Top Page > Browsing
How to assign Hubbard U values to the two d basis orbitals of Fe atom (LDA+U)?
Date: 2017/07/03 16:58
Name: Xiangyang Peng   <xiangyang_peng@xtu.edu.cn>

Dear openmx developers and users,

I am using openmx to study the magnetic properties related to Fe atoms where the on site Coulomb interaction has to be considered by using Hubbard model. There are some suggested U values (Dudarev’s approach) for Fe atoms in the literature. I want to reproduce the results in the literature first.

I have read the manual of openmx and found that there is an example for LDA+U in the ‘work ‘ directory of openmx package: openmx3.8/work/large_example/GGFF.dat.

In GGFF.dat, one can find
....................................................
Species.Number 3
<Definition.of.Atomic.Species
Ga Ga7.0-s1p1d1 Ga_PBE13
Fe Fe6.0S-s1p1d2f1 Fe_PBE13S
O O5.0-s1p1d1 O_PBE13
Definition.of.Atomic.Species>
.
.
.
<Hubbard.U.values # eV
Ga 1s 0.0 1p 0.0 1d 0.0
Fe 1s 0.0 1p 0.0 1d 4.0 2d 2.0 1f 1.0 (two different values for 1d and 2d orbitals)
O 1s 0.0 1p 0.0 1d 0.0
Hubbard.U.values>
.....................................................

In the above example, the two d basis orbitals of Fe atom are given two different U values. However, in the published literature, only one single U value is given. If I want to follow the U value used in the literature, I would like to ask how to define the U value to the two d orbitals of Fe atom in openmx.

I think this question should be clarified before one can start using LDA+U with openmx.

Thank you very much for your help.

Best regards
Xiangyang Peng
メンテ
Page: [1]

Re: How to assign Hubbard U values to the two d basis orbitals of Fe atom (LDA+U)? ( No.1 )
Date: 2017/07/05 00:23
Name: T. Ozaki

Hi,

The eigenenergy of the first d-orbital in atomic limit is located at valence level,
while that of the second one is located at several eV above compared to the first one.
The unoccupied states originating from the first d-orbitals are pushed up by applying
the on-site U for the first d-orbitals, and they may appear around the second d-orbitals
which are not applied with the on-site U. The situation may not cause a serious
problem in a small U. However, if the U applied to the first d-orbitals is large enough,
the positions of the unoccupied states originating from the first d-orbitals pushed by
the on-site U and the second d-orbitals may reverse. Apparently, the electronic structure
is not what we want to realize by the LDA+U method, and thereby one may want to control
the on-site U for the second d-orbital as well. That's the reason why we apply the on-site
U for not only the first, but also the second. Please check carefully your DOS, and if you
find unexpected tail going into the band gap, this may happen due to the reason mentioned above.

Regards,

TO
メンテ
Re: How to assign Hubbard U values to the two d basis orbitals of Fe atom (LDA+U)? ( No.2 )
Date: 2017/07/06 00:48
Name: Xiangyang Peng  <xiangyang_peng@xtu.edu.cn>

Dear Prof. Ozaki,

Thank you very much for your reply and detailed explanation. Now I understand that to avoid the reversion of the order of the unoccupied bands originating from the first and second d orbitals, a U has to be applied to the second d orbital in the case of Fe.

I still have some questions regarding using LDA+U in a practical calculation.

1. If one finds a single U value for Fe in literature, how to implement this U value in Openmx calculation? The possible procedure I can conceive is that: first, assign this U value to the 1st d orbital. If a reversion of the order of the bands described above occurs, then one should try to add a proper U value to the 2nd d orbital. Is this the correct procedure using LDA+U in Openmx?

2. This question is related to the first one: How can one know a priori whether the reversion of the order of the unoccupied bands described above occurs or not, if there are no correct reference band structures? I think only when one knows the correct band structure, one can make the correction by setting a proper U value to the 2nd d orbital.

Thank you very much for your help.

Best regards
Xiangyang Peng
メンテ
Re: How to assign Hubbard U values to the two d basis orbitals of Fe atom (LDA+U)? ( No.3 )
Date: 2017/07/06 09:32
Name: T. Ozaki

Hi,

> 1. If one finds a single U value for Fe in literature, how to implement this U value in
> Openmx calculation? The possible procedure I can conceive is that: first, assign this U
> value to the 1st d orbital. If a reversion of the order of the bands described above
> occurs, then one should try to add a proper U value to the 2nd d orbital. Is this the
> correct procedure using LDA+U in Openmx?

A compromise basis set is Fe5.5H-s2p2d1
as benchmarked at
http://www.jaist.ac.jp/~t-ozaki/vps_pao2013/Fe/Fe_Hard/index.html
which well balances accuracy and efficiency, and the results are well compared to
the corresponding all electron ones. In this case, we have only the single basis set
for d-orbitals, and thereby we only have to provide the U-value for that.
If the basis set does not provide enough convergent results for your systems,
you may introduce the second d-orbital, and may tune the U-value for the second one
starting from the U-value of 0 eV. Also, please be noticed that the details such as
how occupation numbers are evaluated largely depend on the implementation, and
therefore the U-value giving a similar result also depends on the implementation (code).
It would be better to consider the U-value given in literatures as reference when you
start to find a proper value of the U-value. Of course, in case that the same code is
used, we can rely on the value of U in literatures if the computational condition
remains unchanged.

> 2. This question is related to the first one: How can one know a priori whether the
> reversion of the order of the unoccupied bands described above occurs or not, if there
> are no correct reference band structures? I think only when one knows the correct band
> structure, one can make the correction by setting a proper U value to the 2nd d orbital.

Without applying the U, you can get the LDA or GGA electronic structure by changing
the basis function with and without the second d-orbital, which provides information
such as magnitude of exchange splitting and crystal field splitting, and how the second
d-orbital modifies the band structure. Then, one can guess how the electronic structure
will be altered by introducing the on-site U for the first and second d-orbitals.
The procedure is a bit tedious, however, by the procedure one can deeply understand
how the electronic structure is constructed by each constituent.

Regards,

TO
メンテ
Re: How to assign Hubbard U values to the two d basis orbitals of Fe atom (LDA+U)? ( No.4 )
Date: 2017/07/06 11:14
Name: Xiangyang Peng  <xiangyang_peng@xtu.edu.cn>

Dear Prof. Ozaki,

Thank you very much for your nice explanation. I think I know how to apply U to the two d basis orbitals now.

Best regards
Xiangyang Peng
メンテ

Page: [1]

Title (must) Move the thread to the top
Your Name (must)
E-Mail (must)
URL
Password (used in modification of the submitted text)
Comment (must)

   Save Cookie