Pair-delocalization in trigonal mixed-valence clusters: New insight into the vibronic origin of broken-symmetry ground states

A new vibronic mechanism for the stabilization of pair-delocalized electronic states in trigonal trimeric mixed valence complexes (such as iron-sulfur [Fe₃S₄]⁰ proteins) is proposed. Unlike the previously reported mechanism based on the Piepho-Krausz-Schatz model dealing with the local "breathing" vibrations, the present mechanism involves the multicenter vibrations of the triangular complex, which change the metal-metal distances. The former mechanism of the vibronic coupling in combination with the double exchange and Heisenberg type exchange (superexchange) interactions accounts for the existence of the pair-delocalized states of many-electron mixed valence clusters in the intermediate ground spin states. In contrast to the previous model, within which the conditions for the occurrence of pair delocalized states are spin-dependent, the pair delocalization phenomenon in the proposed model is exclusively based on a clear physical mechanism of the interplay between the inter-center vibronic coupling and electron transfer. Therefore, the proposed mechanism demonstrates that the pair delocalization is a more common feature of mixed valence complexes and can appear not only in multi-electron trimers as a result of the interplay between several parameters, but even in one-electron mixed valence trimers in which neither double exchange nor superexchange is operative. The conditions for the pair delocalization in the proposed model are shown to be dependent on the value and sign of the electron transfer parameter as well as on the ratio of the frequencies of the fully symmetric (a₁) and doubly degenerate (e) vibrations of a triatomic molecule.