[QE-users] Strong dependance of DFT+U on projector choice

[Matteo Cococcioni]

Dear Julien,

below I offer my point of view on your questions.

Il giorno mer 17 giu 2020 alle ore 16:13 JULIEN, CLAUDE, PIERRE BARBAUD <
julien_barbaud at sjtu.edu.cn> ha scritto:

> Dear Users,
> I have recently tried to implement DFT+U on a FAPbI3 system, following the
> work reported in J. Phys. Chem. C 2018, 122, 27340−27349. This is not the
> most canonical use of DFT+U on d orbitals of transition metals. Instead,
> the authors used the Hubbard correction on the I 5p and Pb 6p orbitals to
> empirically fit the experimental band gap.
> Since this is used in conjonction with spin-orbit effects, I have to use
> lda_plus_u_kind=1 (but I keep J=0, which should make it equivalent to using
> the default method if I'm not mistaken). I also had to add the atoms in the
> relevant f90 files as they were not initially included.
>
> When initially trying to correct the band gap, I observed very troubling
> results. The band gap actually reduced from ~0.4 eV (DFT w/SOC) to ~0.3 eV
> (DFT+U w/SOC). Even more frustrating, screening multiple U values made very
> little change on that band gap result, and would always yield values lower
> than the U=0 case... Another disturbing result had to do with the occupancy
> eigenvalues, which reported a total occupation of 3.4 on Pb, seemingly
> making it a "Pb-". This is strange because the bonding in this material has
> an ionic character, and I would expect Pb oxidation state  to tend towards
> a Pb2+ (meaning its occupation should at least go below 2). I tried to
> force different behaviors with lower values for starting_ns_eigenvalue, but
> unsuccessfully.
>


I think all this is related to the fact that you are using +U on p states
that are much more spread than d and probably overlap much more in the
interstitial regions. This probably leads to overestimated occupations
(some "piece" of electrons are counted twice) and, since U tries to
stabilize integer occupations suppressing interatomic hybridization (to
which the band gap might be due), you probably also get a reduced band gap
(see J. Phys. Condens. Matter 22, 055602 (2010) for similar cases). Keep in
mind that, as usual, DFT is not a band gap theory, nor is DFT+U.



>
> I then noted that the projectors I was using were not orthogonalized,
> which makes the interpretation in terms of ionic charges more challenging.
> I tried a run with U_projection_type='ortho-atomic', and this changed the
> results completely. I was able this time to obtain much larger band gaps
> and to find pairs of U value reproducing my experimental band gap easily. I
> do observe an occupation of 1.3 on Pb for those values, which seems more
> realistic too.
>
> However, I am not very comfortable with this. Is it normal for my results
> to be so wildly influenced by the choice of projectors (it seems like a
> somewhat arbitrary choice that should not change completely the results
> obtained). The fact that I can't get anything to work with the default
> option (and especially that the band gap was reduced) is still quite
> disturbing, and makes me question the validity of the results obtained with
> orthonormal projectors.
> Has this strong influence been reported before? Is it the symptom of a
> problem that can invalidate further calculations?
>


the reason why the default option ("atomic") is kept alive is that it is
useful for energy derivatives as forces and stresses. We are working on
that and hopefully in the near future we will also have energy derivatives
for the ortho-atomic case.

Best regards,

Matteo



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-- 
Matteo Cococcioni
Department of Physics
University of Pavia
Via Bassi 6, I-27100 Pavia, Italy
tel +39-0382-987485
e-mail matteo.cococcioni at unipv.it <lucio.andreani at unipv.it>
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