METAL-LIGAND AND METAL-METAL COUPLING ELEMENTS

The electronic matrix element coupling a ground and charge-transfer ex cited state can be calculated from the energy and intensity of the app ropriate charge-transfer transition. An expression for the electronic coupling element widely used for this purpose is based on equations de rived by Mulliken and Hush for an effective two-state model and is fre quently assumed to be valid only in the perturbation limit. This expre ssion is shown to be exact within a two-state model. Provided that ove rlap can be neglected and that the spectroscopic transition is polariz ed along the donor-acceptor axis, it can be applied to systems ranging from those which are very weakly coupled to those which are very stro ngly coupled. Application of the Mulliken-Hush expression to (NH3)5RuL 2+ 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 energ ies. With use of the superexchange formalism, the metal-ligand couplin g elements were used to calculate metal-metal coupling elements for bi nuclear mixed-valence complexes. Comparison of these values with those obtained from the Mulliken-Hush expression applied directly to the me tal-to-metal charge-transfer transition yields agreement within a fact or of two or better.