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 tha t it accounts for the molecular origin to the stochastic transitions r ates. A formal solution to the stochastic master equation is given. Th is equation is compared with its truncated cumulant expansion. The sec ond-order cumulant contains the correlation function [kappa(2)(0)kappa (2)(t)], where kappa denotes the orientational dependence on dipole-di pole coupling. The solution of the master equation is used to formulat e the time-dependent fluorescence anisotropy, which is the relevant ob servable of energy transfer within donor-donor (dd) pairs, or bichromo phoric molecules. Depending on symmetry of the local orientational dis tributions of the donor molecules, and their rates of reorientation, t he fluorescence anisotropy decay becomes more or less complicated. Dif ferent simplifying conditions are given. The orientational distributio n 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 c ase (or dynamic Limit), where the rates of transfer are much slower th an those of reorientation, the cumulant expansion is always valid. In the intermediate case the approximation becomes questionable, while fo r 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 trans fer. (C) 1996 American Institute of Physics.