Molecular Orbital Calculation for Trigonally Distorted Octahedral Complexes

A perturbed ligand molecular orbital (PLMO) method is presented for the calculation of magnetic ion properties in diamagnetic cubic lattices at a site having trigonal (C3i) symmetry. Expressions for the anisotropic orbital reduction factors k‖ and k⊥ and spin–orbit coupling constants ζ‖ and ζ⊥ are derived in terms of the coefficients of the molecular orbital. Numerical calculations are reported for the trigonal field υ, cubic field splitting 10Dq, ζ's, and k's for the low-spin 4d5 Ru3+ ion in sixfold O2− coordination as found in the garnets YAlG, LuAlG, YGaG, LuAlG. The PLMO calculation can account for the sign of the trigonal field in the garnets and reasonable values for the effective charge η lead to good agreement with the experimental g values. Analysis of the hyperfine data gives values for the core polarization factor H for 4d electrons in the range of 2.4–2.8.