1/23

Current Status of the OpenMX Code•••••

History of OpenMX
Basic theoretical framework
Parallelization of OpenMX
Some new functionalities
Future developments
https://www.openmx-square.org/Taisuke Ozaki
ISSP, the Univ. of Tokyo
The 4th OpenMX developer's meeting on Nov. 9-10, 2023

2/23

OpenMX Open source package for Material eXplorer•

Software package for density functional calculations of molecules and bulks•

Norm-conserving pseudopotentials (PPs)•

Variationally optimized numerical atomic basis functions

Basic functionalities

Extensions•SCF calc. by LDA, GGA, DFT+U•

O(N) and low-order scaling diagonalization•

Total energy and forces on atoms•

Non-collinear DFT for non-collinear magnetism•

Band dispersion and density of states•

Spin-orbit coupling included self-consistently•

Geometry optimization by BFGS, RF, EF•

Electronic transport by non-equilibrium Green function•

Charge analysis by Mullken, Voronoi, ESP•

Electronic polarization by the Berry phase formalism•

Molecular dynamics with NEV and NVT ensembles•

Maximally localized Wannier functions•

Charge doping•

Effective screening medium method for biased system•Fermi surface•

Reaction path search by the NEB method•

Analysis of charge, spin, potentials by cube files•

Band unfolding method•

Database of optimized PPs and basis funcitons•

STM image by the Tersoff-Hamann method

•etc.

3/23

History of OpenMX
2000 Start of development
2003 Public release (GNU-GPL)
2003 Collaboration:
AIST, NIMS, SNU
KAIST, JAIST,Kanazawa Univ.
CAS, UAMNISSAN, Fujitsu Labs.
etc.
2019

19 public releases
Latest version: 3.9

http://www.openmx-square.org

Development of OpenMX code

4/23ver. 4.0• NPT molecular dynamics by
Dr. Iitaka of RIKEN• Closest Wannier functions• COHP and COOP analysis• Finite electric field method
based on the Berry phase by
Dr. Yamaguchi• Contracted diagonalization• Tensor regression model foron-the-fly machine learningpotential by Mr. Li.
• Rational function method of2024
variable cell optimization
with arbitrary constraint

5/23

Contributors to OpenMX development
T. Ozaki (Univ. of Tokyo)
H. Kino (NIMS)
J. Yu (SNU)
M.J. Han (KAIST)
M. Ohfuchi (Fujitsu Labs.)
F. Ishii (Kanazawa Univ.)
K. Sawada (Kanazawa Univ.)
Y. Kubota (Kanazawa Univ.)
Y.P. Mizuta (Kanazawa Univ.)
H. Kotaka (Kyoto Univ.)
N. Yamaguchi (Kanazawa Univ.)
H. Sawahata (Kanazawa Univ.)
T.B. Prayitno (Kanazawa Univ.)
T. Ohwaki (NISSAN ARC)
T.V.T Duy (AISIN SEIKI)
M. Miyata (JAIST)
G. Jiang (Wuhan Univ. of Sci.&Tech.)T. Iitaka (RIKEN)

P.-H. Chang (George Mason Univ.)
A. Terasawa (TIT)
Y. Gohda (TIT)
H. Weng (CAS)Y. Shiihara (Toyota Tech. Inst.)
M. Toyoda (Tokyo Inst. Tech.)Y. Okuno (FUJIFILM)R. Perez (UAM)
P.P. Bell (UAM)
M. Ellner (UAM)
Yang Xiao (NUAA)
A.M. Ito (NIFS)
M. Otani (AIST)
M. Kawamura (Univ. of Tokyo)
K. Yoshimi (Univ. of Tokyo)
C.-C. Lee (Tamkang Univ.)
Y.-T. Lee (Academia Sinica)
M. Fukuda (Univ. of Tokyo)
S. Ryee (KAIST)
K. Terakura (AIST)

5

6/23

Materials studied by OpenMX
First characterization of silicene on ZrB2 in collaboration with experimental groups
A. Fleurence et al., Phys. Rev. Lett. 108, 245501 (2012).

First identification of Jeff=1/2 Mott state of Ir oxides
B.J. Kim et al., Phys. Rev. Lett. 101, 076402 (2008).

Theoretical proposal of topological insulators
C.-H. Kim et al., Phys. Rev. Lett. 108, 106401 (2012).
H. Weng et al., Phy. Rev. X 4, 011002 (2014).

First-principles molecular dynamics simulations for Li ion battery
T. Ohwaki et al., J. Chem. Phys. 136, 134101 (2012).
T. Ohwaki et al., J. Chem. Phys. 140, 244105 (2014).

Magnetic anisotropy energy of magnets
Z. Torbatian et al., Appl. Phys. Lett. 104, 242403 (2014).
I. Kitagawa et al., Phys. Rev. B 81, 214408 (2010).

Electronic transport of graphene nanoribbon on surface oxidized Si
H. Jippo et al., Appl. Phys. Express 7, 025101 (2014).
M. Ohfuchi et al., Appl. Phys. Express 4, 095101 (2011).

Materials treated so far
Silicene, graphene
Carbon nanotubes
Transition metal oxides
Topological insulators
Intermetallic compounds
Molecular magnets
Rare earth magnets
Lithium ion related materials
Structural materials
etc.

About 1200 published papers

Interface structures of carbide precipitate in bcc-Fe
H. Sawada et al., Modelling Simul. Mater. Sci. Eng. 21, 045012 (2013).

Universality of medium range ordered structure in amorphous metal oxides
K. Nishio et al., Phys. Rev. Lett. 340, 155502 (2013).

7/23

Basic theoretical framework• Density functional theory• LCPAO method• Basis functions• Pseudopotentials• Total energy

8/23

LCPAO method(Linear-Combination of Pseudo Atomic Orbital Method)
One-particle KS orbitalis expressed by a linear combination of atomic like orbitals in the method.

Features:• It is easy to interpret physical and chemical meanings,
since the KS orbitals are expressed by the atomic like basisfunctions.
• It gives rapid convergent results with respect to basis
functions due to physical origin. (however, it is not acomplete basis set, leading to difficulty in getting fullconvergence.)• The memory and computational effort for calculation ofmatrix elements are O(N).
• It well matches the idea of linear scaling methods.

Radial orbitals of carbon atom

Variational optimization of basis functions
One-particle wave functions

9/23

Contracted orbitals

The variation of E with respect to c with fixed a gives→Regarding c as dependent variables on a and assuming KS
eq. is solved self-consistently with respect to c, we have

Ozaki, PRB 67, 155108 (2003)

Radial orbitals of carbon atom

Optimization of basis functions
1. Choose typical chemical environments

2. Optimize variationally the radial functions

3. Rotate a set of optimized orbitals within the subspace, anddiscard the redundant funtions

××

10/23

11/23Norm-conserving Vanderbilt pseudopotential
I. Morrion, D.M. Bylander, and L. Kleinman, PRB 47, 6728 (1993).

The following non-local operator proposed by Vanderbilt guarantees thatscattering properties are reproduced around multiple reference energies.
D. Vanderbilt, PRB 41, 7892 (1990).

If the following generalized norm-conserving condition is fulfilled, thematrix B is Hermitian, resulting in that VNL is also Hermitian.
If Q=0, then B-B*=0

This is the norm-conserving PP
used in OpenMX

12/23

Optimization of pseudopotentials(i) Choice of parameters
1.
2.
3.
4.

Choice of valence electrons (semi-core included?)
Adjustment of cutoff radii by monitoring shape ofpseudopotentials
Adustment of the local potential
Generation of PCC charge

Optimization of PPtypically takes a halfweek per a week.

(ii) Comparison of logarithm derivatives
If the logarithmic derivatives
for PP agree well with thoseof the all electron potential,
go to the step (iii), or returnto the step (i).

good

No good(iii) Validation of quality of PP by performinga series of benchmark calculations.

goodNo goodGood PP

13/23

Reproducibility in DFT calcs
Science 351, aad3000 (2016)15 codes69 researchers
71 elemental bulks
GGA-PBE
Scalar relativistic13

Δ-gauge
A way of comparing accuracy of codes

14/23

15/23Comparison of codes by Δ-gauge

The mean Δ-gauge of OpenMX is 2.0meV/atom.

16/23

Atomic 3D atomic partitioning
How one can partition atoms tominimize communication and memory
usage in the parallel calculations ?
Requirement:• Locality• Same computationalcost• Applicable to anysystems• Small computational
overhead
T.V.T. Duy and T. Ozaki, Comput. Phys.
Commun. 185, 777-789 (2014).

17/23

Recursive atomic partitioning
The method guarantees⚫ Locality of atomicpartitioning⚫ Balanced
computational cost
⚫ Applicability to anysystems⚫ Small computational
cost

T.V.T. Duy and T. Ozaki, CPC 185, 777 (2014).

Allocation of atoms to processess
Diamond 16384 atoms, 19 processes

Multiply connected CNT, 16 processes

18/23

Partitioning of grids

19/23

Uniform grid is used to calculate
matrix elements and solve Poisson’sequation. A hundred million grid
points for a few dozen thousandatoms.
A proper one of four data structures
for grid is used for each calculation.
They are designed to minimize theMPI communication.
These data structure are all constructed in Construct_MPI_Data_Structure_Grid() and
Set_Inf_SndRcv() of truncation.c.
T.V.T. Duy and T. Ozaki, CPC 185, 777 (2014).

20/23

2D-parallelization of 3D-FFT withthe smallest communication→→ccabaCompared to 1D-parallelization, no increaseof MPI communication up to N. Even at N2,
just double communication.

bV. T. Duy and TO, Comput. Phys.
Commun. 185, 153 (2014).

Prediction of quaternary hydrides

21/23

Based on the two densest packing structures, we performed exhaustive
exploration of hydrides under 10 GPa by the NPT-MD developed by Dr. Iitaka.
ഥ𝒎)
13-2-1 (𝑭𝒎𝟑ഥ𝒎)
𝟏𝟑 − 𝟑 − 𝟏 (𝑷𝒎𝟑Among 73,304
candidate hydrides, weidentified 23 hydrides
with static anddynamic stability, andtwo of them exhibits
SC at about 6 K.
R. Koshoji and TO et al.,Phys. Rev. Mat. 6, 114802 (2022).

21

Closest Wannier functions
FCC copper
Wannier interpolated bands
Solid: conventional
Red circle: Wannier interpolated

22/23

By minimizing the distance measure function, one can obtainthe closest Wannier functions to a given set of localized
orbitals such as atomic orbitals.
arXiv:2306.15296
https://www.openmx-square.org/cwf/

CWFs

Tight-binding hopping integrals
as a function of distanceFuture developments
To make OpenMX a further versatile and useful tool for materials science
researches, we have been discussing the following developments.

Efficiency• On-the-fly machine learningpotentials• Contracted and selective
diagonalizations• GPGPU parallelization

Accuracy• PPs and basis functions forlanthanide and core level
spectroscopies• metaGGA, Hybrid functional, GW,BSE, vdW-DFT

Functionality

Community• Electronic excitation spectra• Berry phase related properties• Analysis of magnetic systems
calculate exchange coupling andDzyaloshinskii-Moriya interaction• Phonon related properties• Database of basic computationalresults• Data repository service• Publication of an overview paper

23/23