Exchange and vibronic interactions in a tetrahedral, five-electron mixed-valence cluster

The distribution of an "excess" electron in a model mixed-valence tetranuclear metal cluster with open-shell ion cores is explored as a function of vibronic coupling, electron transfer, and electron exchange interactions. The system comprises five electrons, one "core electron" at each metal center, and one electron in a different local orbital which can delocalize among the sites. Vibronic coupling is introduced as the interaction of the electronic states with nontotally symmetric combinations of the subunit ligand vibrations. An extension of the Anderson-Hasegawa Hamiltonian is developed to describe the system, and adiabatic potential energy surfaces for the different spin states are obtained. From these, the excess electron distribution is deduced. The model is designed to be a prototype for understanding the excess electron distributions in tetranuclear iron-sulfur clusters. Examples of electron delocalization over three sites in an S=3/2 ground state and over two sites in an S=1/2 state are found. These distributions cannot arise in a tetranuclear cluster having closed-shell ion cores and are attributed to favorable double exchange interactions. The occurrence of pair delocalization in an S=1/2 ground state is consistent with experimental observations of (Fe₄S ₄)³⁺ iron-sulfur clusters.