METAL-LIGAND AND METAL-METAL COUPLING ELEMENTS

The electronic matrix element coupling a ground and charge-transfer excited state can be calculated from the energy and intensity of the appropriate charge-transfer transition. An expression for the electronic coupling element widely used for this purpose is based on equations derived by Mulliken and Hush for an effective two-state model and is frequently assumed to be valid only in the perturbation limit. This expression is shown to be exact within a two-state model. Provided that overlap can be neglected and that the spectroscopic transition is polarized along the donor-acceptor axis, it can be applied to systems ranging from those which are very weakly coupled to those which are very strongly coupled. Application of the Mulliken-Hush expression to (NH3)5RuL2+ complexes, for which metal-ligand backbonding is important, yields metal-ligand coupling elements of 5000-6000 cm-1 with pyridyl ligands (donor-acceptor separation 3.5 angstrom), in very good agreement with estimates obtained from a molecular orbital analysis of the band energies. With use of the superexchange formalism, the metal-ligand coupling elements were used to calculate metal-metal coupling elements for binuclear mixed-valence complexes. Comparison of these values with those obtained from the Mulliken-Hush expression applied directly to the metal-to-metal charge-transfer transition yields agreement within a factor of two or better.