Franck-Condon Approximation for Second Order Reduction Factors. Application to Vibronic Reduction in Fullerenes

Abstract

We present the general theory of the Franck-Condon approximation applied to the problem of second-order Jahn-Teller reduction factors. It is based upon the assumption that, at strong coupling, the major contributions to the reduction factors originate from ‘vertical transitions’ from a minimum in the ground adiabatic potential energy surface (APES) to excited vibronic states associated with the upper sheets of the APES. This reduces the otherwise infinite number of excited vibronic states to a finite number. This theory is applied to the example of spin-orbit coupling in the fullerene anion C₆₀ ^-.