My symmetry-equivalent sites don’t have the same energy

Hello!

Help, my symmetry-equivalent sites don’t have the same energy!

__The problem:__

My system is insulating and antiferromagnetic Cr2O3 with a positive interstitial H in a hexagonal supercell. There are 6 equivalent* sites in a ‘doughnut’ around a large interstitial region. When I compute the total energy of these sites using CP2K, I get some weird artifacts that I’ve not been able to get rid of, namely that pairs of sites opposite each other in this ring have exactly the same energy (to about 1e-6 eV) but these pairs have different energy to one another (by about 1e-3 eV).

Normally this sort of energy discrepancy is not so important, but in my case it’s crucial and I would like to know how to get rid of it. I think it’s an egg-box effect of some kind, but I’ve tried a bunch of things to no avail.

* equivalent in that I generated them using symmetry operations from one initial relaxed structure, confirmed using pymatgen’s structure matcher tool that they are indeed structurally the same and with VASP that they have the same total energy to 1e-6 eV.

__What I’ve tried so far:__

• – Crank up EPS_DEFAULT to 1e-18, CUTOFF to 3000 Ry and REL_CUTOFF to 500 Ry (with 4 grids)
• – Go down to just NGRID=1 at 1400 Ry
• – Switch between GAPW and GPW
• – Uniform translations of the structure (made ~ no difference to total energy)
• – Rotated unit cell by 120 degrees, keeping fractional coordinates the same (this resulted in a significant change in energy ~1 meV).
• – Flip all magnetic moments (no change in energy, as expected)
  
• – Switch to diagonalisation (rather than OT) (slight change in total energy but if anything adjacent equivalent sites got further from each other in energy)
  
• – Larger supercell (2x2x1 -> 3x3x2)
  
• – Changed from LDA+U Mulliken to LDA+U Lowdin
• – Changed from LDA+U to hybrid
• – Increased basis set on O from DZVP to TZVP (had to switch to Lowdin PLUS_U_METHOD due to convergence issues).
• – CP2K versions 7.1, 8.0, 8.1 and 8.2

__Minimal working example:__

Attached are 1) a cif file containing all six sites and 2) a tarball of six sets of cp2k inputs and outputs these sites (with a adjacent sites having an difference in energy of about 1 meV) that should all be energetically equivalent. These are for the relatively cheap 2x2x1 supercell and parameters that hopefully serve as a minimal working example.

Can someone explain why I’m getting different energies for these equivalent sites and how I might reduce this discrepancy.

Thanks and best wishes,

Kane