  The fluctuations of optical gap induced by the environment play crucial roles
in electronic energy transfer dynamics. One of the simplest approaches to
incorporate such fluctuations in energy transfer dynamics is the well known
Haken-Strobl-Reineker model, in which the energy-gap fluctuation is
approximated as a white noise. Recently, several groups have employed molecular
dynamics simulations and excited-state calculations in conjunction to take the
thermal fluctuation of excitation energies into account. Here, we discuss a
rigorous connection between the stochastic and the atomistic bath models. If
the phonon bath is treated classically, time evolution of the exciton-phonon
system can be described by Ehrenfest dynamics. To establish the relationship
between the stochastic and atomistic bath models, we employ a projection
operator technique to derive the generalized Langevin equations for the
energy-gap fluctuations. The stochastic bath model can be obtained as an
approximation of the atomistic Ehrenfest equations via the generalized Langevin
approach. Based on the connection, we propose a novel scheme to correct
reorganization effects within the framework of stochastic models. The proposed
scheme provides a better description of the population dynamics especially in
the regime of strong exciton-phonon coupling. Finally, we discuss the effect of
the bath reorganization in the absorption and fluorescence spectra of ideal
J-aggregates in terms of the Stokes shifts. For this purpose, we introduce a
simple relationship that relates the reorganization contribution to the Stokes
shifts - the reorganization shift - to three parameters: the monomer
reorganization energy, the relaxation time of the optical gap, and the exciton
delocalization length. This simple relationship allows one to classify the
origin of the Stokes shifts in molecular aggregates.
