Extended lattice generalized Jahn-Teller model

EXTENDED (LATTICE) GENERALIZED JAHN-TELLER MODEL 

We investigate ID lattice of spinless double degenerated electron states linearly coupled to two intramolecular phonon modes described by Hamiltonian 

In terms of the creation-annihilation electron and phonon operators the Hamiltonian can be cast as follows  

Taking removes the degeneration of the vibronic states breaking the rotational symmetry of the electron-phonon interactions, the model still staying within the class of JT models [1,2]. 

The dispersionless optical phonon mode / , splits the degenerated unperturbed electron level (j = 1,2) while the mode b2 mediates the electron transitions between the levels. This latter term represents phonon-assisted tunneling, a mechanism of the 

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Extended (lattice) generalized Jahn-Teller model 633... 

The spectacular relationship between the nature of the X3 species and the promotion energy shows that the VBSCD is in fact a general model of the pseudo-Jahn-Teller effect (PJTE). A qualitative application of PJTE would predict all the X3 species to be transition-state structures that relax to the distorted X ---X-X and X-X— X entities. The VBSCD makes a distinction between strong binders, which form transition states, and weak binders that form stable intermediate clusters. Thus, the VBSCD model is in tune with the general observation that as one moves in the periodic table from strong binders to weak ones (e.g., metallic) matter changes from discrete molecules to extended delocalized clusters and/or lattices. The delocalized clusters of the strong binders are the transition states for chemical reactions. 

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