Using relaxation theory to compute the electronic absorption spectrum of a chromophore coupled to a condensed phase environment

Abstract

A time-dependent method for computing the electronic absorption spectrum of a chromophore in a condensed phase environment is presented. The cumulant expansion-based relaxation theory of Nitzan and Silbey [J. Chem. Phys. 60, 4070 (1974)] is adapted to enable approximate calculation of the absorption spectrum of a general system coupled to an arbitrary bath. The system–bath interaction potential operator is expanded to second order in a time-dependent perturbation series and then exponentiated in an attempt to capture the long-time dynamics. The dynamics of the bath is contained in Heisenberg correlation functions of the bath operators which are related to their classical counterparts. The formalism is applied to a harmonic and an anharmonic (Morse) system oscillator coupled to a harmonic bath. The exactly solvable harmonic model, a two-dimensional model of a Morse oscillator coupled to a single bath oscillator and a comparison to the time-dependent Hartree approximation are used to illustrate the accuracy of the formalism.