Relativistic Effects in Ligand Field Theory (I): Optical Properties of d Atoms in Symmetry.

Ligand field theory, which explains the splitting of degenerate d atomic orbitals due to static electric fields from point-charge ligands, is rederived using Dirac orbitals instead of Schrödinger orbitals, specifically using the d and d spinors. This formalism is, to some extent, equivalent to incorporating the spin-orbit interaction either in the d atomic orbitals or in the ligand field orbitals (e.g., the t and e orbitals arising from symmetry). The spin-orbit interaction is of fundamental importance in the description of the magnetic and optical properties of the 4d and 5d transition metal complexes. Algebraic equations for the relativistic energy levels of d octahedral complexes as functions of the spin-orbit coupling constant ξ and the ligand field parameters and are derived. It is demonstrated that these parameters allow a direct link between the ligand field theory and ab initio relativistic calculations, consistent with the emerging ab initio ligand field theory. The spin-orbit coupling constant and ligand field parameters of ReF obtained from optical absorption spectra are carefuly in the light of the new theory.