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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 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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