The d-Hamiltonian – A new approach for evaluating optical spectra of transition metal complexes

The full multicentre molecular Hamiltonian in local density approximation for a mononuclear transition metal complex is transformed into a single-centre Hamiltonian explicitly including overlap, covalency and ligand-field effects. The orbital interactions of the metal d-orbitals with the ligand orbitals appear as a repulsive pseudopotential yielding the dominant contribution to the ligand-field splitting. This repulsive pseudopotential exhibits the same angular dependence as the electrostatic potential from the ligands entering the Hamiltonian of ligand-field theory. For this reason, ligand-field theory very often yields the correct splitting pattern of the d-orbitals. The radial part, however, is considerably different from the simple expression of ligand-field theory. In particular, there is no general theoretical justification for a R−5-dependence of the ligand-field splitting even for complexes of cubic symmetry. The reliability and capability of this new approach is demonstrated by calculating the d-orbital splitting pattern for a number of selected systems.