Mixed-valence polyoxometalate clusters. I. Delocalization of electronic pairs in dodecanuclear heteropoly blues with keggin structure

The problem of delocalization of a pair of electrons over dodecanuclear polyoxometalate clusters with the Keggin structure is considered with the aim of explaining the spin pairing in these multi-nuclear mixed-valence systems. A general approach that considers the Coulomb interactions between the two delocalized electrons, as well as the single and double electron transfer processes which can be operative in delocalization of the electronic pairs is developed. The new approach is based on the site-symmetry concept which makes possible a group theoretical classification for the delocalized states of electronic pairs. This procedure proves to be very efficient in the calculation of the transfer matrices which are expressed in terms of the Coulomb energy, and the single- and double-transfer parameters. The influence of these electronic parameters on the spectrum of the low-lying energy levels of the cluster is discussed, and the conditions giving rise to the stabilization of a singlet ground spin state for the electronic pair are elucidated.