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Ionic contribution of sawtooth potential for electric fields to force on atoms
Date: 2020/11/05 18:00
Name: Naoya Yamaguchi

Dear developers,

Now I have calculated systems under uniform electric fields for our research, but I wonder if there is lack of the Ionic contribution of sawtooth potential for electric fields to force on atoms.
I calculated a H2O molecule, whose input file is
#
# File Name
#

System.CurrrentDirectory ./ # default=./
System.Name H2O_EF
level.of.stdout 1 # default=1 (1-3)
level.of.fileout 0 # default=1 (0-2)

#
# Definition of Atomic Species
#

Species.Number 2
<Definition.of.Atomic.Species
O O7.0-s2p2d1 O_PBE19
H H7.0-s2p1 H_PBE19
Definition.of.Atomic.Species>

#
# Atoms
#

Atoms.Number 3
Atoms.SpeciesAndCoordinates.Unit Ang # Ang|AU
<Atoms.SpeciesAndCoordinates # Unit=Ang.
1 O 0.00000011715023 -0.00883050466640 -0.00000020153370 3.0 3.0
2 H 0.76378969635377 0.59062099572170 0.00000000523121 0.5 0.5
3 H -0.76379002740839 0.59062001887690 -0.00000001901232 0.5 0.5
Atoms.SpeciesAndCoordinates>
Atoms.UnitVectors.Unit Ang # Ang|AU
<Atoms.UnitVectors
20.0 0.0 0.0
0.0 20.0 0.0
0.0 0.0 20.0
Atoms.UnitVectors>

#
# SCF or Electronic System
#

scf.XcType GGA-PBE # LDA|LSDA-CA|LSDA-PW|GGA-PBE
scf.SpinPolarization off # On|Off|NC
scf.ElectronicTemperature 100.0 # default=300 (K)
scf.energycutoff 300.0 # default=150 (Ry)
scf.maxIter 60 # default=40
scf.EigenvalueSolver cluster # DC|GDC|Cluster|Band
scf.Kgrid 1 1 1 # means 4x4x4
scf.Mixing.Type rmm-diis # Simple|Rmm-Diis|Gr-Pulay|Kerker|Rmm-Diisk
scf.Init.Mixing.Weight 0.10 # default=0.30
scf.Min.Mixing.Weight 0.001 # default=0.001
scf.Max.Mixing.Weight 0.400 # default=0.40
scf.Mixing.History 7 # default=5
scf.Mixing.StartPulay 5 # default=6
scf.criterion 1.0e-11 # default=1.0e-6 (Hartree)
scf.Electric.Field 0.0 1.0 0.0

#
# MD or Geometry Optimization
#

MD.Type Nomd # Nomd|Opt|NVE|NVT_VS|NVT_NH
# Constraint_Opt|DIIS2|Constraint_DIIS2
MD.Opt.DIIS.History 4
MD.Opt.StartDIIS 5 # default=5
MD.maxIter 100 # default=1
MD.TimeStep 1.0 # default=0.5 (fs)
MD.Opt.criterion 1.0e-7 # default=1.0e-4 (Hartree/bohr)

First I got the optimized atomic structure with "MD.Opt.criterion" of "1.0e-7", and applied an electric field with "scf.Electric.Field" of "1.0 0.0 0.0".
Then, I obtained the following xyz file.
3

O 0.00000 -0.00883 -0.00000 -0.000000078345834 0.012322115669513 0.000000000821928
H 0.76379 0.59062 0.00000 0.000141455700314 0.001623009623155 0.000000000989435
H -0.76379 0.59062 -0.00000 -0.000141363898035 0.001622911478218 0.000000001437855

And, I modified source codes of "Force.c" and "Total_Energy.c" to replace "tden" with "dden" in calculations of terms for sawtooth potential.
Then, I calculated it again and obtained
3

O 0.00000 -0.00883 -0.00000 -0.000000078347465 0.000653815447951 0.000000000823072
H 0.76379 0.59062 0.00000 0.000141457281028 -0.000321674593694 0.000000000989444
H -0.76379 0.59062 -0.00000 -0.000141365478755 -0.000321772740194 0.000000001437861

The modified codes are found in https://gist.github.com/Ncmexp2717/4a669c843f5a118ca87c65a2a98b5357
This behavior looks more natural because the latter means that the Born effective charges Z*yy of oxygen and hydrogen atoms are -0.34 and +0.17, respectively, while the former means that those are -6.34 and -0.83. And the above result from the modified codes is close to the following result of Berry phase method for electric fields we have developed.
3

O 0.00000 -0.00883 -0.00000 -0.000000081422919 0.000694645220396 -0.000000004200967
H 0.76379 0.59062 0.00000 0.000168801301231 -0.000330832127612 0.000000000099261
H -0.76379 0.59062 -0.00000 -0.000168708921543 -0.000330929293296 0.000000000101775

So, I think that forces under sawtooth potential are not evaluated right in the current OpenMX codes. However, this part remains at least from version 3.7, and I might miss something.

Best regards,
Naoya Yamaguchi
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