Evaluation of Kerker factor. |
- Date: 2022/06/20 15:45
- Name: Takuma Takeda
- Dear developers,
Let me ask about determination of Kerker-factor.
When I conducted scf-calculation by scf.Mixing.Type=Kerker, I tried two Kerker-factor, obtained manually and automatically.
However, they showed different values.
#Input Code-----------------------------------------------------------------------------------
System.CurrrentDirectory ./
System.Name test
level.of.stdout 1
level.of.fileout 1
Species.Number 2
<Definition.of.Atomic.Species #precise
O O6.0-s3p2d2 O_PBE19
Ti Ti7.0-s3p2d2f1 Ti_PBE19
Definition.of.Atomic.Species>
<Hubbard.U.values #eV
O 1s 0.0 2s 0.0 3s 0.0 1p 0.0 2p 5.6 1d 0.0 2d 0.0
Ti 1s 0.0 2s 0.0 3s 0.0 1p 0.0 2p 0.0 1d 2.9 2d 0.0 1f 0.0
Hubbard.U.values>
Atoms.Number 16
Atoms.SpeciesAndCoordinates.Unit FRAC
<Atoms.SpeciesAndCoordinates
1 Ti 0.62755594911239 0.37244227356788 0.05128509798425 7.0 5.0 on
2 Ti 0.37244002387390 0.62755813208614 0.94871451619810 5.0 7.0 on
3 Ti 0.30015438960552 0.69984577734319 0.25000567076007 5.0 7.0 on
4 Ti 0.69982292734663 0.30017704311593 0.75001630103353 7.0 5.0 on
5 Ti 0.63300963153220 0.36699019243762 0.42072222184749 6.0 6.0 on
6 Ti 0.36700579653961 0.63299369254725 0.57926923430272 6.0 6.0 on
7 O 0.44368965806196 0.55630956695698 0.38831312812443 3.0 3.0 off
8 O 0.55631229243677 0.44368760870581 0.61168327080359 3.0 3.0 off
9 O 0.17685305480877 0.82314653853640 0.05818001886912 3.0 3.0 off
10 O 0.82315514084934 0.17684443404245 0.94182181326018 3.0 3.0 off
11 O 0.75237720115747 0.24762263029294 0.23813423101361 3.0 3.0 off
12 O 0.24763440288155 0.75236544603376 0.76184934780144 3.0 3.0 off
13 O 0.54530253922425 0.45470076005253 0.86404120525012 3.0 3.0 off
14 O 0.45467962978551 0.54532394310718 0.13595085769106 3.0 3.0 off
15 O 0.18457704018948 0.81542255220195 0.43684391822112 3.0 3.0 off
16 O 0.81543957632688 0.18455995339279 0.56318074740957 3.0 3.0 off
Atoms.SpeciesAndCoordinates>
Atoms.UnitVectors.Unit Ang
<Atoms.UnitVectors
4.918900000000000 1.893370000000000 0.000000000000000
-4.918900000000000 1.893370000000000 0.000000000000000
-0.205603881490000 0.000000000000000 9.370202559488000
Atoms.UnitVectors>
scf.XcType GGA-PBE
scf.SpinPolarization on
scf.Hubbard.U on # on|off, default=off
scf.DFTU.Type 1 # 1:Simplified(Dudarev)|2:General, default=1
scf.dc.Type sFLL
scf.ElectronicTemperature 300.0
scf.energycutoff 500
scf.maxIter 1
scf.EigenvalueSolver band
scf.Kgrid 7 7 3
scf.Mixing.Type Kerker
#scf.Kerker.factor 4.60
scf.Init.Mixing.Weight 0.0010
scf.Min.Mixing.Weight 0.0001
scf.Max.Mixing.Weight 0.3000
scf.Mixing.History 30
scf.Mixing.StartPulay 80
scf.Mixing.EveryPulay 1
scf.criterion 3.67e-6
scf.stress.tensor on
scf.restart on
MD.Type nomd
MD.Opt.DIIS.History 3 # default=3
MD.Opt.StartDIIS 10 # default=5
MD.Opt.EveryDIIS 200 # default=200
MD.maxIter 1
MD.TimeStep 1.0
MD.Opt.criterion 7.35e-4
<MD.Fixed.Cell.Vectors
0 0 1
0 0 1
0 1 0
MD.Fixed.Cell.Vectors>
geoopt.restart off
#-----------------------------------------------------------------------------------
I evaluated Kerker's factor Alpha manually as 16.69137035(Bohr^-2), by the procedure shown below.
Reciprocal vectors from output file.(Bohr^-2)
RA=(0.337973807, 0.878042516, 0.007415926)
RB=(-0.337973807, 0.878042516, -0.007415926)
RC=(0, 0, 0.354839577)
*)Obtained from standard output.
A_q=(1/3)*(|RA|^2+|RB|^2+|RC|^2)=0.632130341
D_q=(1/3)*(||RB|^2-|RA|^2|+||RC|^2-|RA|^2|+||RC|^2-|RB|^2|)=0.506219216
b_min^2=RC^2=0.12591112565
Alpha=0.5*(1.0+(4*D_q/A_q))/(b_min)^2
These formula was found in the manual(http://www.openmx-square.org/openmx_man3.9/node41.html).
On the other hand, Kerker's_factor obtained automatically was different value as below;
Automatic determination of Kerker's_factor: 2.885930783677
(*)Received from standard output (system log) from the input code above.
My purpose is to assume how amount to be increased the Kerker's factor when the scf convergence is not good.
Your Sincerely,
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