This thread is locked.Only browsing is available.
Top Page > Browsing
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,
メンテ
Page: [1]

Re: Evaluation of Kerker factor. ( No.1 )
Date: 2022/06/20 19:04
Name: T. Ozaki

Hi,

Thank you for your detailed report.
In fact, the equations shown in the manual was not updated, although the equations used were changend.
(We just simply overlooked the change.)

You can confirm the equations used in OpenMX Ver. 3.9 at the part starting from the 1996 lines.
I am going to update the change in the next release.

> My purpose is to assume how amount to be increased the Kerker's factor when the scf convergence is not good.

If the charge sloshing happens, one may increase the Kerker factor by a factor of 1.5.
Also, note that a too large value of the Kerker factor degrades the SCF convergence.

Regards,

TO
メンテ

Page: [1]