Mixed-valence polyoxometalate clusters. III. Vibronic problem for the 2-electron reduced heteropoly blue with the Keggin structure

Abstract

Abstract A general approach to the vibronic problem of delocalized electronic pairs in mixed-valence compounds is developed and applied to understand the ways of electron delocalization in dodecanuclear polyoxometalate clusters containing two moving electrons. The interplay between electronic and vibronic interactions is examined. The electronic spectrum is shown to consist of two spin triplets 3 T 1 and 3 T 2 and three spin singlets 1 A 1 , 1 E and 1 T 2 levels determined by the double-transfer processes (parameter P ). Jahn-Teller and pseudo-Jahn-Teller problems ( 3 T 1 + 3 T 2 ) ⊗ ( e + t 2 ) and ( 1 A 1 + 1 E + 1 T 2 ) ⊗ ( e + t 2 ) have been considered in the framework of the Piepho-Krausz-Schatz model dealing with the only vibronic parameter. Several kinds of spatial electronic distribution have been found corresponding to the stable points of the energy surfaces. For spin-triplet states, potential surfaces contain six minima in e space corresponding to partially delocalized electronic pairs over four sides of the T d structure (limiting case of weak coupling), or delocalized over two opposite sides (limiting case of strong coupling). The former situation restricts electron delocalization to two of the three metal octahedra of each M 3 O 12 triad in such a way that each electron moves over a tetrameric unit in which the metal sites are alternatively sharing edges and corners. In the t 2 space the electronic pair can be either delocalized over three sides, giving rise to a trigonal-type distortion of the cluster and a partial electron delocalization over two opposite M 3 O 12 triads (four trigonal minima in the case of strong transfer or relatively weak vibronic interaction), or be completely localized (case of strong vibronic coupling). For spin-singlet states the system possesses a stable point in the high-symmetrical nuclear configuration, corresponding to a full delocalization of the electronic pairs in the Keggin cluster. The influence of vibronic interaction on the nature of the spin of the ground states is considered.