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

[JULIEN, CLAUDE, PIERRE BARBAUD]

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 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?