Relativistic Effects in Ligand Field Theory (I): Optical Properties of d¹ Atoms in O^' Symmetry

Ligand field theory, which explains the splitting of degenerate nd atomic orbitals due to static electric fields from point-charge ligands, is rederived using Dirac orbitals instead of Schrödinger orbitals, specifically using the nd_3/2 and nd_5/2 spinors. This formalism is, to some extent, equivalent to incorporating the spin-orbit interaction either in the nd atomic orbitals or in the ligand field orbitals (e.g., the t_2g and e_g orbitals arising from O 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 d¹ octahedral complexes as functions of the spin-orbit coupling constant ξ and the ligand field parameters Dq and Dp 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 ReF₆ obtained from optical absorption spectra are carefuly in the light of the new theory.