Mixed valence and double exchange: a symmetry adapted approach to the non-adiabatic electron-vibrational problem

 

The talk includes a tutorial part within which the concept of mixed valency will be introduced and the main models for the electron-vibrational interaction  will be discussed. We will demonstrate the consequences of the vibronic coupling like localization vs. delocalization and intervalence light absorption.  Then the concept of the double exchange will be introduced and the magnetic properties of  many-electron systems will be discussed. In this part of the talk we discuss also  the crucial (in context of  the theme) question: when the framework of  the adiabatic approximation (assuming rapid motion of the electrons and slow motion of the nuclei)  is enough for the adequate description of mixed-valence compounds and under which conditions  this conventionally accepted  approach fails. In the last case the system entire can not be divided into the “slow” (nuclei)  and “rapid” (electrons) subsystems and therefore the  dynamical vibronic problem is to be solved.

In the original part of the talk I will first demonstrate the difficulties which appear when we are trying to solve a quantum-mechanical (dynamic) problem in mixed valence systems      (or, more commonly, for the systems exhibiting degeneracy) especially in the large nano-sized metal clusters [1,2].  It will be shown how to efficiently  use the symmetry and to design a set of the symmetry adopted basis set in which huge vibronic matrices can be diagonalized [3].  The results will be employed   in the description of the intervalence optical absorption in trimeric mixed valence compounds and dodecanuclear polyoxometalates  with Keggin structure.

References:

    B. Tsukerblat,  High-Nuclearity Mixed Valence Clusters and Mixed Valence Chains:

     Inorganic Chemistry,  48 (2009) 4557-4568.

 2. J.M. Clemente-Juan, J.J. Borrás-Almenar,  E. Coronado, A.V. Palii,  B.S. Tsukerblat,

     nuclearity mixed valence clusters, J. Compt. Chemistry, 31(2010) 1321-1332.

 3. B. Tsukerblat,  A. Palii,  J.M. Clemente-Juan,  E. Coronado, A symmetry adapted  approach to   

     the dynamic  Jahn-Teller problem, in Series: Progress in Theoretical   Chemistry and Physics,

     Vol. 23: Vibronic Interactions and the Jahn-Teller Effect  (2011) 39-58.