High-Nuclearity Mixed-Valence Clusters and Mixed-Valence Chains: General Approach to the Calculation of the Energy Levels and Bulk Magnetic Properties

A general approach to the problem of electron delocalization in the high-nuclearity mixed-valence (MV) clusters containing an arbitrary number of localized spins and itinerant electrons is developed. Along with the double exchange, we consider the isotropic magnetic exchange between the localized electrons as well as the Coulomb intercenter repulsion. As distinguished from the previous approaches dealing with the MV systems in which itinerant electrons are delocalized over all constituent metal sites, here, we consider a more common case of systems exhibiting partial delocalization and containing several delocalized domains. Taking full advantage of the powerful angular momentum technique, we were able to derive closed form analytical expressions for the matrix elements of the full Hamiltonian. These expressions provide an efficient tool for treating complex mixed-valence systems, because they contain only products of 6j-symbols (that appear while treating the delocalized parts) and 9j-symbols (exchange i...