Classical formulation of the spectroscopy of nonadiabatic excited-state dynamics

Abstract

A general classical formulation of the spectroscopy of nonadiabatically coupled electronic states is developed within the theoretical framework of the classical electron analog model due to Meyer and Miller. Adopting the Heisenberg representation for the calculation of the electric polarization, several approaches are presented to establish a quantum-classical correspondence. It is shown that a consistent classical formulation is obtained by replacing the quantum-mechanical commutators, which appear in quantum-mechanical perturbation theory, by the corresponding classical Poisson brackets which come from classical perturbation theory. The more usual practice of replacing the Heisenberg dipole operators directly by the corresponding classical dipole functions is shown to be an approximation to classical perturbation theory. For a coupled electronic three-state system explicit expressions are derived for the nonlinear polarization. Furthermore the practical application to femtosecond pump-probe spectroscopy is discussed in some detail.