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 dorbital 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 dorbitals are pushed up by applying the onsite U for the first dorbitals, and they may appear around the second dorbitals which are not applied with the onsite U. The situation may not cause a serious problem in a small U. However, if the U applied to the first dorbitals is large enough, the positions of the unoccupied states originating from the first dorbitals pushed by the onsite U and the second dorbitals 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 onsite U for the second dorbital as well. That's the reason why we apply the onsite 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

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

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 Fe5.5Hs2p2d1 as benchmarked at http://www.jaist.ac.jp/~tozaki/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 dorbitals, and thereby we only have to provide the Uvalue for that. If the basis set does not provide enough convergent results for your systems, you may introduce the second dorbital, and may tune the Uvalue for the second one starting from the Uvalue 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 Uvalue giving a similar result also depends on the implementation (code). It would be better to consider the Uvalue given in literatures as reference when you start to find a proper value of the Uvalue. 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 dorbital, which provides information such as magnitude of exchange splitting and crystal field splitting, and how the second dorbital modifies the band structure. Then, one can guess how the electronic structure will be altered by introducing the onsite U for the first and second dorbitals. 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

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

