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 3T1 and 3T2 and three spin singlets 1A1, 1E and 1T2 levels determined by the double-transfer processes (parameter P). Jahn-Teller and pseudo-Jahn-Teller problems (3T1 + 3T2) ⊗ (e + t2) and (1A1 + 1E + 1T2) ⊗ (e + t2) 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 Td 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 M3O12 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 t2 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 M3O12 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.
ASJC Scopus subject areas
- Physics and Astronomy (all)
- Physical and Theoretical Chemistry