Dynamical effects in line shapes for coupled chromophores: time-averaging approximation.

For an isolated resonance of an isolated chromophore in a condensed phase, the absorption line shape is often more sharply peaked than the distribution of transition frequencies as a result of motional narrowing. The latter arises from the time-dependent fluctuations of the transition frequencies. It is well known that one can incorporate these dynamical effects into line shape calculations within a semiclassical approach. For a system of coupled chromophores, both the transition frequencies and the interchromophore couplings fluctuate in time. In principle one can again solve this more complicated problem with a related semiclassical approach, but in practice, for large numbers of chromophores, the computational demands are prohibitive. This has led to the development of a number of approximate theoretical approaches to this problem. In this paper we develop another such approach, using a time-averaging approximation. The idea is that, for a single chromophore, a motionally narrowed line shape can be thought of as a distribution of time-averaged frequencies. This idea is developed and tested on both stochastic and more realistic models of isolated chromophores, and also on realistic models of coupled chromophores, and it is found that in all cases this approximation is quite satisfactory, without undue computational demands. This approach should find application for the vibrational spectroscopy of neat liquids, and also for proteins and other complicated multichromophore systems.