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

3.6

Software Advancement Projectsand Workshop Support341Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Improvement of Quantum ESPRESSO implementing
the ESM-RISM method
Minoru OTANICenter for Computational Sciences, University of Tsukuba
1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8577

In this project, we modiﬁed the source codeof the Quantum ESPRESSO (QE) package, a
popular open-source code for studying the electronic structure of materials with the density
functional theory (DFT).
Before starting the project, we implemented
several simulation techniques to elucidate a microscopic detail of an electrochemical reaction
and atomic geometry under an electrochemical
environment at the electrode and electrolyte
interface, called the electrochemical interface.
To reduce the calculation time for obtaining
the equilibrium electrolyte distribution, we utilized the classical liquid theory, called the reference interaction site model (RISM), in a particular part of the electrolyte region [1]. The
RISM region can describe the electric double
layer near the interface, which includes the accumulation and depletion of the counter-ionsin the electrolyte when introducing an excess
charge on the electrode surface by applying abias voltage. These techniques are made possible by introducing a grand canonical ensemble
for both electrons on the electrode [2] and ionsin the electrolyte [1] and solving the Poisson
equation of the system under the open boundary condition along the perpendicular direction of the interface [3]. We call this hybrid
simulation technique applicable to interfacial
electrochemistry the ESM-RISM method.
In the ESM-RISM method, we need to solve
the Laue represented Poisson and RISM equations.
{∂z2 − g∥2 }V (g ∥ , z) = −4πρ(g ∥ , z),(1)hγ (g ∥ , z) =∑∫dz ′ cα (g ∥ , z ′ )α×χαγ (g ∥ , |z − z ′ |),(2)

where g ∥ , g∥ , ρ, h, c, χ, α, and γ represent, respectively, a wave vector parallel to the interface, the absolute value of g ∥ , the total charge
density, the total correlation function, the direct correlation function, the solution susceptibility, the atomic sites of implicit and explicit
solutions. These two equations are related
through the electrostatic potential V (g ∥ , z) [1].
In the ﬁrst implementation of ESM-RISM, weused a common z mesh points for both Eqs. (1)and (2). Figure 1(a) shows the schematic illustration of the z mesh in the calculation cell.
Since the mesh points along the z direction
are common, the electrostatic potential can beeasily shared in the equations, and this modelis relevant for the thin electric double layer(EDL) system. However, we need to solve
the RISM equation in a wide range of solution regions at low electrolyte concentrations
because the EDL becomes thicker according tothe Debye-Hückel theory. In this situation, it
is more versatile to be able to solve the Eqs. (1)and (2) with diﬀerent mesh spacing and diﬀerent unit cell along z direction, LDFTand LRISMzz(see Fig. 1(c)). Thus we modify our ESMRISM code from the original common mesh to
an individual one.
To accomplish the goal, we need to map anarbitrary function f on the common mesh ontof˜ on the individual mesh. As seen in the ﬁgure. 1(d), we employ the Fourier interpolation

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Activity Report 2021 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo(a) Common mesh ((d))

SlabDFT unit cell

RISM
RISM unit cell(b) Common meshh()Slab(e))Slab(c) Individual mesh (RISM

RISM

Figure 1: Schematic illustrations of a calculation cell. The z-mesh points used in DFT and RISM
calculations for (a) a common mesh with same cell sizes along z-direction (LDFT= LRISM), (b)zza common mesh with diﬀerent cell sizes, and (c) an individual mesh with diﬀerent cell size. The
horizontal red and blue lines with grids represent the unit cell size along the z-direction for theDFT and RISM calculations. Conceptually, the zxy indicates a grid point of x (= long or short)unit cell for y (= DFT or RISM) calculation. (d) The mapping sequence of an arbitrary function
dense ) to f˜(g sparce ), where F and F −1 are the forward and backward Fourier transform,f (gcutcut
dense and g sparse ).
respectively. (e) Schematic illustration of cutoﬀ radii in the reciprocal space (gcutcutsparce
The “sparse” in (c) means a sparse mesh with a small cutoﬀ radius, gcut .
scheme. First, we did the backward Fourierdense ) to f (z DFT ), and thentransform from f (gcutshort
we map the f in the DFT cell onto the f˜ inthe RISM cell by the following condition:{DFT ,f (z) z = zshortf˜(z) =(3)DFT .
0z ̸= zshort
After the forward Fourier transformation, thedense is reduced to the sparsedense FFT grids gcutsparse
FFT grids gcut (see Fig. 1(e)). In the program, we ﬁrst apply the mapping sequence
from ρ to ρ̃. Secondly, by solving the Eq. (1)with ρ̃, the electrostatic potential in the RISM
cell can include the contribution from the DFTcharge. Finally, we solve the RISM equation
RISM,sparse
Eq. (2) on the sparse grids zlong.
After ﬁnishing the code development, wechecked the validity of our implementation bycomparing the total energy and the force acting on atoms between the two calculations withFigs. 1 (a) and (c) conﬁgurations.
I would like to acknowledge Dr. Y. Motoyama, Dr. K. Yoshimi, and Dr. S. Hagiwara
for their enthusiastic contribution to code development. This function is implemented under the support of Project for advancementof software usability in materials science inﬁscal year 2021 by The Institute for Solid State
Physics, The University of Tokyo.

References[1] S. Nishihara and M. Otani: Phys. Rev. B
96 (2017) 115429.
[2] N. Bonnet, T. Morishita, O. Sugino, andM. Otani: Phys. Rev. Lett. 109 (2012)
266101.
[3] M. Otani and O. Sugino: Phys. Rev. B 73(2006) 115407.

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

Unified platform of experiment-data analysis
for 2D material structure
Takeo HOSHI1,2
1

Department of Mechanical and Physical Engineering, Tottori University,
4-101 Koyama-Minami, Tottori 680-8550, Japan.

2Slow Positron Facility, Institute of Materials Structure Science, High Energy Accelerator
Research Organization (KEK), Oho 1-1, Tsukuba, Ibaraki, 305-0801, Japan

In a PASUMS project at FY2021, an open-also for supercomputers. Among the above fivesource data-analysis framework 2DMAT [1-4]methods, the PAMC method was implemented

hasexperimental

in the present project. In addition, the forward

measurements of two-dimensional material

problem solver of TRHEPD was also publishedstructures. The present project is the successor

as an open-source software package by theof one at FY2020. The current version ofpresent project [6,7].

beendevelopedfor

2DMAT is an unified platform for the analysis

2DMAT was applied to the structure

experimental

measurement

analysis of Si4O5N3 / 6H-SiC(0001)-( √3 ×total-reflection

high-energy√3 )R30 ° surface, a novel two-dimensional

positron diffraction (TRHEPD) [5], surface X-semiconductor, by TRHEPD experiment [2]. A

raylow-energy

data-driven sensitivity analysis was proposed

electron diffraction (LEED) experiments byfor the quantitative analysis of experimental

installingproblemuncertainties. The variation over individual

solvers that generate diffraction intensity data

fitting parameters was analyzed by solving thefrom a given dataset of the atomic positions.

eigenvalue problem of the variance-covariance

Amongwerematrix. 2DMAT was used also in othersupported as a result of the present project. The

application studies by TRHEPD experimentcurrent version of 2DMAT offers five analysis

and the study by T. Takeda (Waseda U.) et al.

methods: (i) Nelder-Mead optimization, (ii)

won a poster-session prize [8]. The analysis

grid search, (iii) Bayesian optimization, (iv)methods in 2DMAT are general and can be

replica exchange Monte Carlo (REMC) method,

applied also to other problems and was appliedand (v) population-annealing Monte Carloto a performance prediction of massively(PAMC) method. Methods (ii) through (v) are

parallel computation by Bayesian inference [4].

implemented by parallel computation, which isAs activities to promote 2DMAT, hands-on

efficient not only for personal computers butworkshops were held in April 2021 and April

ofdifferenttechniques,diffraction(SXRD),

corresponding

them,

SXRD

andforward

andLEED344

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

2022, and a study group was held in September[4] H. Kohashi, et al., JSIAM Letters 14, 13

2021. Test calculations in massively parallel(2022).

computations by the Fugaku supercomputer are[5] (Review) Y. Fukaya, et al, J. Phys. D: Appl.

underway (hp210228, hp210267).

Phys. 52, 013002 (2019).
[6] https://github.com/sim-trhepd-rheed/

References[7] T. Hanada, et al., Comp. Phys. Commun., in[1]press; Preprint: arXiv: 2110.09477

https://www.pasums.issp.utokyo.ac.jp/2DMAT[8] T. Takeda et al., the Best Poster Presentation[2] T. Hoshi, et al., Comp. Phys. Commun. 271

Award at the 2022 Kanto Chapter Conference

108186 (2022).

of the Surface and Vacuum Society of Japan.

[3] Y. Motoyama et al., Preprint:
arXiv:2204.04484

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

Report of CCMS hands-on sessions in the 2021 fiscal year
Kota IDO
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
In the 2021 fiscal year, Center for

Table 1: List of CCMS hands-on sessions where

Computational Materials Science (CCMS) in thethe ISSP supercomputer was used in the 2021

Institute for Solid State Physics (ISSP) heldfiscal year.

three hands-on sessions where the ISSP

DateApr. 20
May 24Oct. 1supercomputer was used [1-3]. In this report, webriefly summarize the hands-on sessions.
Table 1 shows the list of the hands-on

Lecturer
T. Hoshi et al.
K. Tsuda et al.
Y. Yamaji et al.

Software
2DMAT[4]PHYSBO[5]HΦ[6]References

sessions in the 2021 fiscal year. Software used in[1] https://ccms.issp.u-tokyo.ac.jp/event/4570

the hands-on sessions are 2DMAT, PHYSBO,[2] https://ccms.issp.u-tokyo.ac.jp/event/4881

and HΦ: 2DMAT is a Python package to search[3] https://ccms.issp.u-tokyo.ac.jp/event/5078

an optimal result by applying a search algorithm[4] https://www.pasums.issp.u-

to a direct-problem solver [4], PHYSBO is a

tokyo.ac.jp/2dmat/

Python library to perform a fast and scalable[5] https://www.pasums.issp.u-

Bayesian optimization [5], and HΦ is a package

tokyo.ac.jp/physbo/

of solvers for quantum many body systems [6].

[6] https://www.pasums.issp.u-tokyo.ac.jp/hphi/

Development of these software was supported[7] https://www.pasums.issp.u-tokyo.ac.jp/

by “Project for advancement of software[8] https://www.pasums.issp.u-

usability in materials science” (PASUMS) [7]. In

tokyo.ac.jp/2dmat/doc/paper/

all of the hands-on sessions, lecturers explained[9] https://www.pasums.issp.u-

the basics of each software and gave its tutorial.

tokyo.ac.jp/physbo/doc/paper/

Materials of these hands-on sessions are[10] https://www.pasums.issp.u-

available on each official page (in Japanese) [8-tokyo.ac.jp/hphi/doc/presentation/10].

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

Supercomputer course of Computational Materials Design(CMD®) workshop
Masaaki GESHI1, Yoshitada MORIKAWA2, Tomoya ONO3
1

Institute for NanoScience Design,

Osaka University, Machikaneyama, Toyonaka, Osaka 560-0043
2

Department of Precision Engineering,Osaka University, Yamada-oka, Suita, Osaka 565-0871
3

Center for Computational Science,

University of Tsukuba, Tenno-dai, Tsukuba, Ibaraki 305-8577

The 39th Computational Materials Design

oxygen reduction reaction on carbon electrodes,(CMD®) workshop (CMD39) has been heldand so on. The participants performed thefrom September 6th to September 10th and thecalculations and examined the results.

40th CMD® workshop (CMD40) has been done

In CMD38 two participants took thefrom February 21st to February 25th. Both weresupercomputer

held online. In this workshop we have thesupercomputer of ISSP. They got a tutorial onsupercomputer course to train up human

RSPACE developed by T. Ono. After giving theresources to advance research by using system B

introductory lecture of large-scale computing by

supercomputer of ISSP, the University of Tokyo.

M. Geshi and introducing the calculation

In CMD39 eight participants took themethod of electronic states and electron

supercomputer course and got a tutorial on

conduction property using RSPACE, exercises

STATE-Senri developed by Y. Morikawa. After

instructed in the manual were carried out. Then,giving the introductory lecture of large-scale

electronic structure calculations were carried out

computing by M. Geshi and explaining how tofor various molecules, and the electronic density

use the supercomputer of ISSP, participants

distribution was visualized. The attendees also

started constructing calculation models of theirperformed massively parallel calculations toown research subjects with the help of theconfirm the efficiency for parallel computing.

lecturers. Then they carried out calculations

Finally, the electron conduction property ofusing supercomputers. Concrete themes weremolecules connected to atomic wires wasmolecularanalyzed.

adsorption

on

solid

surfaces,chemical reactions at electrode interfaces,

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courseandusedthe