Electronic and vibronic problems of nanosized mixed valence clusters: Advances and challenges

Here we discuss the electronic and vibronic problems of mixed valency (MV) in molecular clusters which are of current interest in areas as diverse as solid-state chemistry, biochemistry, and molecular magnetism. Modern research in these areas is focused on the nanosized clusters at the border between classical and quantum scales and for this reason they are particularly difficult to study. First, we describe a general approach to the evaluation of the energy pattern of MV systems containing arbitrary number of localized spins and itinerant electrons with due account for the double exchange and other relevant interactions, like interelectronic Coulomb repulsion in instantly localized configurations. Then we present a symmetry adapted approach to the dynamic vibronic problem in large scale multimode Jahn-Teller (JT) systems, in particular, molecular MV clusters. The developed techniques are applied to the analysis of nanosized MV systems with emphasis on the 2e-reduced MV Keggin anion in which the electronic pair is delocalized over twelve sites (Td) giving rise to the (¹T2+¹E+¹A1)⊗(e+t2) and ( ³T1+³T2)⊗(e+t2) combined JT/pseudo JT problems for the spin-singlet and spin-triplet states. The delocalization of the two itinerant electrons in this remarkable systems was shown to lead to an effective spin paring. We study the energy pattern of this MV system and show that the vibronic interaction results in the ferromagnetic contribution.