The fate of molecular excited states: modeling donor-acceptor dyes.

We investigate the relaxation of a coherently excited molecule in the Redfield approximation. The molecular model, parametrized to describe donor-acceptor dyes that represent a large family of molecules of interest for several applications, accounts for two diabatic electronic states non-adiabatically coupled to a few vibrational coordinates. The proposed approach successfully describes the fast vibrational relaxation, followed by a much slower relaxation towards the ground state, a physically relevant result that is robust vs . the specific model adopted for the system-bath coupling and the specific (reasonable) choice of the bath spectral density. We demonstrate that, when dealing with more than a single vibration, it is important that each vibration is separately coupled to an independent bath so as to avoid the cross-talking of the modes through their coupling to the same bath. Provided that the overall strength of the electron-vibration coupling is maintained constant, the number of molecular vibrations introduced in the model does not affect the system dynamics, supporting the use of effective and easy models for donor-acceptor dyes accounting for a single coupled vibration.