High-nuclearity mixed-valence magnetic clusters: A general solution of the double exchange problem

Abstract

We report here a general solution of the double-exchange problem in the high-nuclearity mixed valence systems containing arbitrary number P of the electrons delocalized over the network of N (P<N) localized spins. The developed approach is based on the successive (chainlike) spin-coupling scheme and takes full advantage from the quantum angular momentum theory. In the framework of this approach the closed-form analytical expressions are deduced for the matrix elements of the double exchange interaction, two-electron transfer, and three-center interaction that can be referred to as the potential exchange transfer. For the arbitrary nuclearity mixed-valence systems the matrix elements of all named interactions are expressed in terms of all relevant spin quantum numbers and 6j symbols and do not contain higher order recoupling coefficients. We describe also the combined approach taking into account both angular momentum consideration and advantages of point symmetry adapted basis set.