Localization-Delocalization in Bridged Mixed-Valence Metal Clusters: Vibronic PKS Model Revisited

Here we describe a new vibronic model of mixed valence (MV) dimer inspired by the conventional Piepho, Krausz, and Schatz (PKS) approach. We attempted to partially lift the main restriction of the PKS model dealing with the vibronically independent moieties of a MV molecule. The refined version of the PKS model in which the bridging ligands are included deals with the three main interactions: electron transfer (integral t₀) related to the high-symmetric ligand configuration, on-site vibronic coupling (parameter ν) arising from the modulation of the crystal field on the metal sites by the breathing displacements of their nearest ligand surroundings, and intercenter vibronic coupling (parameter ζ) describing the dependence of the electron transfer on ligand positions in the course of their breathing movement. We apply the modified model to the analysis of the adiabatic potentials and electronic density distributions in the minima of their lower sheets for the cases of one-electron MV dimer with long and short bridges and for the two-electron MV dimer exhibiting a valence disproportionation effect. The inclusion of the intercenter interaction in addition to the conventional PKS coupling is shown to produce a strong effect on the degree of localization in MV dimers and, in particular, on the assignments to the Robin and Day classes and on the conditions of stabilization of valence disproportionated states in bielectron transfer systems.