Energy migration and rotational motion within bichromophoric molecules .2. A derivation of the fluorescence anisotropy

A generalized Forster theory is presented which includes reorientation of the interacting molecules. The stochastic master equation is, for the first time, derived from the stochastic Liouville equation, so that it accounts for the molecular origin to the stochastic transitions rates. A formal solution to the stochastic master equation is given. This equation is compared with its truncated cumulant expansion. The second-order cumulant contains the correlation function [kappa(2)(0)kappa(2)(t)], where kappa denotes the orientational dependence on dipole-dipole coupling. The solution of the master equation is used to formulate the time-dependent fluorescence anisotropy, which is the relevant observable of energy transfer within donor-donor (dd) pairs, or bichromophoric molecules. Depending on symmetry of the local orientational distributions of the donor molecules, and their rates of reorientation, the fluorescence anisotropy decay becomes more or less complicated. Different simplifying conditions are given. The orientational distribution of the bichromophoric molecules is assumed to be isotropic and their rotational motion is taken to be negligible. The effect of using the cumulant expansion on the excitation probability and the fluorescence anisotropy was numerically examined. Brownian dynamics simulations are used to describe isotropic rotation of the d molecules. Tn the fast case (or dynamic Limit), where the rates of transfer are much slower than those of reorientation, the cumulant expansion is always valid. In the intermediate case the approximation becomes questionable, while for the static limit, a numerical evaluation of the formal solution must be performed. The theory presented here is easily modified to account for the influence of reorientation in studies of donor-acceptor transfer. (C) 1996 American Institute of Physics.