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Forces and symmetry
Date: 2006/07/07 04:55
Name: Peter Winey   <peterwiney@gmail.com>

Dr. Ozaki,

In a test energy calculation of a high symmetry system, I noticed that the final forces obtained are non-zero.
Although the maximal force is only ~0.002 Hatree/Bohr, I am still a little bit concerned about it since the
symmetry of the crystal implys perfect zero forces on the atoms.

The system I tested is a 2x2x2 supercell of a TiH2 crystal:
---------------------------------
The structure of TiH2 crystal

a, b, c, alpha, beta, gamma:
3.11510 3.11510 3.11510 118.14570 118.14570 93.24290

Two irreducible atoms:
0.75 0.25 0.5 H
0.0 0.0 0.0 Ti
---------------------------------


The following is my input file.
---------------------------------
#
# File Name
#

System.CurrrentDirectory ./ # default=./
System.Name openmx
DATA.PATH /home/winey/openmx3.0/DFT_DATA_2006/ # default=../DFT_DATA/
level.of.stdout 1 # default=1 (1-3)
level.of.fileout 1 # default=1 (1-3)

#
# restart using a restart file, *.rst
#

scf.restart off # on|off,default=off

#
# Definition of Atomic Species
#

Species.Number 2
<Definition.of.Atomic.Species
Ti Ti6.5-s2p1d1 Ti_PBE
H H5.5-s1 H_PBE
Definition.of.Atomic.Species>


#
# SCF or Electronic System
#

scf.XcType GGA-PBE # LDA|LSDA-CA|LSDA-PW
scf.SpinPolarization Off # On|Off
scf.partialCoreCorrection Off # On|Off
scf.ElectronicTemperature 300.0 # default=300 (K)
scf.energycutoff 150.0 # default=150 (Ry)
scf.maxIter 120 # default=40
scf.EigenvalueSolver Band # Recursion|Cluster|Band
scf.Kgrid 6 6 6 # means 4x4x4
scf.Mixing.Type rmm-diisk # Simple|Rmm-Diis|Gr-Pulay
scf.Init.Mixing.Weight 0.010 # default=0.30
scf.Min.Mixing.Weight 0.001 # default=0.001
scf.Max.Mixing.Weight 0.200 # default=0.40
scf.Mixing.History 7 # default=5
scf.Mixing.StartPulay 12 # default=6
scf.criterion 1.0e-8 # default=1.0e-6 (Hartree)

#
# 1D FFT
#

1DFFT.NumGridK 900 # default=900
1DFFT.NumGridR 900 # default=900
1DFFT.EnergyCutoff 3600.0 # default=3DFFT.EnergyCutoff*3.0 (Ry)

#
# Orbital Optimization
#

orbitalOpt.Method Off # Off|Unrestricted|Restricted
orbitalOpt.InitCoes Symmetrical # Symmetrical|Free
orbitalOpt.initPrefactor 0.1 # default=0.1
orbitalOpt.scf.maxIter 12 # default=12
orbitalOpt.MD.maxIter 2 # default=5
orbitalOpt.per.MDIter 2 # default=1000000
orbitalOpt.criterion 1.0e-4 # default=1.0e-4 (Hartree/borh)^2

#
# output of contracted orbitals
#

CntOrb.fileout off # on|off, default=off
Num.CntOrb.Atoms 1 # default=1
<Atoms.Cont.Orbitals
1
Atoms.Cont.Orbitals>

#
# SCF Order-N
#

orderN.HoppingRanges 6.0 # default=5.0 (Ang)
orderN.NumHoppings 1 # default=2

#
# MD or Geometry Optimization
#

MD.Type Nomd # Nomd|Constant_Energy_MD|Opt
MD.maxIter 1 # default=1
MD.TimeStep 0.5 # default=0.5 (fs)
MD.Opt.criterion 1.0e-4 # default=1.0e-4 (Hartree/bohr)

#
# Band dispersion
#
# if <Band.KPath.UnitCell does not exist,
# the reciprical lattice vector is employed.

Band.dispersion off # on|off, default=off
Band.Nkpath 5
<Band.kpath
15 0.0 0.0 0.0 1.0 0.0 0.0 g X
15 1.0 0.0 0.0 1.0 0.5 0.0 X W
15 1.0 0.5 0.0 0.5 0.5 0.5 W L
15 0.5 0.5 0.5 0.0 0.0 0.0 L g
15 0.0 0.0 0.0 1.0 1.0 0.0 g X
Band.kpath>

#
# MO output
#

MO.fileout off # on|off
num.HOMOs 1 # default=1
num.LUMOs 1 # default=1
MO.Nkpoint 1 # default=1
<MO.kpoint
0.0 0.0 0.0
MO.kpoint>

#
# DOS and PDOS
#

Dos.fileout off # on|off, default=off
Dos.Erange -20.0 20.0 # default = -20 20
Dos.Kgrid 12 12 12 # default = Kgrid1 Kgrid2 Kgrid3

#
# Atoms
#

Atoms.Number 24

Atoms.UnitVectors.Unit Ang # Ang|AU
<Atoms.UnitVectors # unit=Ang.
6.2302 0 0
-0.352436607784 6.22022350704 0
-2.93888084493 -3.11011085274 4.52830894518
Atoms.UnitVectors>

Atoms.SpeciesAndCoordinates.Unit Ang # Ang|AU
<Atoms.SpeciesAndCoordinates # Unit=Ang.
1 H 1.5575502128 2.2519392906e-07 1.13207723629 0.5 0.5
2 H 0.0881097903331 -1.55505520118 3.39623170888 0.5 0.5
3 H 1.3813319089 3.11011197871 1.13207723629 0.5 0.5
4 H -0.0881085135591 1.55505655234 3.39623170888 0.5 0.5
5 H 4.6726502128 2.2519392906e-07 1.13207723629 0.5 0.5
6 H 3.20320979033 -1.55505520118 3.39623170888 0.5 0.5
7 H 4.4964319089 3.11011197871 1.13207723629 0.5 0.5
8 H 3.02699148644 1.55505655234 3.39623170888 0.5 0.5
9 H -0.0881089391504 1.55505610195 1.13207723629 0.5 0.5
10 H -1.55754936161 6.75581786957e-07 3.39623170888 0.5 0.5
11 H -0.264327243043 4.66516785547 1.13207723629 0.5 0.5
12 H -1.73376766551 3.1101124291 3.39623170888 0.5 0.5
13 H 3.02699106085 1.55505610195 1.13207723629 0.5 0.5
14 H 1.55755063839 6.75581786957e-07 3.39623170888 0.5 0.5
15 H 2.85077275696 4.66516785547 1.13207723629 0.5 0.5
16 H 1.38133233449 3.1101124291 3.39623170888 0.5 0.5
17 Ti 0.0 0.0 0.0 6 6
18 Ti -1.46944042246 -1.55505542637 2.26415447259 6 6
19 Ti -0.176218303892 3.11011175352 0.0 6 6
20 Ti -1.64565872635 1.55505632715 2.26415447259 6 6
21 Ti 3.1151 0.0 0.0 6 6
22 Ti 1.64565957754 -1.55505542637 2.26415447259 6 6
23 Ti 2.93888169611 3.11011175352 0.0 6 6
24 Ti 1.46944127365 1.55505632715 2.26415447259 6 6
Atoms.SpeciesAndCoordinates>
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Re: Forces and symmetry ( No.1 )
Date: 2006/07/10 23:36
Name: T.Ozaki

Hi,

It is a limitation of OpenMX which originates from the use of
a conventional regular grid for FFT and numerical integrations.

Since a set of the conventional regular grids is generated without
depending on the symmetry of atomic structure, the symmetry of atomic
structure is not conserved in principle, while in practice for many
cases the symmetry is conserved.

A simple remedy of recovering the symmetry is to increase the
scf.enerycutoff. In fact the use of 500 Ryd reduces the maximum
force to around 0.0001 Hartree/bohr.

Although another possible way is to introduce a set of radial
and angular grids, this scheme is a highly time-consuming compared
to the regular grid scheme in my experiences, and it is not so easy
to take account of the infinite contribution of Hartree term in
bulk systems.

Regards,

TO

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Re: Forces and symmetry ( No.2 )
Date: 2006/07/10 23:28
Name: Peter Winey  <peterwiney@gmail.com>

Dr. Ozaki,

Thanks a lot for the reply!
I found that increasing energycutoff indeed helps.

Peter
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