Vibronic theory applied to the magnetic properties of tetrahedral mixed-valence clusters

Abstract

The influence of vibronic interactions on the magnetic properties of tetrahedral mixed-valence clusters is investigated for a system having one “core” electron at each metal center, and one “excess”, delocalisable electron. The aim of the model is to provide a first step towards an understanding of the magnetic properties of tetranuclear iron—sulfur clusters. The electronic Hamiltonian is based on a generalisation of the Anderson—Hasegawa model Hamiltonian and vibronic interactions are introduced as the interaction of the electronic states with non-totally symmetric combinations of local ligand vibrations. A dynamic vibronic coupling model analogous to that of Piepho, Krausz and Schatz is developed to obtain the spin-vibronic states of the cluster. In clusters having antiferromagnetic exchange interactions, the magnetic moment is found to be significantly influenced by vibronic coupling. When the sign of the electron transfer interaction ϵ is negative, vibronic coupling reduces the magnitude of the magnetic moment, but if ϵ > 0 it increases the magnetic moment. When ϵ<0, the magnitude of the intra-atomic exchange interaction also influences the magnetic moment.