Time-averaging approximation in the interaction picture: Absorption line shapes for coupled chromophores with application to liquid water

Abstract

The time-averaging approximation (TAA), originally developed to calculate vibrational line shapes for coupled chromophores using mixed quantum/classical methods, is reformulated. In the original version of the theory, time averaging was performed for the full one-exciton Hamiltonian, while herein the time averaging is performed on the coupling (off-diagonal) Hamiltonian in the interaction picture. As a result, the influence of the dynamic fluctuations of the transition energies is more accurately described. We compare numerical results of the two versions of the TAA with numerically exact results for the vibrational absorption line shape of the OH stretching modes in neat water. It is shown that the TAA in the interaction picture yields theoretical line shapes that are in better agreement with exact results.