A second-order Kubo response theory-centroid approach to vibrational energy relaxation for single-mode excitations

Abstract

We consider an approach for describing vibrational energy relaxation processes in liquids for solutes excited to states which are dominated by single-mode excitations. The method utilizes the fact that adding a suitable linear term to the solute intramolecular potential, creates excitations in the first excited state of a chosen vibrational mode. The fully quantum energy decay rate of the vibrational excitation can then be derived using quadratic response theory, which expresses the decay rate as the decay of a second-order Kubo transformed correlation function. This correlation function can be exactly related to a path integral centroid second-order correlation function, which can be evaluated approximately by centroid molecular dynamics. The abilities and limitations of the approach are discussed. It is shown that the method should work best when only a single vibrational state is occupied prior to excitation. Practical matters require also that the relaxation is in the pico-second regime or shorter. In contrast to the usual golden rule approach, the present method incorporates quantum effects and does not require explicit evaluation of vibrational coupling elements or Fourier transforms. It also incorporates the intramolecular vibrational coupling, whereby intramolecular relaxation can be monitored explicitly. The approach is tested on asymmetric stretch excited OClO(aq), using a classical bath, and gives results which are in good accord with earlier findings. The theory also points in the direction of how to improve the so-called classical approach to vibrational energy relaxation, where energy is put directly into the mode subsequently undergoing relaxation.