Electronic energy gap correlation function and spectral density of anharmonic molecules at low temperatures. II: Spectroscopy

A simple line broadening function of anharmonic molecules that may be fit into the Brownian oscillator model and directly be used in calculating nonlinear spectroscopic signals without actually evaluating nonlinear response/correlation functions over different intervals is presented. Dipole moment time correlation functions and their corresponding linear absorption spectra of model systems are calculated at zero temperature. Franck-Condon factors of the zero-phonon line using both an approximate and exact expressions for comparison purposes. Pump-probe spectra of the same systems are calculated to test the reliability, utility and applicability of the derived line broadening function in extracting the homogeneous structure of the systems due to local environmental heterogeneities. The agreement is very good.