Time domain formulation of optical spectroscopy involving three potential energy surfaces

We consider the computation of electronic absorption and Raman scattering spectra when three potential energy surfaces are involved; namely, a ground state surface coupled radiatively to one excited state which is in turn coupled nonadiabatically to a second excited surface. Frequency domain formulas are given for both kinds of spectra under the (standard) assumption of weak radiative coupling, but with no restriction on the nonadiabatic coupling strength. These formulas are transcribed into the time domain so that the computational burden is shifted to determination of the temporal evolution of wave packets simultaneously on both excited surfaces. We show how to implement the appropriate dynamics utilizing a perturbation expansion in the nonadiabatic coupling strength. Finally, extensive numerical results are presented for a one dimensional test system. Lowest order nonvanishing perturbation theory corrections are found to account accurately for nonadiabatic effects of ∼15%. Concentrating mainly on low resolution spectra such as arise in the case of direct photodissociation, the general effect of nonadiabatic coupling is observed to be broadening of absorption spectra and suppression of Raman scattering intensities.