can be
regarded as small pieces of hydrogen-terminated diamond as
shown in Fig. 3 and is known to exhibit negative electron
affinity. Using this molecule, we discussed how the vibrational

207

Fig. 3. Adamantane

properties of a monolayer of the molecule are affected by a surface. For this purpose, we
performed first-principles calculations and compared the results with the newly developed
infrared scanning tunneling microscopy (IRSTM) technique. The results indicate that the IR
spectrum is significantly modified due to both intermolecular and molecule-substrate interaction.
The theoretical calculations agree well with IRSTM experiments, suggesting that thesetechniques are is useful to discuss the properties of few-layer materials on substrate[10].
3) Evaluation of model parameters in κ-(ET)2X
To design a superconducting material, organic compounds are one of the most promisingmaterials. For example, A15 Cs3C60 has high transition temperature of Tc=38K, which is one of
the highest Tc within phonon-mediated superconductors. On the other hand, organic conductors
such as κ-(ET)2X also host superconductivity. However, these materials are close to the Mott
insulator in the phase space, and thus, the Coulomb
0.4
interaction is considered to be important for
0.2
superconductivity. In other words, even though both0.0
systems can be regarded as carrier doped organic-0.2
compounds, completely different mechanisms are
-0.4
-0.6
considered to be important for superconductivity. To-0.8clarify the difference of these organic compounds,-1.0
systematic approaches from the first-principles
M
Y
Γ
Z
M
Γ
calculations are of great importance. For this end, we
0.4
first obtained the electronic structures of several
0.2
κ-(ET)2X and constructed tight-binding models.
0.0-0.2
Figure 4 shows the obtained DFT band structures-0.4
and tight-binding fits. Analyzing the obtained-0.6
tight-binding model, we concluded that the material-0.8
dependences in κ-ET compounds come mainly from
-1.0
U
Z
Γ
X
U
Γ
anisotropy of the transfer integrals in anisotropic
triangular lattice model rather than the on-site Fig. 4. DFT (red lines) and(on-dimer) Coulomb interaction[7]. Based on this tight-binding (blue lines) bandstudy, we will discuss the intra-dimer degrees of structures of κ-(ET)2Cu(NCS)2
freedom,thephononproperties
and and κ-(ET)2Cu[N(CN)2]Cl.
superconductivity in these compounds.
4) Large surface relaxation in the organic semiconductor tetracene
In organic crystals, inter-molecular interactions play an important role in determining theirstructures as well as their phonon properties. In particular, the surface relaxation is a key issue
for the design of organic nanodevices. Thus, we studied surface relaxation in semiconductor
tetracene theoretically and experimentally. Using X-ray crystal truncation rod scattering
measurements, a significant surface relaxation was observed only in the first monolayer. Thisstrong relaxation can be reproduced by the first-principles calculations. We also found that the208transfer integrals and as a result transport properties are completely different between the bulk
and surface of the semiconductor[4].
3. References
1) Y. Fujimoto and S. Saito, “Electronic structures and stabilities of bilayer graphene
doped with boron and nitrogen”, Surface Science 634 57 (2015)
2) Y. Fujimoto and S. Saito “Adsorption of Molecules on Nitrogen-Doped Graphene: A
First-Principles Study”, JPS Conf. Proc. 4 012002 (2015)3) Y. Aoki and S. Saito “Thermodynamic Effects on Energetic, Structural, and Elastic
Properties of Titanium Dioxide Polymorphs”, JPS Conf. Proc. 4 012005 (2015)4) H. Morisaki, T. Koretsune, C. Hotta, J. Takeya, T. Kimura and Y. Wakabayashi, “Largesurface relaxation in the organic semiconductor tetracene”, Nature Communications 55400 (2014)
5) Y. Sakai, S. Saito, and M.L. Cohen, “Lattice matching and electronic structure offinite-layer grapheme/h-BN thin films”, Phys. Rev. B 89 115424 (2014)6) T. Bazhirov, Y. Sakai, S. Saito and M.L. Cohen, “Electron-phonon coupling andsuperconductivity in Li-intercalated layered borocarbide compounds”, Phys. Rev. B 89
045136 (2014)7) T. Koretsune and C. Hotta, “Evaulating model parameters of the κ- and β’-type Mott
insulating organic solids”, Phys. Rev. B 89 045102 (2014)8) Y. Fujimoto, T. Koretsune and S. Saito, “Electronic structures of hexagonalboron-nitride monolayer: strain-induced effects”, J. Ceramic Soc. Japan 122 346 (2014)9) Y. Fujimoto, T. Koretsune and S. Saito, “Electronic Structures of Carbon-Doped
Hexagonal Boron Nitride Sheet: A Density-Functional Study”, JPS Conf. Proc. 1
012066 (2014)
10) Y. Sakai, G.D. Nguyen, R.B. Capaz, S. Coh, I.V. Pechenezhskiy X. Hong, F. Wang,
M.F. Crommie, S. Saito, S. G. Louie and M. L. Cohen, “Intermolecular interactions andsubstrate effects for an adamantine monolayer on a Au(111) surface”, Phys. Rev. B 88
235407 (2013)11) H. Watanabe, T. Koretsune, S. Nakashima, S. Saito, and S. Shikata, “Isotope
composition dependence of the band-gap energy in diamond”, Phys. Rev. B 88 205420(2013)
12) Y. Aoki and S. Saito, “Energetics and electronic properties of heavily nitrogen-doped
titanium dioxide”, J. Ceramic Soc. Jpn. 121 373 (2013)
4. Invited talks
4 invited talks in the international conferences and 7 in domestic conferences.

209

Development of Computational Code of Electron Excitation Dynamics
in Green’s Function Method
Kaoru Ohno1, Shota Ono1, and Riichi Kuwahara1,2
1

Department of Physics, Graduate School of Engineering, Yokohama National University, 79-5
Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
2

Dassault Systems BIOVIA K.K., ThinkPark Tower, 2-1-1 Osaki, Shinagawa-ku,
Tokyo 141-6020, Japan

1. INTRODUCTION
The Green's function method in the many-body perturbation theory plays a powerful role infirst-principles calculations of excited states of materials. Almost 50 years ago, Hedin
proposed a closed set of equations for Green's function, the dynamically screened Coulombinteraction W (composed of the polarization function P), and the vertex function Γ. Its
simplest approximation is called the GW approximation or the self-consistent GW approach,where the vertex function is replaced by unity. In this approximation, P and W become those of
the random phase approximation (RPA) and the self-energy Σ is given by iGW symbolically.
However, as a deficiency of the self-consistent GW approximation, the Ward-Takahashi
identity, which is derived from gauge invariance, is not satisfied. Consequently, the band gap
is overestimated. In order to satisfy the Ward-Takahashi identity, the vertex function must be
included in the self-energy and the polarization function, which is a very difficult task.
Another difficulty in the quasiparticle representation is that the quasiparticle wavefunctions
are non-orthonormal and linearly dependent due to the energy dependence of the self-energy.
One way to solve this problem is to use Löwdin's symmetrized orthonormalization procedure,
but there is a big question how to deal with this energy dependence when the quasiparticle
equation is solved self-consistently.
Here, we propose a simple and practical way to solve these problems. Our idea is to linearize
the energy dependence of the self-energy. The key point in the present formulation is toguarantee its relation to the Ward identity, i.e., the q = 0 and ω – ω’ = 0 limit of WardTakahashi identity. As a result, the quasiparticle energies are greatly improved for Li and Na(atoms and dimers). Within this approach, we also calculate the total energy for the groundstate. Since the direct calculation of the Luttinger-Ward functional Φ is a heavy task, we
propose more convenient formulae on the basis of a plasmon-pole model. Here we use the allelectron mixed basis approach (the name of our program is TOMBO), in which quasiparticle
wavefunctions are expanded with atomic orbitals and plane waves.
On the other hand, it has been highly desired to go beyond the time-dependent density
functional theory (TDDFT) within the local (time and space) density approximation in theinvestigation of time-dependent correlated electron systems, because there is a delay inelectron dynamics, and correlation between two electrons or two holes cannot be treated in thisframework. One possibility to go beyond the TDDFT is to invoke the time-dependent Green’s
function formalism in the quantum many-body perturbation theory. We have formulated such atheory, and now implementing it into TOMBO.

210

2. THEORY
The quasiparticle equation can be written as( T + vnuc + Σ(εn) ) | n > = εn | n >,(1)

where the eigenstates | n > are the quasiparticle states, the eigenvalues εn are the quasiparticle
energies, T is the kinetic energy operator, vnuc is the nucleus Coulomb potential, and Σ(εn) is theself-energy operator. Note that the self-energy operator is energy dependent, and therefore thequasiparticle states are non-orthonormal and linearly dependent. This fact makes thesubsequent formulation very difficult. To avoid this difficulty, we expand the self-energy withrespect to the eigenvalue εn to obtainH | n > = εn Λ | n >,H = T + vnuc + Σ(µ) – µ dΣ(ω)/dω|ω=µ,(2)

where Λ is defined byΛ = 1 – dΣ(ω)/dω|ω=µ.

(3)

Here, µ can be set, for example, at the mean eigenvalue of the highest occupied molecularorbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) levels. Here we use nindependent µ and Λ, and the Cholesky decomposition with the lower triangular matrix L as

Λ = L L†

(4)

Then we can naturally define the orthonormalized quasiparticle states and the corresponding
Hamiltonian as| ñ > = L† | n >,

Õ = L–1 H L–1†.

(5)

As a consequence, we have the linearized quasiparticle equation:
Õ | ñ > = εn | ñ >(6)The orthonormalized states satisfy the following orthonormality and completeness conditions:< ñ | ã > = δna,

Σn | ñ > < ñ | = 1.

(7)

The occupation number of these states is purely zero or one according to whether thecorresponding quasiparticle energy is above or below the Fermi level. In contrast, the originalquasiparticle states satisfy < n | Λ | a > = δna and Σn | n > < n | = Λ–1. Since | n > do notsatisfy the completeness condition, Green's function defined in this linearized framework,
G(ω) = Σn | n > 1/(ω – εn – iηn) < n | = Σn Λ / [(ω – iηn)Λ – H] | n > < n |,(8)

(εn is 0+ for occupied states n and 0– for empty states n.) does not have a ``resolvent" form.
This Green's function does not satisfy the charge conservation law. In fact, it is easy to see that–i∫dr∫dω/2π exp(iηω ) < r | G(ω) | r > ≠ N, where η is a positive infinitesimal number (0+).
This violation of the charge conservation is related to the existence of the incoherent part inGreen's function. In order to avoid this difficulty, we introduce the renormalized Green's
function as:

211Ã(ω) = L† G(ω) L = Σn | ñ > 1 / (ω – εn – iηn) < ñ | = Σn | ñ > < ñ | 1 / (ω – iηn – Õ).

(9)In this representation, since the quasiparticle states are orthonormal, Eq.(¥ref{Charge}) withtilde G(w) in place of G satisfies the charge conservation,∫ρ(r) dr = –i ∫dr∫dω/2π exp(iηω ) < r | Ã(ω) | r > = N,

(10)

and the electron charge density ρ(r) is given byρ(r) = Σnocc | < r | ñ > |2,(11)

where occ means to take the summation over all occupied states. Note that the coherent part ofthe original Green's function is given by G(ω) = L–1†Ã(ω) L–1, and the matrices L–1† and L–1
correspond to the square root of the renormalization factor Z = Λ–1. Then we should write theHartree term as

ΣH (r) = –i∫dr’v(r – r’) ∫dω/2π exp(iηω )Ã(r, r’; ω) = ∫dr’v(r – r’)ρ(r’),(12)

where v(r – r’) is the bare Coulomb interaction.
The most important fact here is that the vertex function is related to Λ via the Ward identity,i.e., the Ward--Takahashi identity in the q = 0 and ω – ω’ = 0 limit,Γ(ω = µ, ω’ = µ; q = 0) = 1 – dΣ(ω)/dω|ω=µ = Λ.

(13)This relation can be also written as the well-known formula ΓZ = 1. The formulation up to here
is very general and can be applied to any Green's function-based framework. Then, according
to the Hedin's set of equations, the self-energy Σxc(ω) except for the Hartree term isapproximated as iÃW, the dynamically screened Coulomb interaction W is described by thepolarization function P and the interaction kernel dΣH/dG as W = [1 – i (dΣH/dG)P]–1v. Since
the exact polarization function P is given by P = –iGGΓ and the interaction kernel is given by–ivΛ, we find that W is equal to W = [1-vΠ] –1v, where we defined the renormalized
polarization function Π as Π = ΛP = –iΛGGΓ ~ –iΛGGΛ = –iÃÃ. Therefore Σxc(ω) and W arefunctionals only of Ã. Thus, our formulation is identical to that of the non-linearized selfconsistent GW approach with G replaced by Ã. (Ref.: PUBLICATION No.5.)
3. RESUSLTS
Table 1. IP and EA of LGW and other results of Li, Na atoms and dimers
compared with the preexisting experimental data. (Ref.: PUBLICATION No.5.)
(eV)
LDA
HF
B3LYP
GW
LGW
Previous GW
Experiment

Li
IP
3.14
5.34
3.34
5.78
5.66
-5.39

Li2
EA
1.83
0.04
1.00
0.22
0.28
-0.62

IP
3.24
4.88
3.30
5.56
5.32
4.6
5.15

Na
EA
1.84
0.08
0.99
0.20
0.35
-0.44

212

IP
3.08
4.94
3.16
5.32
5.20
5.49
5.14

Na2
EA
2.04
0.14
1.09
0.25
0.31
-0.55

IP
3.27
4.53
3.19
5.11
4.92
5.10
4.93

EA
1.97
0.01
1.01
0.32
0.45
-0.43

Using this linearized self-consistent GW (LGW) approach implemented in TOMBO, wehave calculated the ionization potential (IP) and the electron affinity (EA) of Li, Li2, Na, andNa2. Table 1 shows the result together with the results obtained by other methods (LDA, HF,
and B3LYP) as well as the preexisting experimental data. Because the LGW values are theclosest to the experimental values except for the HF, IP of Li, we find that the LGW
significantly improves the results of the ordinary self-consistent GW result and other results.
(Ref.: PUBLICATION No.5.)
4. SUMMARY
We have formulated the linearized the self-consistent GW approach, implemented it into the
all-electron mixed basis program, TOMBO, and found that the resulting quasiparticle energies
are greatly improved compared to the ordinary self-consistent GW and other approaches suchas LDA, HF, B3LYP. Although we did not show explicitly here, we have also proposed theconvenient formula to evaluate the Luttinger-Ward functional Φ using a plasmon pole modeland calculated the total energy of Li and Na (atoms and dimers).
Futhermore, we have succeeded in formulating the time-dependent Green’s function theory
for the excited state by extending the ordinary Green’s function theory for the ground state. We
are now implementing it into TOMBO and submitting a paper.
5. PUBLICATIONS
1. Chao Li, Ming Zhang, Lei Miao, Jianhua Zhou, Yi Pu Kang, C. A. J. Fisher, Kaoru Ohno,
Yang Shen, and Hong Lin, “Effects of environmental factors on the conversion efficiency
of solar thermoelectric co-generators comprising parabola trough collectrors andthermoelectric modules without evacuated tubular collector”, Energy Conversion andManagement 86, 944-951 (2014). DOI: 10.1016/j.enconman.2014.06.010
2. Shota Ono, Riichi Kuwahara, and Kaoru Ohno, “Heterojunction of single-walled cappedcarbon nanotube and zinc phthalocyanine with high energy conversion efficiency”, J. Appl.
Phys. 116, 054305;1-4 (2014). DOI: 10.1063/1.4892093
3. Riichi Kuwahara and Kaoru Ohno, “Stable spin states of boron, aluminum, and silicon
dimers in a self-consistent GW calculation”, Mod. Phys. Lett. B 28 (No.20) 1450166; 1-9(2014). DOI: 10.1142/S0217984914501668
4. Riichi Kuwahara, Yoichi Tadokoro, and Kaoru Ohno, “Validity of virial theorem in allelectron mixed basis density functional, Hartree--Fock, and GW calculations”, J. Chem.
Phys. 141, 084108;1-6 (2014). DOI: 10.1063/1.4893477
5. Riichi Kuwahara and Kaoru Ohno, “Linearized self-consistent GW approach satisfying theWard identity”, Phys. Rev. A 90, 032506;1-9 (2014). DOI: 10.1103/PhysRevA.90.032506
6. Shota Ono, Yoshifumi Noguchi, Ryoji Sahara, Yoshiyuki Kawazoe, and Kaoru Ohno,“TOMBO: All-electron mixed-basis approach to condensed matter physics”, Computer
Physics Communications 189, 20-30 (2015). DOI: 10.1016/j.cpc.2014.11.012
7. Yusuke Noda, Shota Ono, and Kaoru Ohno, “Geometry Dependence of Electronic andEnergetic Properties of One-Dimensional Peanut-Shaped Fullerene Polymers”, J. Phys.
Chem. A, accepted for publication (2015): DOI: 10.1021/jp512451u

213Large Scale First-Principles Calculations on
Transition Metal Oxide Superlattices

F. Ishii and M. Saito
Institute of Science and Engineering, Kanazawa University
Introduction
Recently, the two-dimensional electron gas (2DEG) formed at the transition metal oxides
interface has attracted much attention for applications in the next generation device. The
perovskite heterostructure composed dielectric materials LaAlO3/SrTiO3 is one of such systems
extensively studied. The polar interface induces large built-in electric field. Therefore, theelectric-field induced spin-orbit interaction(SOI) in the perovskite heterostructure is quite
important in understanding the electronic
structures.
In this research, by using large-scale
first-principles calculations based on thedensity functional theory implemented
OpenMX[1], we revealed specific electronic
states and properties formed at the interface ofthe transition metal oxides modeled bysuperlattice. We focused on how spins can becontrolled by electric field (electric
polarizations and charge carriers). In additions
to the 2DEG in the oxides heterostructure, we
also revealed that the effect of SOI in strained
ZnO bulk and film, the spin textures at thesurfaceoftopologicalinsulators,
carrier-induced
magnetisminbilayerzigzag-edged graphene nanoribbons, andtriangular lattice multiferroic oxides. The
applications of 2DEG at the oxide interface,
we proposed anomalous Seebeck effect.
Rashba effect in the (LaAlO3)n/(SrTiO3)nsuperlattice
We have performed first-principles calculationsof (LaAlO3)n/(SrTiO3)n (n=2-8). We evaluatedthe spin-orbit coupling constant, the Rashba
parameter, for the interface states. In addition,
we investigated the spin textures, i.e.,
momentum vector dependent magnetic field214

Figure 1 (a) Structure of (LaAlO3)6/(SrTiO3)6 and(b) atom projected density of states. The numbers
in parenthesis is layer index. The dotted line in
the density of states show the bottom of the Ti 3dstates in the conduction bands.

B(k) in the Brillouin zone. Figure 1(a) shows
artificial superlattice (LaAlO3)6/ (SrTiO3)6. As we
assumed SrTiO3 substrate, the in-plane lattice
constants are SrTiO3 as 0.395nm. Lattice constant c,
the period of superlattice, is determined by constantvolume approximation where the volume isequivalent to bulk. Figure 1(b) shows atom projected
density of states. We can evaluated built-in electricfield by energy level at the bottom of the empty Ti 3dstates . The estimated value of electric field 768
meV/nm is in good agreement with experimental
value 801 meV/nm[2]. Figure 2 shows atomic
Figure 2 Atomic displacement
relative to ideal structure in(LaAlO3)6/(SrTiO3)6.

displacement relative to ideal structure, i.e., bulk-like
locally non-polar structures. If we assumed point
charge ionic model as Sr2+, La3+, Al3+, Ti4+, and O2-, theelectric field can beunderstood by theatomic displacement.
The direction ofelectric
field
isreflected in the spin
textures of interface
states as in figure 3(a) and (b).

Figure 3 Spin textures of interface states for (LaAlO3)6/(SrTiO3)6 ,(a) lower energy band, (b) higher energy band. The background isband energy and white color is Fermi energy.

Spin-orbit effect in the ZnO
We have perform first-principle calculations of wurtzite ZnO bulk and thin-film (1010)
surface system based on the density-functional theory(DFT) within the generalized gradient approximation byusing the OpenMX code [1]. For the film case, we have
performed large scale computation up to 120 ZnO bilayer
and the period of unitcell is about 20 nm. We evaluated thespin texture whose energy is slightly higher than that of the
conduction band bottom in bulk and surface banbs in (1010)
surface. We find that the Rashba spin rotations can beinversed by applying biaxial strain. This inversion of therotation is due to the fact that the biaxial strain inverse thedirections of the electronic polarization around the Zn atom.
These findings suggest that the Rashba effect can becontrolled by substrates. In the (1010) film case, we findthat in-plane electric polarization induces the
Figure 4 Calculated band structure ofquasi-one dimensional orientations of the spin! 0) ideal structure(purple line),ZnO (101
textures. Figure 4 shows calculated band structure of
relaxed structure (blue line) and bulk
(gray line).

215

relaxed film and unrelaxed film, and bulk. We find surface states above bulk valence band top.
The atomic relaxation drastically changes surface states. The atomic relaxation also changes theelectric field at the surface. Therefore the spin textures and spin-orbit coupling constant of thesurface states is strongly affected by the atomic relaxations. We find that the values of thespin-orbit strength and the wavelength of the spin-helix are comparable with those observed forvarious zinc-blende quantum well structures.
References[1] T. Ozaki et al., http:// www.openmx-square.org/[2] Singh-Bhalla et all, Nat. Phys. 7, 80 (2001).
Publications and Invited Talks
Publications
1)

M.A.U. Absor, H. Kotaka, F. Ishii, and M. Saito, “Tunable Rashba effect on strained ZnO:First-principles density-functional study”, Appl. Phys. Express, 7, 053002(2014).
 K. Sawada, F. Ishii, and M. Saito, “First-principles study of carrier-induced ferromagnetismin bilayer and multilayer zigzag graphene nanoribbons”, Appl. Phys. Lett. 104, 143111(2014).
3) M. Nishida, F. Ishii, M. Saito, Magnetism-Driven Electric Polarization of Multiferroic
Quasi-One-Dimensional Ca3CoMnO6: First-Principles Study Using Density Functional
Theory, J. Phys. Soc. Jpn., 83, 124711 (2014).
4) M. Nishida, F. Ishii, and M. Saito“First-principles study of Exchange Interaction in
Ising-type Multiferroic Ca3CoMnO6”, JPS. Conf. Proc., 3, 014040(2014).
5) F. Ishii, T. Onishi, and H. Kotaka, “Spin-Orbit Interaction Effects in the Electronic Structureof B20-type CoSi: First-Principles Density Functional Study”, JPS. Conf. Proc.,
3,016019(2014).
6) Y.P. Mizuta, and F. Ishii, “Contribution of Berry Curvature to Thermoelectric Effects”, JPS.
Conf. Proc., 3, 017035(2014).
7) T. Kato, H. Kotaka, and F. Ishii, First-principles study of surface states in topologicalinsulators Bi2Te3 and Bi2Se3 :Film thickness dependence, Mol. Simul., in press, published
online DOI:10.1080/08927022.2014.964476.
8) M. Nishida, F. Ishii, H. Kotaka, and M. Saito, First-Principles Study of Rashba Effect in the(LaAlO3)2/(SrTiO3)2, Mol. Simul., in press, published online
DOI:10.1080/08927022.2014.987986.
9) T. Kato, H. Kotaka, and F. Ishii, First-Principles Study of Topological Insulators A2B3(A=Biand Sb, and B=O, S, Se and Te), JPS Conf. Proc. 5, 011022 (2015).
10) Y. P. Mizuta, and F. Ishii, Thermopower of Doped Quantum Anomalous Hall Insulators: Thecase of Dirac Hamiltonian, JPS Conf. Proc. 5, 011023 (2015).
11) M. Nishida, Ph.D. Thesis, “Theoretical studies on spin structures and physical properties oftransition metal oxides”, in Japanese, Kanazawa University, 2015.

Invited talks
1) F. Ishii, “First-Principles study on pyrochlore iridates and rhodates: metal-insulator transition,
magnetism, and topology", International Workshop on Frustration and Topology inCondensed Matter Physics (February 13-16, 2014, Tainan, Taiwan).
2) F. Ishii, “Spin-Orbit Effects in Ferroelectric Oxides: Towards Oxide Spintronics”,
IUMRS-ICA 2014 (August 24-30, 2014, Fukuoka, Japan).

216

Development of quantum multi-component molecular theory
and its application to material design
Masanori Tachikawa
Graduate School of Nanobiosystem, Yokohama City University,
Kanazawa-ku, Yokohama 236-0027, Japan
1. Introduction
Recently, in our group, we have developed and improved some first-principles approaches forquantum multi-component systems including both electrons and nuclei (sometimes positron, ormuon) quantum-mechanically: Multi-component molecular orbital (MC_MO) [1], density
functional theory (MC_DFT) [2], quantum Monte Carlo (MC_QMC) [3], and ab initio path
integral (PI) [4] methods. In this KAKENHI research project, we have focused on the developmentof these quantum multi-component molecular theories and its microscopic (molecular level)
application to material design as follows, Nuclear quantum effect and temperature dependency on the hydrogen-bonded structure ofbase pairs: path integral hybrid Monte Carlo approach with semi-empirical method
 Systematic theoretical investigation of a positron binding to amino acid molecules: ab initio
multi-component molecular orbital approach Accurate prediction of hyperfine coupling constants in muoniated and hydrogenated ethyl
radicals: ab initio path integral approach with density functional theory method
 Can formaldehyde molecule bind a positron? Theoretical prediction with state-of-the-art firstprinciples calculation: multi component quantum Monte Carlo approach
Here, we would like to show main results, one by one.

2. Main results of our research project2.1. Nuclear quantum effect and temperature dependency on the hydrogen-bonded
structure of base pairs
The structure of Watson-Crick type Adenine-Thymine andGuanine-Cytosine pairs (Figure 1) has been studied by hybridMonte Carlo (HMC) and path integral hybrid Monte Carlo(PIHMC) simulations (Figure 2) with the use of semi-empirical
PM6-DH+ method in the gas phase. We elucidated the nuclear
quantum effect and temperature dependency on the hydrogenbonded moiety of base pairs. It was shown that the contribution of
nuclear quantum effect on the hydrogen-bonded structure issignificant not only at low temperature 150 K but also attemperature as high as 450K. The relative position ofhydrogen-bonded proton between two heavy atoms, and thenuclear quantum nature of the proton are also shown (Figure 3).

217

Guanine-Cytosine pair

Adenine-Thymine pairFigure 1. Schematic illustrationof Watson-Crick type base pairsFurthermore, we have applied principal component analysis to HMC and PIHMC simulations inorder to analyze the nuclear quantum effect on intermolecular motions. We found that the ratio of
Buckle mode (lowest vibrational mode from normal mode analysis) decreases due to the nuclear
quantum effect, while that of Propeller mode (second lowest vibrational mode) increases. In
addition, non-planar structure of base pairs was found to become stable due to the nuclear quantum
effect from two-dimensional free energy landscape along Buckle and Propeller modes.

H2 molecule with 8 beads
Figure 2. Schematic illustration of path integral scheme for H2 molecule

Figure 3. One-dimensional distributions of (a) RN1H1 and (b) RN1…O1

2.2. Systematic theoretical investigation of a positron binding to amino acid moleculeswith ab initio multi-component molecular orbital approach
The feature of positron binding to twenty neutral amino acid molecules having the global minimum(GM) and the intramoleculear hydrogen-bonded (HB) structures was analyzed with ab initio
multi-component molecular orbital method. All amino acid molecules in the intramoleculear HB
structures have positive positron affinity (PA, the binding energy of a positron) values, whichmeans that a positron can be attached to parent molecules, while in the GM structures only threeamino acid molecules of Gln, Trp, and His have positive PA values. Analyzing the positronic
orbitals of each positronic amino acid molecule and the electrostatic potential maps of thecorresponding parent molecules, we found that the long-range electrostatic interaction is the most
crucial role in the positron binding to neutral amino acid molecules (Figure 4). The strong
correlation is observed between the PA and dipole moment, that is, a polar molecule with a large
dipole moment has a large PA value (Figure 5). The critical dipole moment of neutral amino acidmolecules for binding a positron is found as about 3.46 Debye. From the systematic analysis fortwenty kinds of amino acid molecule, we theoretically confirmed the possibility of positron binding
to conformers of amino acid molecules having strong dipole moment.

218

Figure 4. (a) The positronic molecular orbital and the electronic highest occupied molecularorbital (HOMO) of [Gly; e+] system in the hydrogen-bonded (HB) structure with Hartree-Fock(HF) level of the multi-component molecular orbital (MC-MO) method. Contours of isovalue
0.01 are drawn. The meshed region denotes the contour of the positronic orbital, while the red
and green regions are of the positive and negative parts of the electronic HOMO, respectively.
(b) The electrostatic potential (ESP) map of Gly in the HB structure. The intensity of ESP iscoloured on electronic charge density surface with contours of isovalue 0.0004. The charges on
nitrogen and oxygen atoms (δ) obtained with natural bond orbital (NBO) analyses are also
shown.

Figure 5. The correlation between dipole moment values (Debye) and positron affinity values(meV) of amino acid molecules. The solid circles and squares denote the hydrogen-bonded (HB)
and global minimum (GM) structures, respectively. The correlation coefficient (R2) in linear
regression analysis is also shown.

219

2.3. Accurate prediction of hyperfine coupling constants in muoniated andhydrogenated ethyl radicals: ab initio path integral simulation study with density
functional theory method
We performed ab initio path integral molecular dynamics (PIMD) simulation (Figure 1) withdensity functional theory (DFT) method to accurately predict hyperfine coupling constants(HFCCs) in ethyl radical (CβH3—CαH2) and its Mu-substituted (muoniated) compound(CβH2Mu—CαH2) (Figure 6). The substitution of Mu atom, an ultra-light isotope of the H atom,with larger nuclear quantum effect is expected to strongly affect the nature of ethyl radical. The
static conventional DFT calculations of CβH3—CαH2 find that the elongation of one Cβ—H bondcauses a change in the shape of potential energy curve along the rotational angle via the imbalanceof attractive and repulsive interactions between the methyl and methylene groups. Investigation of
the methyl-group behavior including the nuclear quantum and thermal effects shows thatunbalanced CβH2Mu group with the elongated Cβ—Mu bond rotates around the Cβ—Cα bond in
muoniated ethyl radical, quite differently from the CβH3 group with the three equivalent Cβ—H
bonds in ethyl radical. These rotations couple with other molecular motions such as the
methylene-group rocking motion (inversion), leading to difficulties in reproducing thecorresponding barrier heights. Our PIMD simulations successfully predict the barrier heights to beclose to the experimental values, and provide a significant improvement in muon and proton
HFCCs given by static conventional DFT method. Further investigation reveals that the Cβ—Mu/H
stretching motion, methyl-group rotation, methylene-group rocking motion, and HFCC values
deeply intertwine with each other. Because these motions are different between the radicals, aproper description of the structural fluctuations reflecting the nuclear quantum and thermal effects
is vital to evaluate HFCC values in theory to be comparable to the experimental ones (Table 1).
Accordingly, a fundamental difference in HFCC between the radicals arises from their intrinsic
molecular motions at a finite temperature, in particular the methyl-group behavior.

Figure 6. Schematic illustration of muonated ethyl radical.

Table 1. Bond lengths and HFCC values.
PIMD
Exptl.
Propert Convention
y
al MO
Mu
H
Mu
H
Bond Length [Å]R(Cβ–X)
1.104
1.17 1.12
Isotropic HFCC [mT]A′(Mu)a
5.36
4.2
3.70
A(Me)b2.67
3.0
2.8
2.82 2.69
a Reduced Mu HFCC: A′(Mu) = 0.31413 × A(Mu)b Averaged HFCC for CH2Mu or CH3 group2202.4. Can formaldehyde molecule bind a positron?
Theoretical prediction with state-of-the-art first principles calculation
The vertical positron affinity (PA) value at the equilibrium position of formaldehyde molecule ispredicted as +25(3) meV with highly accurate quantum Monte Carlo method. Applying theanharmonic vibrational analysis, we have found that the vibrational excitation of C=O stretchingmode drastically enhances the PA value, due to the increment of molecular dipole moment along
this mode (Table 2). Our most accurate prediction of the vibrational averaged PA values at thefundamental and overtone states are 31 and 36 meV, respectively, which strongly supports theconclusion that a positron can bind to formaldehyde (Figure 7).

Table 2 The vibrational positron affinities ( PA ),absolute value of dipole moments ( ), and isotropic
polarizabilities ( ) for vibrational ground state (gs)and fundamental tones (X1)a.

[Å3]



P A [meV]gs

25.78(3)

2.80

2.46

11

24.51(3)

2.76

2.51

21

30.69(3)

2.83

2.48

31

26.03(3)

2.80

2.47

41

24.88(6)

2.77

2.47

51

23.60(2)

2.74

2.51

[debye]6125.91(2)2.80
2.47
X denotes normal mode: symmetric C–H stretching(1), C=O stretching (2), CH2 bending (3), out-of-planebending (4), anti-symmetric C–H stretching (5), andCH2 rocking (6) modes. The quantum number for themode X is denoted as subscript, and for other modes,
quantum numbers are set to zero.
a

Figure 7 Vibrationally averaged positron
affinity fit as described by eq. (4), using the
dipole moment ( ) and polarizability ( ) for
CH2O. The 2 denotes vibrational quantum
number for C=O stretching mode, andPA(LSQ) denotes the value calculated using
Eq. (4). The_ adjusted coefficient ofdetermination ( R 2) for this fitting is also
shown in this figure.

2.5. References[1] M. Tachikawa, H. Mori, H. Nakai, and K. Iguchi, Chem. Phys. Lett., 290, 437 (1998), M.
Tachikawa, Chem. Phys. Lett., 350, 269 (2001), 360, 494 (2002).
[2] T. Udagawa and M. Tachikawa, J. Chem. Phys., 125, 244105 (2006).
[3] Y. Kita, R. Maezono, M. Tachikawa, M. Towler, and R. J. Needs, J. Chem. Phys., 131, 134310(2009), 135, 054108 (2011).
[4] M. Shiga, M. Tachikawa, and S. Miura, Chem. Phys. Lett., 332, 396 (2000). M. Tachikawa and
M. Shiga, J. Am. Chem. Soc., 127, 11908 (2005).

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3. Co-workers
Dr. Yukiumi Kita, Dr. Yukio Kawashima, Dr. Kenta Yamada (Yokohama City Univ.)
Mr. Masashi Daido, Mr, Katsuhiko Koyanagi, Ms. Yurika Yamada (Students)

4. Outreach
4.1. Selected publication (Total 63 papers)
1.

K. Egashira, Y. Yamada, Y. Kita, and M. Tachikawa, "Ferromagnetic spin coupling in thechromium dimer cation: Measurements by photodissociation spectroscopy combined withcoupled-cluster calculations", J. Chem. Phys., 142, 054309 (4pages) (2015).
2. Y. Kanematsu and M. Tachikawa, "Theoretical analysis of geometry and NMR isotope shift inhydrogen-bonding center of photoactive yellow protein by combination of multicomponent
quantum mechanics and ONIOM scheme", J. Chem. Phys., 141, 185101 (8pages) (2014).
3. M. Tachikawa, "Positron-attachment to acetonitrile, acetaldehyde, and acetone molecules:
Vibrational enhancement of positron affinities with configuration interaction level ofmulti-component molecular orbital approach", J. Phys.: Conf. Ser., 488, 012053 (7pages)(2014).
4. Y. Yamada, Y. Kita, and M. Tachikawa, "Theoretical prediction of the binding of a positron toa formaldehyde molecule using a first-principles calculation", Phys. Rev. A, 89, 062711(5pages) (2014).
5. Oyamada and M. Tachikawa, "Multi-component molecular orbital study on positronattachment to alkali-metal hydride molecules: nature of chemical bonding and dissociation
limits of [LiH; e+]", Eur. Phys. J. D, 68, 231-239 (2014).
6. T. Udagawa, T. Tsuneda, and M. Tachikawa, "Electron-nucleus correlation functional for
multicomponent density-functional theory", Phys. Rev. A, 89, 052519 (5pages) (2014).
7. Y. Kanematsu and M. Tachikawa, "Development of multicomponent hybrid density functional
theory with polarizable continuum model for the analysis of nuclear quantum effect andsolvent effect on NMR chemical shift", J. Chem. Phys., 140, 164111 (7pages) (2014).
8. K. Yamada, Y. Kawashima, and M. Tachikawa, "Accurate prediction of hyperfine coupling
constants in muoniated and hydrogenated ethyl radicals: ab initio path integral simulation
study with density functional theory method", J. Chem. Theor. Comput., 10, 2005-2015(2014).
9. Y. Kita and M. Tachikawa, "Theoretical investigation of the binding of a positron tovibrational excited states of hydrogen cyanide molecule", Eur. Phys. J. D, 68, 116-122 (2014).
10. Y. Yamada, Y. Kita, M. Tachikawa, M. Towler, and R. J. Needs, "Quantum Monte Carlo andhigh-level ab initio molecular orbital investigation of dissociation channels of the positronic
alkali-metal hydrides, [XH;e+] (X = Li, Na, and K)", Eur. Phys. J. D, 68, 63-68 (2014).
11. Y. Oba and M. Tachikawa, "Theoretical investigation of a positron binding to aspartame
molecule using the ab initio multi-component molecular orbital approach", Int. J. Quant.
Chem., 114, 1146-1149 (2014).
12. Y. Kawashima and M. Tachikawa, "An Ab Initio Path Integral Molecular Dynamics Study of
the Nuclear Quantum Effect on Out-of-plane Ring Deformation of Hydrogen Maleate Anion",
J. Chem. Theor. Comput., 10, 153-163 (2014).
13. T. Udagawa and M. Tachikawa, "Why is N...Be distance of NH3H+...DBeH shorter than that of
NH3D+...HBeH? Paradoxical geometrical isotope effects for partially isotope-substituted
dihydrogen-bonded isotopomers", J. Comput. Chem. (Communication), 35, 271-274 (2014).
14. Y. Ogata, M. Daido, Y. Kawashima, and M. Tachikawa, "Nuclear quantum effect on

222

protonated Lysine with asymmetric low barrier hydrogen bond: ab initio path integral
molecular dynamics study", RSC Advances, 3, 25252-25257 (2013).
15. K. Koyanagi, Y. Takeda, T. Oyamada, Y. Kita, and M. Tachikawa, "Positron-attachment tononpolar or small dipole CXY (X, Y = O, S, and Se) molecules: Vibrational enhancement of
positron affinities with configuration interaction level of multi-component molecular orbital
approach", Phys. Chem. Chem. Phys., 15, 16208-16213 (2013).
16. K. Koyanagi, Y. Kita, Y. Shigeta, and M. Tachikawa, "Binding of a Positron to Nucleic Base
Molecules and Their Pairs", ChemPhysChem (Communication), 14, 3458-3462 (2013).
17. M. Daido, Y. Kawashima, and M. Tachikawa, "Nuclear quantum effect and temperaturedependency on the hydrogen-bonded structure of base pairs", J. Comput. Chem., 34,
2403-2411 (2013).
18. Y. Kawashima, K. Suzuki, and M. Tachikawa, "Ab initio path integral simulations for the
fluoride ion-water clusters: Competitive nuclear quantum effect between F--water andwater-water hydrogen bonds", J. Phys. Chem. A, 117, 5205-5210 (2013).
19. T. Udagawa, T. Ishimoto, and M. Tachikawa, "Theoretical Study of H/D Isotope Effects on
Nuclear Magnetic Shieldings Using an ab initio Multi-Component Molecular Orbital Method",
Molecules, 18, 5209-5220 (2013).
20. K. Suzuki, M. Tachikawa, and M. Shiga, "Temperature dependence on the structure of Zundelcation and its isotopomers", J. Chem. Phys., 138, 184307 (7pages) (2013).
21. Y. Kawashima and M. Tachikawa, "Nuclear quantum effect on intramolecular hydrogen bondof hydrogen maleate anion: An ab initio path integral molecular dynamics study", Chem. Phys.
Lett., 571, 23-27 (2013).
22. Q. Wang, K. Suzuki, U. Nagashima, M. Tachikawa, and S. Yan, "Path integral molecular
dynamic study of nuclear quantum effect on small chloride water clusters of Cl-(H2O)1-4",
Chem. Phys., 419, 229-236 (2013).
23. T. Ishimoto and M. Tachikawa, "Theoretical analysis of phase transition temperature ofhydrogen-bonded dielectric materials induced by H/D isotope effect", Progress in Theoretical
Chemistry and Physics, B27, 303-329 (2013).
24. A. Koizumi, M. Tachikawa, and M. Shiga, "Quantum fluctuation and vibrational dynamics ofaqueous Cu+ and Ag+ clusters ", Chem. Phys., 419, 44-49 (2013).
25. Y. Kita, H. Kamikubo, M. Kataoka, and M. Tachikawa, "Theoretical analysis of thegeometrical isotope effect on the hydrogen bonds in photoactive yellow protein with
muti-component density functional theory", Chem. Phys., 419, 50-53 (2013).
26. Y. Yamada, K. Hongo, K. Egashira, Y. Kita, U. Nagashima, and M. Tachikawa, "Gold-standard
coupled-cluster study of the ground-state chromium dimer cation", Chem. Phys. Lett., 555,
84-86 (2013).
27. M. Hatakeyama, T. Mashiko, H. Hazama, K. Awazu, and M. Tachikawa, "Theoretical analysis
of correlation between ionization threshold fluence in IR-MALDI and IR absorption spectrumof matrix molecules", Int. J. Quant. Chem., 113, 125-129 (2012).
28. M. Tachikawa, Y. Kita, and R. J. Buenker, "Bound states of positron with simple carbonyl andaldehyde species with configuration interaction multi-component molecular orbital and local
vibrational approaches", New J. Phys., 14, 035004 (10pages) (2012).
29. K. Koyanagi, Y. Kita, and M. Tachikawa, "Systematic theoretical investigation of
positron-binding to amino acid molecules with ab initio multi-component molecular orbital
approach", Eur. Phys. J. D, 66, 121 (7pages) (2012).
30. Y. Kita, R. Maezono, M. Tachikawa, M. Towler, and R. J. Needs, "Ab initio quantum Monte
Carlo study of the binding of a positron to alkali-metal hydrides", J. Chem. Phys., 135, 054108(5pages) (2011).

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31. M. Hatakeyama and M. Tachikawa, “Ab initio quantum chemical study on the mechanism of
exceptional behavior of lysine for ion yields in MALDI - Role of vibrational entropic
contribution in thermally averaged proton affinities -”, J. Mass Spectrometry, 46, 376-382(2011).
32. A. Koizumi, K. Suzuki, M. Shiga, and M. Tachikawa, "A concerted mechanism between
protron transfer of Zundel anion and displacement of counter cation", J. Chem. Phys.
(Communication), 134, 031101 (3pages) (2011).
33. M. Tachikawa, Y. Kita, and R. J. Buenker, "Bound states of positron with nitrile species withconfiguration interaction multi-component molecular orbital approach", Phys. Chem. Chem.
Phys., 13, 2701-2705 (2011).

4.2. Cover gallery
Ref. 8

Ref. 11

Ref. 13

Ref. 17

Ref. 314.3. Invited talk (total 30)

4.4. Prize
1.

2.

Takayuki Oyamada, Best Poster Presenter Award in The 8th General Meeting of ACCMS-VO(Asian Consortium on Computational Materials Science - Virtual Organization), “Role ofelectron-positron correlation in positron attachment to LiH”, @ Sendai, Japan, on 7-9,
November 2013.
Yudai Ogata, Best student poster award in 3rd International Conference on Molecular
Simulation, “Nuclear quantum effect on OH-(H2O)2 with ab initio path integral molecular
dynamics”, @ Kobe, Japan, on 18-20, November 2013.

224