orbital ordering patterns in KBF (B = Sc, Ti, Fe, Co) perovskites.

The orbital ordering (OO) resulting from the partial occupancy of the subshell of the transition metals in KBF (B = Sc, Ti, Ffe, Co) perovskites, and the many possible patterns arising from the coupling between the B sites, have been investigated at the quantum mechanical level ( Gaussian type basis set, B3LYP hybrid functional) in a 40 atoms supercell. The numerous patterns are distributed into 162 classes of equivalent configurations. For each fluoroperovskite, one representative per class has been calculated.

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

The occupancy of the d shell in KFeF3 is t2g4eg2, with five α and one β electrons. The Jahn-Teller lift of degeneracy in the t2g sub-shell produces a tetragonal relaxation of the unit cell (4.09 vs.

Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids.

A symmetry-adapted algorithm producing uniformly at random the set of symmetry independent configurations (SICs) in disordered crystalline systems or solid solutions is presented here. Starting from Pólya's formula, the role of the conjugacy classes of the symmetry group in uniform random sampling is shown. SICs can be obtained for all the possible compositions or for a chosen one, and symmetry constraints can be applied.

On the use of symmetry in configurational analysis for the simulation of disordered solids.

The starting point for a quantum mechanical investigation of disordered systems usually implies calculations on a limited subset of configurations, generated by defining either the composition of interest or a set of compositions ranging from one end member to another, within an appropriate supercell of the primitive cell of the pure compound. The way in which symmetry can be used in the identification of symmetry independent configurations (SICs) is discussed here. First, Pólya's enumeration theory is adopted to determine the number of SICs, in the case of both varying and fixed composition, for colors numbering two or higher.