Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

3.5

SCCMS Projects

324Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of machine learning-aided simulations
methods for molecular liquids
Hayato SHIBA
Information Technology Center, University of Tokyo
6-2-3 Kashiwa-no-ha, Kashiwa, Chiba 277-0882

Thanks to the present status of the art where
basic simulation methodology for parallel MD
simulations is approaching its maturity, many
open source packages are commonly available
for usage on supercomputers. However, how tosimulate long-time phenomena remains a longstanding unresolved issue in molecular dynamics simulations. It is difficult to perform numerical time integration over 1010 steps whichcorresponds to 10 µs in all-atom modeling. I
am pursuing a methodology for realizing simulation that can allow computations on bothlarge-scale and long-time. The key to realizing this is the efficient usage machine learning for capturing the dynamical paths in thephase space. For a class of glassy materials,
it is recently found that static structure havethe power to predict in which regions particles
have a high tendency to move over a long timeby means of deep learning in terms of the graphneural networks (GNNs) [1]. In FY 2021, after
October, we have started to further extend thepredictive power of GNN.
Firstly I confirmed that results of a previous study [1] can be fully reproduced, bothquantitatively and qualitatively, by using thedataset provided by its authors. The system I
consider is Kob-Andersen-type Lennard-Jones(KALJ) liquid, wherein two types of particles
are enclosed in a box with different interaction
parameters and particle radii to bypass crystallization.
In Fig. 1, predicted propensity map is compared with the ground data in which the parti-

Figure 1: Color map indicating the predictive
ability of particle propensity in KALJ liquid ata low temperature. where the 2D cross sections
are shown here in the 3D system.
cle propensity is evaluated from direct molecular dynamics simulation. Further, I haveextended the GNN learning model so thatchangeover in each neighbor pair distances canbe learned as an edge feature on the GNN. As
a result, the predictive ability has been extended into a wider temporal range, exceeding the propensity ability of the node feature(particle propensity) in Ref. [1] in the rangefrom 103 to 108 MD steps. I have also clarified
that predictive ability of the original model isdecreased because of its inability to treat thecollective motion induced by strain displacement.
Most of the resources allocated for my ISSP
project in FY2021 are spent on extending
the dataset to longer-time. I have extended
the dataset to cover the time region up to100τα , where τα represents glassy relaxation
time called α-relaxation time. As a large num-325

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

ber of simulation snapshot is required for learning, the dataset is, in fact, very large. By
providing 32 different random initial velocities
500 independent initial particle configurations
which are fully relaxed at a target temperatureof consideration, I have conducted 16,000 simulation in total of 3D KALJ liquids with 4,096
particles by my in-house simulation code. As
a result, I have successfully revealed that the
GNN begins to lose its predictive ability at thetime scale close to τα . All the above results
mentioned will be soon submitted as an original paper [2]. In association with this work,
we have conducted machine learning performance evaluation by using the same model on
NVIDIA A100 GPUs, wherein the evaluation
itself is performed on Wisteria/BDEC-01 supercomputer at ITC, Univ. of Tokyo [3].
Further, I have analyzed the internal structure of the code and rewritten it in full for PyTorch Geometric (PyG) code which is a libraryfor training on GNNs on PyTorch, while all
the original code written for TensorFlow and
JAX is distributed by the authors of Ref. [1].
This PyTorch extension will enable the community to further combine these prediction
methods with existing tools used in molecular simulations, because PyTorch has now become the most popular frameworks used in
ML-aided molecular simulations. The PyG
code will soon be made publicly available via
our GitHub repository [4].

References[1] V. Bapst et al.: Nat. Phys. 16, 448-454(2020).
[2] H. Shiba et al.: in preparation.
[3] H. Shiba and T. Shimokawabe: IPSJ SIG
Technical Report, Vol. 2020-HPC-183(22),1-11 (2022) (in Japanese).
[4] https://github.com/h3-Open-BDEC/

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Finite temperature dependence of ab-initio Hamiltonians andits analysis for two-dimensional organic conductors Pd(dmit) 2 Salts
Kazuyoshi YOSHIMI1, Takao TSUMURAYA2, and Takahiro MISAWA3
1Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
2

Priority Organization for Innovation and Excellence, Kumamoto University,
Kumamoto 860-8555, Japan

3Beijing Academy of Quantum Information Sciences, Haidian District, Beijing 100193, China

The molecular solids β’-X[Pd(dmit)2]2 (where

In this study [4,5], we used the program

X represents a cation) exhibit various phases

RESPACK [6], which can derive the effective

such as an antiferromagnetic phase, a quantum

Hamiltonian describing low-energy degrees ofspin liquid, and a charge-ordered phase

freedom based on band structures obtained bydependingfirst-principles

on

the

choice

of

X

[1].

calculations,toderiveanComprehensive analyses of band calculations

effective Hamiltonian for the crystal structures

and transfer integrals based on the extended

reported in Ref. [3]. As a result, the transfer

Hückel method and first-principles calculations

integrals tend to increase with decreasing

have

and quantitative

temperature, while the effective interactions

evaluation of the electronic states has been

tend to decrease. The ratio of the transfer

successfully performed [2]. However, electron

integral to the effective interaction was found tocorrelation effects are expected to play a major

be about 20% smaller than that at roomrole in order to elucidate the origin of thesetemperature.

phenomena. Therefore, a quantitative derivation

effectiveofthediagonalization method with the boundary

constrained Random Phase Approximation

condition average by HΦ[7]. We find that the(cRPA)

thespin correlation function varies with themicroscopic origin of the stability of thetemperature dependence of the effective model,

quantum spin liquid. Moreover, it has been

and in particular, the antiferromagnetic orderreported that the temperature dependence of the

moment decreases at β’-EtMe3Sb[Pd(dmit)2]2,

transfer integral is large for these materials [3].

where the emergence of the quantum spin liquid

The effective interactions are expected to have ais reported experimentally.

similar temperature dependence.

The overall tendency of the compound

been carried out,theeffectiveisinteractions

necessary

for

using

clarifying

327

We also analyzed the obtained

Hamiltonians

using

the

exact

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

dependence of the antiferromagnet ordered

References

moment is consistent with the available[1] R. Kato, Chem. Rev., 104, 5319–5346

experimental results. Our results demonstrate(2004).

that the comprehensive derivation of the[2] K. Kanoda and R. Kato, Annu. Rev. Condens.

effective Hamiltonian and its analysis is a

Matter, Phys. 2, 167 (2011).

powerful[3] K. Ueda, T. Tsumuraya and R. Kato, Crystals

methodforelucidatingthemicroscopic origin of exotic quantum states

8, 138(2018).

found in organic materials. In future research,[4] T. Misawa, K. Yoshimi, T. Tsumuraya, Phys.

we plan to apply this method to other organic

Rev. Research 2, 032072(R) (2020).

materials that exhibit exotic quantum phases.

[5] K. Yoshimi, T. Tsumuraya, T. Misawa, Phys.
Rev. Research 3, 043224 (2021).
[6] K. Nakamura, Y. Yoshimoto, Y. Nomura etal., Comp. Phys. Comm. 261, 100781(2021).
[7] M Kawamura, K Yoshimi, T Misawa et al.,Comp. Phys. Comm. 217, 180(2017).

328

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Large-Scale GW/BSE electronic structure
calculations for metal-organic hybrid materials
Takatoshi Fujita
National Institutes for Quantum Science and Technology
Tokai-mura, Naka-gun, Ibaraki 319-1106

Accurate calculations of electronic states
are essential for computational studies of organic materials which are directed toward understanding of fundamental processes in organic electronic devices. We have recently
developed the large-scale GW method basedon the fragment molecular orbital method.
The fragmentation approximation for the total polarization function and the ∆COHSEX
approximation have been employed for eﬃcient evaluations of GW quasiparticle energies
from localized molecular orbitals. More recently, we have proposed the novel large-scale
excited-state methods based on the FMO, exicton model, and GW/BSE with Tamm-Dancoﬀ
approximation (TDA). In this method, theexcited-state Hamiltonian matrix elements at
the GW/TDA-BSE level is calculated in thebasis of fragment conﬁguration state functions
which describe intrafragment excitations or interfragment charge-transfer excitations. The
excited-state Hamiltonian is then diagonalized
to approximate the adiabatic excited states ofan entire system. We have conﬁrmed thatfor molecular clusters, the novel fragmentbased GW/TDA-BSE can reasonably reproduce the excited states obtained from conventional GW/TDA-BSE method. Our developments enables the applications of GW/TDABSE method to large molecular assemblies,
which will be useful for investigating charge
separation in condensed phase.

systematically improved by including the twobody correction terms. At the static COHSEX
level, errors of less than 10 meV relative canbe achieved for realistic molecular aggregates.
However, residual errors of up to 100 meV are
still present, originating from the ∆ COHSEX
approximation. In addition, we assessed thedependence of the total polarization function
on the threshold distance and found that theconvergence with respect to the threshold isslow. However, the threshold distance rangeof 1.5–2.0 nm was determined to be a reasonable compromise between the accuracy andcomputational eﬀort, and the HOMO–LUMO
gap and excitation energies reasonably reproduced in comparison with the results obtained
without the cutoﬀ. The present implementation oﬀers a practical scheme for investigating large molecular systems. Applications torealistic molecular systems, such as organic
light-emitting device materials and organic solar cells, are currently underway.

References[1] T. Fujita, Y. Noguchi, J. Phys. Chem. A
13 (2020) 2728.

Recently, we have demonstrated that the accuracy of the total polarization function can be329

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Doping effects on P2 NaxMn1−yMyO2 (M=Li, Mg, Al, Ti, V, Cr,
Fe, Co, Ni) for sodium-ion rechargeable batteries: Ab initio
investigations
Huu Duc LUONG1,2, Hiroyoshi MOMIDA2,3, Tamio OGUCHI2,3
1

Graduate School of Engineering, Osaka University, Suita, Osaka 565-0871, Japan
2

SANKEN, Osaka University, Ibaraki, Osaka 567-0047, Japan
3

ESICB, Kyoto University, Kyoto 615-8245, JapanP2 layered oxide NaxMnO2 exhibits a voltage

Throughthehighlymethodaccuratehybrid(HSE06),wewindow from 2.0 to 3.5V and high specificfunctional

capacity up to 220mAh/g. However, the material

computationally evaluate the doping influences

suffers from the serious phase transformationon the lattice distortions, stabilities, electronic

during its charging/discharging.

structures, redox potentials, and diffusion
mechanisms [1]. The model for calculation isshown in Fig. 1. Our calculations indicate that
dopants not only reduce the lattice distortion
degree, especially for Li, Mg, Ti, and V cases,
but also increase the stability of the structure,
implying the dopants would alleviate the JahnTeller lattice distortion, as shown in Figs. 2(a)and 2(b). Figure 2(c) illustrates that at full Na
concentrations, all the considered dopants,
except for Ti and V, have a small effect on theredox potential. At low Na concentrations, the Li

Crystal structure of doped structure

dopant preferably diffuses out of the MnO2 layer,

NaMn1–yMyO2(y=0.0625, M = Li, Mg, Al, Ti, V, Cr,

but hardly moves to the Na layer, suggesting that

Fe, Co, and Ni) along c-axis. Purple, red, blue,

P2-layered oxides can prevent the dopant's

yellow and green balls illustrate Mn, O, M, upper-migrations during the Na extractions due to thelayered and lower-layered Na atoms. Surrounding

high relative energies.

Fig. 1:each dopant, there are two nearest Mn1NN and four

The effect on the diffusion mechanism issecond nearest Mn2NN atoms.

described through the diffusion of a Na ion–

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Fig. 2: a) Lattice distortion. b) Formation energy. c) Redox potential of NaMn1–yMyO2. d) Dopant’s
migration path from Mn-layer site (blue balls) to intermediate site (brown balls) and to Na-layer faceshared sites (green balls) or edge-shared site (pink balls). e) Relative site energies of structures containing
dopants at the Mn-layer site, intermediate site, edge-shared site and face-shared site in the Na-layer
calculated along the dopant’s migration paths (M=Li, Mg) at rich and poor Na contents. f) Diffusion pathof a Na ion near the dopants. Green, yellow, red, purple, blue and black balls represent Na atoms at lower
and upper layers, O, Mn, dopant M, and Na-vacancy trace. A and B stand for the initial and final positionof Na ion for diffusion. An arrow indicates the polaron hopping between two adjacent Mn sites.

polaron complex near the dopant's environments,

increase significantly. It is found that the doping

as shown in Fig. 2(f). Fe, Mg, Ti, and Cr dopants

influence on the activation energy for Na ion

can hinder the Na ion-polaron complex diffusion

diffusion is associated with the M–O bondwith significantly higher activation energies,change and charges of the neighboring dopants.

respectively, while the Al dopant almost remains
the activation energy as well as the perfectstructure. However, Li, V, Co, and Ni dopants

References

benefit from such complex diffusion with much

[1] H. D. Luong, H. Momida, V. A. Dinh, T.

lower activation energy so the ion diffusivities

Oguchi, Phys. Rev. Materials 6, 015802 (2022).

331

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab initio study toward abundant element
nanocatalysts with less precious metals
Tetsuya TAKETSUGU
Faculty of Science, Hokkaido University
N10W8, Sapporo, Hokkaido 060-0810

DFT computations with QuantumEspresso(QE) are used to gain chemical insights andto design novel catalysts with abundant elements such as hexagonal boron-nitride (h-BN)
for reducing costs and dependences on precious
metals used in various heterogeneous catalysts.
We have elucidated the catalytic activity ofoxygen functionalized hexagonal boron nitride(h-BN) with B-O-O-B and B-O-B active sites
at the zigzag edges for oxidative dehydrogenation (ODH) of light alkanes, speciﬁcally ethane(C2 H6 ), propane (C3 H8 ), butane (C4 H10 ), andisobutane (HC(CH3 )3 ) [1]. It has been foundthat the reaction pathway involves two H atomtransfer steps with small activation energies.
We have demonstrated that the synergy of two
active sites, B-O-O-B and B-O-B, is crucial forthe ﬁrst and second H-transfer, respectively.
We have demonstrated that these active sites
play an important role in producing alkenes
counterpart of the mentioned alkanes. The
charge redistribution during H-transfers andlocalized oxygen atomic states in the conduction band are explored to suggest possible descriptors for the rational design of new catalysts. The universal action of the B-O-O-B
and B-O-B active sites for ODH of the lightalkanes paves the way for metal-free BN-basedmaterials for future catalytic applications.
Alumina-supported nickel-based catalysts,
Ni@Al2 O3 , constitute an important class ofcatalytic materials with a wide range of industrial applications, such as natural gas reforming for syngas production and oxidative dehy-

drogenation (ODH) of alkanes. When used in
ODH catalysis, it has been assumed that theactive species in these materials are NiO crystallites dispersed on alumina and nickel aluminate species (NiAl2 O4 ), both with Ni in its
common +2 oxidation state. These morphologies are believed to be responsible for the highselectivity of this class of catalysts as compared
to unsupported pure NiO crystallites. However, more recently, the formation of a Ni3+
species, which promotes the isolation of electrophilic oxygen (O− ), has been invoked to explain the high selectivity for ethylene formation from ethane. The complexity and inhomogeneity of the condensed phase reaction environment often preclude a complete molecularlevel understanding of the active species andunderlying reaction mechanisms. Therefore, it
proves helpful to study small metal oxide clusters in the gas phase. Such clusters provide
atom-speciﬁc insights into the interactions governing structure-reactivity correlations at themolecular level and ultimately can serve as isolated model systems for active sites in real catalysts. Therefore, we have studied the geometric and electronic structures of Nix Aly O+zclusters to identify such model systems for
Ni@Al2 O3 ODH catalysts [2]. As charged clusters are required for mass selection, we havechosen mixed metal oxide cations with thecomposition (NiOm )(Al2 O3 )n (AlO)+ with m= 1-2 and n = 1-3. For m = 1, the addition of the NiO moiety ensures formally fully
oxidized clusters with all metal atoms in their332

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

most common oxidation state (Al3+ and Ni2+ ).
Addition of one more O atom in the m = 2 series allows for the study of oxygen-rich species,
which may contain less common Ni3+ centersin combination with O− species such as those
invoked to explain enhanced ODH selectivity.
Borophene is a collective name for twodimensional (2D) boron sheets or crystalline
atomic monolayers of boron. Typically, such
sheets have to contain periodic B vacancies tomaintain structural stability, and these vacancies may appear in a great variety of diﬀerent motifs. This makes borophene a highly
polymorphic material. A great variety ofborophene structures were extensively studied
in the past decade in the quest for graphenelike materials with potential for advanced applications in catalysis and technology. Amongthem, the 2D honeycomb boron is of speciﬁc
interest as a structural analog of graphene. Recently it has been synthesized on the Al(111)substrate; however, it remains unknown towhat extent does honeycomb boron behaves
like graphene. Therefore, we have elucidated
the structural and electronic properties of thisunusual 2D material using extensive DFT calculations in order to explain recent experimental ﬁndings [3]. We have demonstrated thatin contrast to graphene on lattice-mismatched
metal surfaces, honeycomb boron cannot wiggle like a blanket on Al(111), but rather induces reconstruction of the top metal layer,
forming a stoichiometric AlB2 sheet on top of
Al. Our conclusions from theoretical modelingare fully supported by X-ray absorption spectra showing strong similarity in the electronic
structure of honeycomb boron on Al(111) andthick AlB2 ﬁlms. On the other hand, a clear
separation of the electronic states of the honeycomb boron into π− and σ−subsystems indicates an essentially 2D nature of the electronicsystem in both one-layer AlB2 and bulk AlB2 .
In other words, honeycomb boron essentiallymatched the metallic substrate aluminum s
structure so closely that it could not be con-sidered an independent, freestanding layeredmaterial.

References[1] S. Kumar, A. Lyalin, Z. Huang, and T.
Taketsugu, Catalytic Oxidative Dehydrogenation ofLight Alkanes over Oxygen Functionalized Hexagonal Boron Nitride, ChemistrySelect 7, e202103795(2022).
[2] Y. Li, M. C. Babin, S. Debnath, T. Iwasa, S. Kumar, T. Taketsugu, K. R. Asmis, A. Lyalin, D. M.
Neumark, Structural Characterization of NickelDoped Aluminum Oxide Cations by Cryogenic Ion
Trap Vibrational Spectroscopy, J. Phys. Chem. A
125, 9527-9535 (2021).
[3] A. Preobrajenski, A. Lyalin, T. Taketsugu,
N. A. Vinogradov, and A. S. Vinogradov, Honeycomb Boron on Al(111): from the Concept ofBorophene to the Two-Dimensional Boride, ACS
Nano 15, 15153 ‒ 15165 (2021).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of fundamental simulation code for magnetic
materials
Tetsuya FUKUSHIMA
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

This year, we have developed a fundamental simulation code for calculating the magnetic properties of permanent magnets andspintronics materials. The automatic exhaustive calculations in this study are based on
the all-electron full-potential (Korringa-KohnRostoker) KKR Green’s function method (FPKKR). Since the potential is anisotropic rather
than spherically symmetric, we can calculate not only the magnetization and Curie
temperature but also the magnetocrystalline
anisotropy energy constant (Ku ) with high accuracy. The KKR Green’s function method
can also be conveniently combined with thecoherent potential approximation (CPA). It
is free from using supercells, resulting in reduced computational costs drastically. Therefore, it is possible to perform efficient calculations for a huge number of compositions of disordered alloys. We have applied this calculation method to YCo5 SmCo5 , and Sm2 Fe17 N3
based alloys.
Fig. 1 shows the calculated Ku and magnetization (Js ) of Y(Co,Fe,Ni,Cu)5 . The addition of low concentrations of iron, nickel, andcopper alone increases Ku as compared to thevalue of YCo5 . On the other hand, Js decreases at low concentrations regardless of thetype of added elements. For high concentration ranges, the addition of cobalt and nickel
constantly decreases the Js . In contrast, an increase in Js can be confirmed for the iron additions in the high concentration region; fromthe upper right of Fig. 1, YFe3 Co2 can be rec-Figure 1: Calculated Ku and Js for disordered
Y(Co,Fe,Ni,Cu)5 .

ognized as the material with the largest Ku
and Js among calculated compositions.
In practice, the 1-5 phases cannot exist stably at high iron concentrations. In samarium
systems, nickel has been added as a stabilizing
element to the 1-5 phases [1]. A similar composition, YFe3 (Co1−z Niz )2 , is also considered forthe yttrium system. However, the performance
deteriorates as a trade-off for phase stability;
thus it is necessary to search for the optimum
composition. In the present study, it was confirmed that up to z ∼ 0.5, the anisotropy field
is comparable to that of YCo5 .

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References[1] A. Landa, P. Söderlind, E. E. Moore, and
A. Perron, Appl. Sci. 10, 1 (2020).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Novel chloride solid electrolytes for all solid-state sodium
metal battery (2)Masanobu NAKAYAMA, Naoto TANIBATA, Ryo KOBAYASHI
Department of Advanced Ceramics,
Nagoya Institute of Technology, Gokiso-chi, Showa-ku, Nagoya, Aichi 466-8555
Since discovery of fast Li+ conductive

containing compound calculated by FPMD andchloride, Li3YCl6, by Asano et al. in 2018[1],FFMD, showing good accordance between twomuch attention

approaches.

hasbeen developed forHence,

theoptimizedFF

searching high ionic conductive chlorides. In

parameters are reliable.

this study, we focused on search for novel Na+

histogram of Na ion conductivity at room

conductive chlorides in terms of “element

temperature for 86 Na-Cl containing materials.

strategy” (Japanese government policy in

The results indicate a few samples show fastscience and technology since 2007).

Na+ conductivities, > 10-3 S/cm. Currently, we

Usinghigh-throughput force field (FF) calculations,

are

Na

conductivity experimentally.

ion

conductivities

areevaluatedsynthesizing

andFigure 2 displays

evaluating

ionic

exhaustively for chloride materials registered in
the Materials Project database.[2]Total 135

compounds

and

which

contains

NaCl(excluding H, Li, B, C, N, O, F, S, and so on)
are selected from the database, and their FF
potential parameters are optimized by using
cuckoo search algorithm.

So far, ~ 80compounds are optimized by referring firstprinciples

molecular

dynamics(FPMD)

datasets and their Na ionic conductivities areevaluated by using FF molecular dynamics

Fig. 1: Comparison between FPMD and(FFMD) approach.

FFMD derived RDF. FF parameters are

Note that FF parameter

optimized by cuckoo search algorithm.

optimization and FFMD calculations were
performed using NAP software.[3,4]Figure 1 shows a typical example of radial
distribution function (RDF) for a Na and Cl-

336

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

dma.201803075.
[2]

A. Jain, S.P. Ong, G. Hautier, W. Chen,
W.D. Richards, S. Dacek, S. Cholia, D.
Gunter, D. Skinner, G. Ceder, K.A.
Persson, Commentary: The Materials
Project: A materials genome approachto accelerating materials innovation,

Fig. 2: Histogram of Na+ conductivities

APL Mater. 1 (2013) 11002.

for Na-Cl containing materials.

https://doi.org/10.1063/1.4812323.
[3]

References

R. Kobayashi, nap: A molecular
dynamics package with parameteroptimization programs for classical and[1]

T. Asano, A. Sakai, S. Ouchi, M.

machine-learning potentials, J. Open

Sakaida, A. Miyazaki, S. Hasegawa,Source Softw. 6 (2021) 2768.

Solid Halide Electrolytes with Highhttps://doi.org/10.21105/joss.02768.

Lithium-Ion Conductivity for[4]

R. Kobayashi, Y. Miyaji, K. Nakano, M.

Application in 4 V Class Bulk-Type

Nakayama, High-throughput production

All-Solid-State Batteries, Adv. Mater.

of force-fields for solid-state electrolyte

30 (2018) 1803075.

materials, APL Mater. 8 (2020).

https://doi.org/https://doi.org/10.1002/ahttps://doi.org/10.1063/5.0015373.

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of high-performance permanent
magnets by large-scale simulation and data-driven
approach
Takashi MIYAKE
CD-FMat, AIST
Umezono, Tsukuba, Ibaraki 305-8568

Rare-earth transition-metal compounds arepotential main-phase for strong permanent
magnets. High content of 3d transition metals(Fe or Co) leads to high saturation magnetization, whereas rare-earth elements are essential
for strong magnetocrystalline anisotropy. Because of this, structure search for Fe/Co-richrare-earth compounds have attracted greatinterest.
There are several known structures, such as the CaCu5 -type structure, theTh2 Zn17 -type structure and the ThMn12 -type
structure. The CaCu5 -type structure is thesimplest among them, and the others are obtained by substituting transition-metal pairs(dumbbells) for rare-earth sites. There are variety of other structures obtained by diﬀerent
arrangement of dumbbells. In this study, we
have investigated stability of these structures[1].
As a first step, we prepare a 2×2×2supercell of SmFe5 and SmCo5 in the CaCu5 type structure, and generate hypotheticalstructures by replacing a part of Sm atoms
with dumbbells. We compute the formationenergy of all possible arrangements by density
functional theory in the generalized gradientapproximation. We then construct a cluster
expansion model. We evaluate the formationenergy of complex structures using the cluster expansion model. The result is shown in
Fig.1, where the formation energies for various
structures are plotted against dumbbell concentration (x). We see many structures be-

tween x=1/3 and x=1/2 whose formation energy is comparable with those of the Th2 Zn17 and ThMn12 -type structures. In contrast, theformation energy increases for x > 1/2.
The black solid line in the figure is the formation energy of disordered phase (so-called
TbCu7 -type structure). We compute the configuration entropy in the Bragg-Williams approximation, and evaluate the formation freeenergy. We found that as the temperature increases, the disordered phase is stabilized, andthe solubility limits of dumbbells in SmFez and
SmCoz are estimated to be z ∼ 9 at high temperature (T =0.15 eV).

Figure 1: Formation energy of Sm-Fe and SmCo systems as a function of dumbbell concentrations [1].

References[1] Fumiaki Kuroda, Taro Fukazawa andTakashi Miyake, Phys. Rev. Materials 5,
124405 (2021).

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Search for the optimum interface structure withsodium ion and ion liquid on graphene using
topological descriptor and machine learning
Yohei Shimizu & Hitoshi Washizu
Graduate school of simulation studies, University of Hyogo
7-1-28 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047

1

Background and Objective

1.1

Importance of controlling the Interface of sodium ion battery

Inexpensive and large-capacity sodium-ion
batteries are attracting attention as a stationary secondary power source. Ionic liquids aselectrolyte is known to have the effect of increasing the diffusion of sodium ions, and optimal compounding is required.

1.2

Needs and challenges of Materials Informatics (MI)MI predicts the properties of unknown materials from information on known materials [1]and are expected to shorten the development
period. Interface MI is difficult and few previous research because of Unknown descriptor
representing interface state and Infinite combinations.

1.3

Objective of our research

We establish prediction method of optimizing
Interface condition of cathode sodium ion battery with physical backing using by new topolgical descriptor as persistent homology.

2

Simulation and Estimation
methodIn this research, the objective variable is theself-diffusion coefficient of sodium ion. we etsimate optimizing self-diffusion coefficient condition by using results of MD simulation asteaching data. Table 1 is the method of MD
simulation using LAMMPS. Considering machine learning model, we use topological descriptor as persistent homology. In general
method of MI estimation model, experimentail conditions such as temprature and quantity etc. is used as descriptor. The problemof these method applied to the interface simulation MI is that the search range of interface cannot be simulated infinitely and thesedescriptor cannot represent the physical phenomenon directly. In our previous research[2], persistent homology can express amorphas
structure of polymer as persistent diagram in
two dimensions based on atomic coordinates(Fig. 1). We consider persistent homology as
descriptor of interface MI.

3

Results

3.1

Ability to express Interface condition using persistent homology

We compare the bulk and the interface, thediffusion coefficient in the direction parallel tothe interface increased. The effect on the in-339

Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

terface is clarified by the inverse analysis of thepersistent diagram. In this results, persistentdiagrams can describe the state of the interface
directly (Fig. 2). It can be found of the conditions for controlling the diffusion coefficient.

3.2

Prediction of self-diffusion coefficient

Regardless of the type of ionic liquid, the structure with a high diffusion coefficient shows theuniformity of the cluster. Predictions while
preserving the physical meaning by directly
machine learning the persistent diagram. The
predictability of the interface condition using
the persistent diagram as a descriptor is shown
although improving accuracy is an issue (Fig.
3).

4

Figure 2: Difference between ion liquid bulk
and interface by using persistent homology

Conclutions

Persistent homology can express differences
sodium ion and ion liquid state near graphene.
Optimal interface condition can be predictedfrom the search range by using a persistent diagram as a descriptor.

Figure 3: Prediction of the self-diffusion coefficient of sodium ion by random forest model

References[1] Fujimura, K., Seko, A. Tanaka, I, et al.:Adv. Energy Mater. 3 (2013) 980-985.
[2] Shimizu, Y., Kurokawa, T., Arai, H.
Washizu, H.: Sci. Rep. 11 (2021) 2274.

Figure 1: Principle of Persistent homology [3,4]Table 1: LAMMPS calculation conditions
conditions
value
Cell size
Boundary condition
Force field & Charge
Graphene LJ parameter
Ion liquid quantity
Calculation method
Temperature
Time[3] I.Obayashi: Siam J. Appl. Algebra Geometry vol.2 No.4 (2018) 508-534.
[4] http://www.wpi-aimr.tohoku.ac.jp/hiraoka labo/homcloudenglish.html

9.12 × 51.048 × 20ÅPeriodic
Lopes’ OPLS & AM1-BCC
σ = 0.319/nm,  = 0.392/KJ/mol
Na+ 79 ∼ 159, TFSI− 134 or BF4− 214, EMI+ (Total charge = 0)
NVT ensemble
250K, 300K, 350K, 400K, 450K
100ns (Used to create the initial structure)340