PKS vibronic coupling

Fig. 12 Effect of the PKS vibronic coupling on the effective magnetic moment of MV dimer ...

To perform a PO analysis of nonadiabatic quantum dynamics, we employ a quasi-classical approximation that expresses time-dependent quantities of a vibronically coupled system in terms of the vibronic POs of the system [123]. Considering the quasi-classical expression (16) for the time-dependent expectation value of an observable A, this approximation assumes that the integrable islands in phase space represent the most significant contributions to the dynamics of the observables considered [236]. As a consequence, the short-time dynamics of the system is determined by its shortest POs and can be approximated by a time average over these orbits. Denoting the A th PO with period 7 by qk t),Pk t) we obtain [123]... 

Piepho has responded to the criticisms of the PKS model by developing an improved version, the MO vibronic coupling model for mixed-valence complexes (32). Multicenter vibrations are now considered and a molecular orbital basis set (as with the three-site model) is used. This model was used to calculate band shape and g values for the Cretuz-Taube ion (33). The MO vibronic coupling model is admittedly more empirical than the three-site model but it has the advantage in being applicable to all mixed-valence complexes. 

The vibronic coupling model of Piepho, ausz and Schatz (PKS) has been introduced recently in order to treat correctly electron transfer by using the complete Hamiltonian. The PKS model emphasizes in particuliar the breakdown of the Born Oppenheimer approximation. 

LAUNAY - About the solvent effect on the degree of delocalization, one could effectively imagine a situation in which changing the solvent would change the vibronic coupling parameter (Ain PKS treatment) enough to drive the system from a rather localized to a rather delocalized state. However I do not know examples of such an effect. 

A treatment of vibronic coupling by Fischer includes anharmonic effects, and like the Piepho-Krausz-Schatz (PKS) model, it avoids using the adiabatic potential surfaces, when the coupling is strong. " ... 

Let us discuss the Robin and Day classification scheme from the point of view of the generalized vibronic model. In the case of strong PKS - coupling (Case 1), depending on the magnitude of the electron transfer parameter, MV compounds can belong to Classes I, II or III. So, when ts — A / 2 the system is... 

The vibronic PKS has enjoyed much success, but do you agree that with its limitation to antisymmetric vibrational modes, it becomes increasingly less valid as the strength of the electronic coupling increases. For the delocalized limits one expects most of the lineshape to be associated with the symmetric vibrational modes. 

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