The d Orbital Multi Pattern Occupancy in a Partially Filled d Shell: The KFeF(3) Perovskite as a Test Case

The occupancy of the d shell in KFeF [Formula: see text] is [Formula: see text] e [Formula: see text] , with five [Formula: see text] and one [Formula: see text] electrons. The Jahn–Teller lift of degeneracy in the [Formula: see text] sub-shell produces a tetragonal relaxation of the unit cell (4.09 vs. 4.22 Å, B3LYP result) not observed experimentally. In order to understand the origin of this apparent contradiction, we explored, with a 2 × 2 × 2 supercell (40 atoms per cell), all possible local structures in which contiguous Fe atoms have a different occupancy of the [Formula: see text] orbitals with the minority spin electron. A total of 6561 configurations (with occupancies from (8,0,0) to (3,2,2) of the 3 [Formula: see text] orbitals of the 8 Fe atoms) have been explored, with energies in many cases lower (by up to 1550 [Formula: see text] E [Formula: see text] per 2 Fe atoms) than the one of the fully ordered case, both for the ferromagnetic and the anti-ferromagnetic solutions. The results confirm that the orientation of the [Formula: see text] d electron of Fe influences the electrostatics (more efficient relative orientation of the Fe quadrupoles of the d shell) of the system, but not the magnetic interactions. Three hybrid functionals, B3LYP, PBE0, and HSE06, provide very similar results.