Franck-Condon transition probability dynamics

In thermally activated ET we are interested in the electronic states at the transition state (TS). When the system is at equilibrium in either the initial or final state (where D and A are well out of resonance), the diabatic states, xj/j and i/y, can be taken to be essentially the same as their adiabatic counterparts, xj/ and xj/2. When the system with weakly coupled D and A is suddenly carried into the TS by a fluctuation, we adopt the picture that the system remains in the (now nonstationary) xf/ state until (with some finite probability) it dynamically tunnels (see below) to i/y and irreversibly relaxes to the equilibrium product. The required resonance of D and A is a statement of the Franck-Condon control of thermally activated electron transfer [6, 8, 60] that is, at the TS,... 

Three novel approaches to the simulation of NA dynamics of large chemical systems have been presented [20-22]. The approaches extend the standard quantum-classical NA MD to incorporate quantum effects of the solvent subsystem that have been traditionally treated by classical mechanics. These effects include quantum trajectory branching (wave packet splitting), loss of quantum coherence directly related to the Franck-Condon overlap contribution to the NA transition probability, and ZPE of nuclear motion that contributes to the NA coupling and must be preserved during the equilibration of the energy released by the NA transition. 

Suppose that the two potential surfaces are dissimilar. Then the Franck-Condon factors are less than imity and you get different probabilities for making transitions to final v" vibrational levels depending on the vibrational overlap. We shall make repeated use of the Franck-Condon principle in imderstanding which vibrational levels are populated in various dynamical processes. In Section 9.2 we will generalize the principle so that it also applies to excitation as a result of a collision (where we need not be in the sudden limit). 

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