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Two questions about PDOS calculation of CoO.
Date: 2021/12/02 13:33
Name: K.Usami

Dear OpenMX developers and users,


I am trying to analyze the electronic state of materials using PDOS for each magnetic quantum 'm' obtained by OpenMX.

As an exercise, I ran the SCF&DOS calculations on the original 'NiO-sFLL.dat' in the 'work' directory and plotted the PDOS for the five d-orbitals of Ni.Then, I could see the double degenerate e_g orbital and the triple degenerate t_2g orbital.

Next, I did the same calculation for CoO, replacing Ni with Co in 'NiO-sFLL.dat', and I have two questions about the results.If anyone knows the cause of one or both, please comment.

(1)
When calculated with the same settings except for the atom species and coordinates, the PDOS of d_xy and d_yz was doubly degenerate, but that of the other three orbitals was a completely non-degenerate shape. So, I raised 'Dos.kgrid' to 30:30:30 and ran the calculation again, and confirmed a reliable degenerate structure.
However, I do not know why it was necessary to increase the 'Dos.kgrid' in the case of CoO.

The input file is shown below,
================================================
# Definition of Atomic Species

Species.Number 2
<Definition.of.Atomic.Species
Co Co6.0S-s2p2d2f1 Co_CA19S
O O5.0-s2p2d1 O_CA19
Definition.of.Atomic.Species>

<Hubbard.U.values # eV
Co 1s 0.0 2s 0.0 1p 0.0 2p 0.0 1d 7.0 2d 0.0 1f 0.0
O 1s 0.0 2s 0.0 1p 0.0 2p 0.0 1d 0.0
Hubbard.U.values>

<Hund.J.values # eV
Co 1s 0.0 2s 0.0 1p 0.0 2p 0.0 1d 1.0 2d 0.0 1f 0.0
O 1s 0.0 2s 0.0 1p 0.0 2p 0.0 1d 0.0
Hund.J.values>

# Atoms

Atoms.Number 4
Atoms.SpeciesAndCoordinates.Unit AU # Ang|AU
<Atoms.SpeciesAndCoordinates
1 Co 0.000000 0.000000 0.000000 9.0 6.0 off
2 Co 3.970000 3.970000 0.000000 6.0 9.0 off
3 O 3.970000 0.000000 0.000000 3.0 3.0 off
4 O 3.970000 3.970000 3.970000 3.0 3.0 off
Atoms.SpeciesAndCoordinates>

Atoms.UnitVectors.Unit AU # Ang|AU
<Atoms.UnitVectors
7.940000 3.970000 3.970000
3.970000 7.940000 3.970000
3.970000 3.970000 7.940000
Atoms.UnitVectors>

# SCF or Electronic System

scf.XcType LSDA-CA # LDA|LSDA-CA|GGA-PBE

# DFT+U part #
scf.Hubbard.U On # On|Off, default=off
scf.Hubbard.Occupation dual # onsite|full|dual, default=dual
scf.DFTU.Type 2 # 1:Simplified(Dudarev)|2:General, default=1
scf.dc.Type sFLL # sFLL|sAMF|cFLL|cAMF, default=sFLL
scf.Slater.Ratio 0.625 # default=0.625
scf.Yukawa off # default=off
##############

scf.SpinPolarization On # On|Off
scf.ElectronicTemperature 300.0 # default=300 (K)
scf.energycutoff 150.0 # default=150 (Ry)
scf.maxIter 200 # default=40
scf.EigenvalueSolver band # Recursion|Cluster|Band
scf.Kgrid 6 6 6 # means 4x4x4
scf.Mixing.Type rmm-diis # Simple|Rmm-Diis|Gr-Pulay
scf.Init.Mixing.Weight 0.20 # default=0.30
scf.Min.Mixing.Weight 0.01 # default=0.001
scf.Max.Mixing.Weight 0.30 # default=0.40
scf.Kerker.factor 1.00 # default=1.00
scf.Mixing.History 5 # default=5
scf.Mixing.StartPulay 6 # default=6
scf.criterion 1.0e-7 # default=1.0e-6 (Hartree)

# DOS and LDOS

Dos.fileout on # on|off , default=off
Dos.Erange -10.0 10.0 # default = -20 20
Dos.Kgrid 9 9 9 # default = Kgrid1 Kgrid2 Kgrid3
================================================

(2)
In the above input file, I replaced the unit vector and atomic configuration with the CIF information prepared from the Net as follows, and performed the same calculations.

================================================
Atoms.SpeciesAndCoordinates.Unit AU # Ang|AU
<Atoms.SpeciesAndCoordinates
1 Co 0.000000 0.000000 0.000000 9.0 6.0 off
2 Co 0.000000 3.970000 3.970000 6.0 9.0 off
3 O 0.000000 3.970000 0.000000 3.0 3.0 off
4 O 3.970000 0.000000 0.000000 3.0 3.0 off
Atoms.SpeciesAndCoordinates>

Atoms.UnitVectors.Unit AU # Ang|AU
<Atoms.UnitVectors
-3.970000 7.950000 3.970000
3.970000 0.000000 3.970000
3.970000 0.000000 -3.970000
Atoms.UnitVectors>

>>>>

Dos.Kgrid 30 30 30 # default = Kgrid1 Kgrid2 Kgrid3
================================================

As a result, despite the high value of 'Dos.kgrid', some d-orbitals show a completely non-degenerate shape.
Is it difficult to get a reliable PDOS for each magnetic quantum number with OpenMX?


Best regards,
K.Usami
メンテ
Page: [1]

Re: Two questions about PDOS calculation of CoO. ( No.1 )
Date: 2021/12/02 20:19
Name: K.Usami

PS,

Regarding question (2), I failed to take into account that the space group is different when I distinguish between two Co by the initial number of electrons and not.

I apologize for the lack of consideration, and as for question (1), if you know anything about it, please let me know.

Regards,
K.usami
メンテ
Re: Two questions about PDOS calculation of CoO. ( No.2 )
Date: 2021/12/02 20:55
Name: T. Ozaki

Hi,

Though I didn't consider your issue thoroughly, I wonder that the degeneracy of five d-orbitals can be broken
by not only crystal symmetry, but also the electron correlation in the plus U method.

In case of NiO, the charge state is Ni^(2+) and O^(2-) which means that Ni^(2+) has 8 electrons.
The 5 of 8 lectrons populate in the majority t2g and eg orbitals, and the remaining 3 electron populate
the minory t2g orbitals, where there is no effect causing orbital ordering.

On the other hand, Co^(2+) in CoO has 7 electrons, and the majority t2g and eg orbitals are occupied by
the 5 of 7 electrons. The remaining 2 electrons try to populate the minory t2g orbitals, and they choose
a situation that only the two t2g orbitals are occupied, and the other is empty. This is so called orbital ordering.
As a result, the degeneracy of the minority t2g orbitals is broken, and the broken symmetry affects to the
majority orbitals via a broken symmetry in the potential, which is a famous example about how the plus U method works.

I guess that this is what you observed.

Regards,

TO
メンテ
Re: Two questions about PDOS calculation of CoO. ( No.3 )
Date: 2021/12/05 00:21
Name: K.Usami

Dear T. Ozaki

Thank you for the reply.

I now understand how localized electron correlation causes the degenerate breakdown.
I think I need to learn more about the Plus-U method.

By the way, according to the theory above, the t2g orbitals should be non-degenerate, but why did the degeneracy recover when <Dos.kgrid> was raised?

Regards,
K. Usami
メンテ

Page: [1]

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