Electron delocalization in mixed-valence Keggin polyoxometalates. Ab initio calculation of the local effective transfer integrals and its consequences on the spin coupling

We present a quantitative evaluation of the influence of the electron transfer on the magnetic properties of mixed-valence polyoxometalates reduced by two electrons. For that purpose, we extract from valence-spectroscopy ab initio calculations on embedded fragments the value of the transfer integrals between W nearest-neighbor atoms in a mixed-valence alphaPW(12)O(40) polyoxowolframate Keggin anion. In contradiction with what is usually assumed, we show that the electron transfer between edge-sharing and corner-sharing WO(6) octahedra have very close values. Considering fragments of various ranges, we analyze the accuracy of calculations on fragments based on only two WO(5) pyramids which should allow a low cost general study of transfer parameters in polyoxometalates. Finally, these parameters are introduced in an extended Hubbard Hamiltonian that models the whole anion. It permits to prove that electron transfers induce a large energy gap between the singlet ground state and the lowest triplet states providing a clear explanation of the diamagnetic properties of the mixed-valence Keggin ions reduced by two electrons.