Division of Materials and Life Sciences:
Computational Condensed Matter Science Group
9 Clarify microscopic mechanisms of phenomena inmaterials,
9 Predict new phenomena and explore new materials
that are fascinating,by computationally solving fundamental equations ofquantum mechanics from first principles¾

Multi-scale in space

50,000 atoms in 10 nm3 Si

Elementary processes of electrons and ions (0.1 – 1 nm)⇔ Structural change and appearance of new phenomena (10 – 100 nm)¾

Multi-scale in time
Electronic transition (10-15 sec) ⇔ Ionic motion (10-12 sec)
⇔ Structural change and appearance of properties (10-9 – 10-6 sec …)

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Evaluation Review of CCS, University of Tsukuba, October 31, 2007

Division of Materials and Life Sciences:
Computational Condensed Matter Science Group¾

Large-scale quantum theoretical calculations– Real-Space Density Functional Theory (RSDFT) Scheme¾

Multi-scale dynamical calculations– Car-Parrinello Molecular Dynamics plus Meta-dynamics(CPMD-MeD)¾

Exploration of new properties in condensed matters– Total-energy or Free-energy calculations based on DFT

People:A. Oshiyama (Prof)
K. Shiraishi (Prof)S. Okada (Associate Prof)
J.-I. Iwata (Researcher)
Y. Fujimoto (JST-Postdoc)[K. Uchida (JST-Postdoc)][K. Kamiya (JST-Postdoc)]
2/17

HPC Division
D. Takahashi, T. Park
M. Sato, A. Ukawa
Life Science Group
M. Boero, M. Tateno
Quantum MB System GroupK. Yabana, T. Nakatsukasa
Evaluation Review of CCS, University of Tsukuba, October 31, 2007

Density Functional Theory (DFT)The total energy of an interacting electron system under nuclear
potentials vnucl with its electron density n is exactly given by:

E [n] = < Ψ | T + Vnucl + Vee | Ψ >r rr r r 1 n(r )n(r ' ) r r= Ts[n] + ∫ vnucl(r ) n(r ) dr + ∫ r r drdr ' + Exc[n]2 | r − r '|n(r)By introducing a non-interacting quasi-particle system which has
the density n identical to the above, we get Kohn-Sham equation:rrrr
1 2n(r ' ) r δE xc [n] r[ − ∇ + vnucl (r ) + ∫ r r dr '+r (r ) ]ϕ j (r ) = ε j (r )δn(r )
2| r − r '|rrn ( r ) = ∑ | ϕ j ( r ) |2n(r)

j

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Evaluation Review of CCS, University of Tsukuba, October 31, 2007

Real-space treatment is better for large-scalecalculations (10,000 – 100,000 atoms)
Real-space Density Functional Theory(RS-DFT)

ya2

Introduce mesh points in a unit cell, compute all thequantities on the mesh. In the case Laplacian isexpressed by finite difference:M∂2φ( x, y, z) ≈ ∑ Cmφ( x + mH , y, z)
2
∂x
m=− M

x

-31.40Total Energy (HR)Totalenergy
Total Energy
(HR)

-31.0

Total energy⎛π ⎞Ec = ⎜ ⎟⎝H⎠2Accuracy is controlled by spacing H of the mesh:
-31.2
-31.4
-31.6
-31.8
H=0.86
H=0.73
H=0.64-32.0-31.42-31.44-31.46-31.48Plane-Wave(TAPP)
Real-Space-31.50-32.2-31.52
-32.4

2

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a1order M
46
Order of FD

8101015(π/H)**2202530

35

Ecut (Ry)

Evaluation Review of CCS, University of Tsukuba, October 31, 2007

Advantage of RS-DFT[ Iwata, Shiraishi & Oshiyama: PRB 2007, and unpublished results ]¾¾

Controlling accuracy systematicallyBenefits of RS-DFT in Next-Generation (maybe substantiallyParallel) Super Computer– Utilize inherent locality of the system– Almost free from FFT, reducing communication burden– Flexible boundary condition to wave-functions

In addition, in our code,¾ Residual minimization method instead of conjugate-gradient

minimization to solve Kohn-Sham equation¾ Change of algorithm for Gram-Schmidt orthgonalization to utilize
BLAS-level3 matrix-matrix operations⇒ almost peak performance¾ Divide-and-Conquer algorithm to solve secular equation in subspace

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Evaluation Review of CCS, University of Tsukuba, October 31, 2007

Some Benchmark Data on PACS-CS
PACS-CS at Tsukuba:
Xeon 5.6 GFLOPS x 2560 nodes through 3D hyper-network
Peak performance (theoretical) 14.3 TFLOPSNet Performance in each computation on 256 nodes (MFLOPS/node)Gram-Schmidt

Si1000Si1728Si2744

Si4096

Operation

2689

3335

3957

3603

Op + Communication

2072

2802

3557

3227

Diagonalization in subspace
Si1000Si1728Si2744

Operation

4117

4125

4329

Op + Communication

3434

2944

3999

Hamiltonian operation (H Psi)
Si10006/17

Si1728Si2744

Si4096

Operation

93132

112

202

Op + Communication

507659126Evaluation Review of CCS, University of Tsukuba, October 31, 2007

Excitation Energies of Si Cluster Containing
Thousands of Atoms
Legitimate Definition of Electron Excitation Energy:

Total-Energy Difference between Charged and Neutral Systems:
i.e., E(N+1) + E(N-1) - 2 E(N)ΔSCF = E(N+1) + E(N-1) - 2 E(N)vs Conventional HOMO-LUMO Gap

Cluster simulates Si Bulk? … Yes!
1.0
Si4006H1038
Si1978H642
Si1050H426

DOS

0.8
0.6
0.4
0.2
0.0
-16
7/17-14-12-10-8Energy (eV)-6-4
Evaluation Review of CCS, University of Tsukuba, October 31, 2007

Car-Parrinello Molecular Dynamics (CPMD)
electron degrees of freedom

additional degreesof freedom (T, Petc)

nuclear degrees of freedom

coupling between
electrons and nuclei
described by DFT

Lagrangian equation of motion

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Evaluation Review of CCS, University of Tsukuba, October 31, 2007

Car-Parrinello + Meta Dynamics to Overcome
Multiscale Problem in Time
Collective (reaction) coordinates: sα11
L = L CP + ∑ M α s&α 2 − ∑ kα ( sα ( R) − sα ) 2 − V ( s, t )α 2α 2usual CP Lagrangean
fictitious kinetic energy

Gaussian potentials added
Restrain potential:
coupling with other coordinates

where the history dependent function V is⎛ 1 (s − si )2 ⎞ ⎡ 1 ((si +1 − si )(s − si ))2 ⎤⎟ exp⎢−
V (s, t ) = ∑Wi exp⎜⎜ −⎥|| 4⊥ 2 ⎟s22()Δ(s)Δti <ti⎝⎠ ⎣⎦and sum of gaussians gives us
Free-energy landscapeFree-energy
landscapethat
we want to get
V(s,t)

limV (s, t ) = −F (s) + const.
t →∞9/17sEvaluation Review of CCS, University of Tsukuba, October 31, 2007

What is Cytochrome c Oxidase (CcO)?
Foods (C6H12O6 etc) , Oxygen ⇒ NADH, NAD+ ⇒ Electrons & Protons

ATP Synthase
produces ATPs

Mechanisms / Pathways / Free-energy Barriers for
the Proton Transfer in CcO?
10/17

Evaluation Review of CCS, University of Tsukuba, October 31, 2007

Candidate Proton Pathways deduced from
X-Ray Measurements
Intermembrane
9 CcO: 40 thousands
spaceof atoms
9 Subunits I and II(7000 atoms)
are responsible for
proton transfer
9 Structures are aset of helices
connected with eachother
9 Reduction andOxidation changes
its structure
9 Biggest andsuggestive changetakes place for ASP51
along H pathway

MatrixTsukihara et al: Proc. Natl. Acad. Sci, 100, 15304 (2003)

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Evaluation Review of CCS, University of Tsukuba, October 31, 2007

Tautomerization Reaction from Enol to Keto Forms

Enol here

K. Kamiya, M. Boero, M. Tateno, K. Shiraishi and A. Oshiyama,J. Am. Chem. Soc. (2007)
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Evaluation Review of CCS, University of Tsukuba, October 31, 2007

Tautomerization Reaction from Enol to Keto Forms

Enol here

Free-energy Landscape
13/17

K. Kamiya, M. Boero, M. Tateno, K. Shiraishi and A. Oshiyama,J. Am. Chem. Soc. (2007)
Evaluation Review of CCS, University of Tsukuba, October 31, 2007

Prediction of Magnetic Carbon Nanotubes
When topological defects in hexagonal network in carbon nanotubes,

Ferromagnetic states appear.

Spin density that is
responsible formagnetism
Okada et al:
Physical Review B (2006);
Applied Physics Letters (2007)¾ Also, calculation predicts that linear line defects generated oncarbon nanotubes by, e.g., electron radiation, selfheals to be theabove topological defects (no energy barrier for healing ).

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Evaluation Review of CCS, University of Tsukuba, October 31, 2007

Nano World Emerges in Post-scaling Technologye.g., Field effect Transistor (More gates to increase channels)
gatedrainsourcePlaner FET

Surrounding-gate FETMulti-gate FETs

An Untimate Cylindrical
Structure: Double-walled
Carbon Nanotube
Quantum Theoretical Free-enerngy
Calculation：

Uchida, Okada, Shiraishi & Oshiyama: PhysicalReview B (2007)

15/17+Q-QμEvaluation Review of CCS, University of Tsukuba, October 31, 2007Two Quantum Effects in Carbon Nanotube Capacitor

Capacitance much bigger thanclassical value（Cclassical)
Quantum spill ofelectron density

Dramatic bias-voltage
dependence
Characteristic feature indensity of states of 1 dimensional conductors

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Evaluation Review of CCS, University of Tsukuba, October 31, 2007

Division of Materials and Life Sciences:
Computational Condensed Matter Science Group¾

Large-scale quantum theoretical calculations– Real-Space Density Functional Theory (RSDFT) Scheme

Collaboration with HPC division was and will be imperative¾

Multi-scale dynamical calculations– Car-Parrinello Molecular Dynamics plus Meta-dynamics(CPMD-MeD)

Collaboration with Life science group has been essential¾

Exploration of new properties in condensed matters– Total-energy or Free-energy calculations based on DFTOur quantum theoretical calculations predict interesting
phenomena that await experimental confirmation

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Evaluation Review of CCS, University of Tsukuba, October 31, 2007