Generalized relations between d-orbital occupancies of transition-metal atoms and electron-density multipole population parameters from X-ray diffraction data

Generalized relations relating multipole population parameters to d-orbital occupancies of transition-metal atoms are presented. The relations are cast in the form of a 15 × 15 matrix which reduces to smaller size for site symmetries higher than . The matrix takes into account differences in normalization of density functions and atomic orbitals. The expressions are applied to diffraction data on Cr(CO)₆, Mn₂(CO)₁₀, Co₂(CO)₈, Co₃(CO)₉CH, Co(NH₃)₆Cr(CN)₆ and Co(NH₃)₆- Co(CN)₆. In all cases crystal-field destabilized orbitals are depopulated relative to stabilized orbitals. Results are in almost quantitative agreement with theoretical populations; small remaining discrepancies are to be analyzed further for their possible significance. Occupancy of e'_g orbitals in the last two compounds indicates a degree of covalency of the metal-ligand interaction in these low-spin complexes which is larger for the cyano ligand than for the ammonia molecule in agreement with generally accepted conclusions based on spectroscopic data. Very little difference is observed between the relative orbital occupancies of the Cr(CN)^3-₆ and Cr(CO)₆ species.