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Kgird dependence of HS.out value
Date: 2021/06/20 22:25
Name: PES217i

Dear OpenMX developers,

I calculated the Hamiltonian matrix of a Si crystal using openmx and analysis_example (real space PAO basis, is it right?).

```
System.CurrrentDirectory ./
System.Name Si
level.of.stdout 1
level.of.fileout 1
HS.fileout on
data.path /usr/share/openmx/DFT_DATA19/

Species.Number 1
<Definition.of.Atomic.Species
Si Si7.0-s2p2d1 Si_PBE19
Definition.of.Atomic.Species>

Atoms.Number 2
Atoms.SpeciesAndCoordinates.Unit Ang
<Atoms.SpeciesAndCoordinates
1 Si 1.9334873 1.1162994 0.7893429 2.0 2.0
2 Si 0.0000000 0.0000000 0.0000000 2.0 2.0
Atoms.SpeciesAndCoordinates>

Atoms.UnitVectors.Unit Ang
<Atoms.UnitVectors
3.8669746 0.0000000 0.0000000
1.9334873 3.3488983 0.0000000
1.9334873 1.1162994 3.1573716
Atoms.UnitVectors>

scf.XcType GGA-PBE
scf.SpinPolarization off
scf.ElectronicTemperature 300.0
scf.energycutoff 200.0
scf.maxIter 100
scf.EigenvalueSolver band
scf.Kgrid 6 6 6
scf.Mixing.Type rmm-diisk
scf.Init.Mixing.Weight 0.05
scf.Min.Mixing.Weight 0.01
scf.Max.Mixing.Weight 0.30
scf.Mixing.History 25
scf.Mixing.StartPulay 15
scf.criterion 1.0e-7
```

When I changed the option scf.Kgrid from 6 6 6 to 8 8 8, values of Hamiltonian matrix have changed slightly.

For example, below shows atom1:1, atom2:1, cell:000 block

Kgird:666

```
-0.4145857 0.0705115 -0.0000410 -0.0000236 -0.0000167 -0.0000282 -0.0000163 -0.0000115 0.0000033 -0.0000038 -0.0000065 -0.0000046 -0.0000027
0.0705115 0.0774684 -0.0000102 -0.0000059 -0.0000041 -0.0000171 -0.0000099 -0.0000070 0.0000143 -0.0000165 -0.0000286 -0.0000202 -0.0000117
-0.0000410 -0.0000102 -0.2145728 0.0000024 0.0000017 0.1120422 -0.0000197 -0.0000139 0.0000166 -0.0000310 0.0474171 0.0335289 0.0000032
-0.0000236 -0.0000059 0.0000024 -0.2145756 0.0000010 -0.0000197 0.1120649 -0.0000080 0.0000096 0.0474528 -0.0000310 0.0000032 0.0335252
-0.0000167 -0.0000041 0.0000017 0.0000010 -0.2145763 -0.0000139 -0.0000080 0.1120706 -0.0581076 0.0000019 0.0000032 -0.0000333 -0.0000192
-0.0000282 -0.0000171 0.1120422 -0.0000197 -0.0000139 0.1450934 0.0000027 0.0000019 0.0000142 -0.0000208 -0.0154554 -0.0109286 -0.0000053
-0.0000163 -0.0000099 -0.0000197 0.1120649 -0.0000080 0.0000027 0.1450903 0.0000011 0.0000082 -0.0154314 -0.0000208 -0.0000053 -0.0109225
-0.0000115 -0.0000070 -0.0000139 -0.0000080 0.1120706 0.0000019 0.0000011 0.1450896 0.0189000 -0.0000031 -0.0000053 -0.0000171 -0.0000098
0.0000033 0.0000143 0.0000166 0.0000096 -0.0581076 0.0000142 0.0000082 0.0189000 0.2275682 0.0000011 0.0000019 0.0000025 0.0000014
-0.0000038 -0.0000165 -0.0000310 0.0474528 0.0000019 -0.0000208 -0.0154314 -0.0000031 0.0000011 0.2412622 -0.0000035 -0.0000018 -0.0193673
-0.0000065 -0.0000286 0.0474171 -0.0000310 0.0000032 -0.0154554 -0.0000208 -0.0000053 0.0000019 -0.0000035 0.2412582 -0.0193694 -0.0000018
-0.0000046 -0.0000202 0.0335289 0.0000032 -0.0000333 -0.0109286 -0.0000053 -0.0000171 0.0000025 -0.0000018 -0.0193694 0.2549545 -0.0000008
-0.0000027 -0.0000117 0.0000032 0.0335252 -0.0000192 -0.0000053 -0.0109225 -0.0000098 0.0000014 -0.0193673 -0.0000018 -0.0000008 0.2549554
```

Kgird:888

```
-0.4145874 0.0705110 -0.0000130 -0.0000075 -0.0000053 0.0000001 0.0000000 0.0000000 -0.0000054 0.0000063 0.0000108 0.0000077 0.0000044
0.0705110 0.0774664 0.0000073 0.0000042 0.0000030 -0.0000068 -0.0000039 -0.0000028 0.0000095 -0.0000109 -0.0000190 -0.0000134 -0.0000077
-0.0000130 0.0000073 -0.2145658 0.0000122 0.0000087 0.1120485 -0.0000120 -0.0000085 0.0000047 -0.0000103 0.0474290 0.0335374 0.0000030
-0.0000075 0.0000042 0.0000122 -0.2145799 0.0000050 -0.0000120 0.1120623 -0.0000049 0.0000027 0.0474409 -0.0000103 0.0000030 0.0335339
-0.0000053 0.0000030 0.0000087 0.0000050 -0.2145834 -0.0000085 -0.0000049 0.1120657 -0.0580980 0.0000017 0.0000030 -0.0000124 -0.0000072
0.0000001 -0.0000068 0.1120485 -0.0000120 -0.0000085 0.1451025 0.0000156 0.0000111 0.0000083 -0.0000021 -0.0154496 -0.0109245 -0.0000174
0.0000000 -0.0000039 -0.0000120 0.1120623 -0.0000049 0.0000156 0.1450844 0.0000064 0.0000048 -0.0154472 -0.0000021 -0.0000174 -0.0109044
0.0000000 -0.0000028 -0.0000085 -0.0000049 0.1120657 0.0000111 0.0000064 0.1450799 0.0189048 -0.0000101 -0.0000174 0.0000102 0.0000059
-0.0000054 0.0000095 0.0000047 0.0000027 -0.0580980 0.0000083 0.0000048 0.0189048 0.2275597 -0.0000050 -0.0000087 0.0000031 0.0000018
0.0000063 -0.0000109 -0.0000103 0.0474409 0.0000017 -0.0000021 -0.0154472 -0.0000101 -0.0000050 0.2412635 0.0000000 0.0000053 -0.0193709
0.0000108 -0.0000190 0.0474290 -0.0000103 0.0000030 -0.0154496 -0.0000021 -0.0000174 -0.0000087 0.0000000 0.2412635 -0.0193648 0.0000053
0.0000077 -0.0000134 0.0335374 0.0000030 -0.0000124 -0.0109245 -0.0000174 0.0000102 0.0000031 0.0000053 -0.0193648 0.2549564 0.0000075
0.0000044 -0.0000077 0.0000030 0.0335339 -0.0000072 -0.0000174 -0.0109044 0.0000059 0.0000018 -0.0193709 0.0000053 0.0000075 0.2549478
```

Why these values have changed?
Is there some optimal Kgrid value to get realistic Hamiltonian matrix?

Best,
PES217i
メンテ
Page: [1]

Re: Kgird dependence of HS.out value ( No.1 )
Date: 2021/06/21 09:33
Name: T. Ozaki

Hi,

scf.Kgrid is used to perform the Brillouin zone integration in calculating density matrix and charge density during the SCF calculation.
So, a different scf.Kgrid gives a different charge density resulting in the slight change of Hamiltonian matrix.
While the larger the better, but we see the almost convergent result for the matrix elements.

Regards,

TO
メンテ
Re: Kgird dependence of HS.out value ( No.2 )
Date: 2021/07/01 23:35
Name: PES217i

Dear Prof. Ozaki,

Thanks for the reply, I changed the analysis_example and increased the number of digits from 7 to 15, and I understand better.

By the way, what is the unit of the Hamiltonian matrix?

Best,
PES217i
メンテ
Re: Kgird dependence of HS.out value ( No.3 )
Date: 2021/07/02 09:10
Name: T. Ozaki

Hi,

> By the way, what is the unit of the Hamiltonian matrix?

It is the Hartree unit.

Regards,

TO
メンテ

Page: [1]

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