Derivation and testing of a molecular orbital description of ligand field spectra

A model for describing the ligand-field spectra of cubic chromophores in a molecular orbital basis is derived and tested by carrying out least-squares-fits of the spectra of the tetrahedral ions CoX2-4 (X = Cl Br). Independent assignments of the ligand-field spectra of the latter ions are obtained by analysing the site-group splittings and vibrational fine-structure in the polarized spectra of Cs3CoCl5 and Cs3CoBr5 at 4.2 K. General expressions are calculated for the electron repulsion matrix elements of pairs of electrons occupying orbitals transforming as e, t1 and t2 in Oh and Td point groups, without further assumption about the functional form of the orbitals. Tanabe & Sugano’s (1954) matrices for d1~d5 configurations are rewritten in the more general form. The two-electron reduced matrix elements appearing in these expressions are further approximated in terms of orbital overlap populations (Mulliken 1955), one- and two-centre coulomb integrals and one-centre exchange integrals. An analogous reduction of the matrix elements of the molecular spin-orbit operator within a molecular orbital basis is also described. The energies of the spin-orbit baricentres of the ligand-field transitions are then calculated as functions of three orbital population parameters and the energy separation between the e and t2 molecular orbitals. From the least-squares analysis of the independently assigned experimental spectra, empirical values of the four parameters are extracted, and their relation to the parameters of conventional ligand-field theory is discussed. The experimentally based molecular orbital parameters are further used to calculate spinorbit splittings of the cubic Russell-Saunders ligand-field states, and the relative dipole strengths of transitions to those which are formally spin-forbidden from the ground state.