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 interactions in localized parts) and do not contain high-order recoupling coefficients and 3j-symbols that essentially constrained all previous theories of mixed valency. The approach developed here is accompanied by an efficient computational procedure that allows us to calculate the bulk thermodynamic properties (magnetic susceptibility, magnetization, and magnetic specific heat) of high-nuclearity MV clusters. Finally, this approach has been used to discuss the magnetic properties of the octanuclear MV cluster [Fe-8(mu(4)- O)(4)(4-Cl-pz)(12)Cl-4](-) and the diphthalocyanine chains [YPc2] center dot CH2Cl2 and [ScPc2] center dot CH2Cl2 composed of MV dimers interacting through the magnetic exchange and Coulomb repulsion.