Fourier analysis, correlation functions and nonadiabatic electron transfer: Wavepackets and exact representations

We investigate the validity of several common approximations in the analysis of nonadiabatic intramolecular electron transfer rate constants. Utilizing the Fourier representation of the golden rule form, we study the evolution of the vibrational correlation function that represents the density-of-states-weighted Franck-Condon factor. In particular, we test the validity of the perturbation theoretic golden rule form and of the Gaussian wavepacket representation for the vibrational wavefunctions against numerically exact quantum mechanical propagations. Although specific cases are found in which both of these break down, for a wide range of conditions (including anharmonic behavior and frequency changes), both the Gaussian wavepacket representation and the golden rule are excellent approximations.