Calculation of Hubbard U parameters for Fe in fayalite

[Heseri]

Dear VASP developers,

I am trying to calculate the Hubbard U parameters for Fe in fayalite using the linear response approach implemented in VASP. Fayalite is the iron-rich end member of (Mg,Fe)2SiO4 olivine, and was used as an example in the original paper by Cococcioni and Gironcoli (2005, Phys. Rev. B 71, 035105). I have followed the VASP tutorial “Calculate U for LSDA+U” (https://vasp.at/wiki/Calculate_U_for_LSDA%2BU), but I have two questions.

First, as described by Cococcioni and Gironcoli (2005), there are two distinct Fe sites in fayalite, and I need to calculate two site-specific U values. In the VASP tutorial on Ni in NiO, only one Ni atom/cation was specified for the linear response calculations. In this way, the POSCAR file will be like:

Code: Select all

Fe Fe Fe Si O
1 31 32 128

For my case, I am wondering whether, for each Fe site, it would be better to include all Fe atom/cation at that site in the linear response calculations, i.e., using the POSCAR file like

Code: Select all

Fe Fe Si O
32 32 32 128

then perform linear fits of the number of d-electrons as a function of the additional potential for each Fe atom at that site, and finally average the derived U values over the 32 Fe atoms?

Second, to be rigorous, if I use only one Fe atom at a given site in the calculations, which LDAUL value (2 or -1) should I assign to the other Fe atoms at the same site? For example, should I use:

Code: Select all

LDAU = .TRUE.
LDAUTYPE = 3
LDAUL = 2 -1 -1 -1 -1
LDAUU = $v 0.0 0.0 0.0 0.0
LDAUJ = $v 0.0 0.0 0.0 0.0

or

Code: Select all

LDAU = .TRUE.
LDAUTYPE = 3
LDAUL = 2 2 -1 -1 -1
LDAUU = $v 0.0 0.0 0.0 0.0
LDAUJ = $v 0.0 0.0 0.0 0.0

Or would these two settings produce in fact the same results?

Thank you very much for your time and consideration.
Sincerely,
Tian Hua