Lba. Johansson et al., ENERGY MIGRATION AND ROTATIONAL MOTION WITHIN BICHROMOPHORIC MOLECULES .2. A DERIVATION OF THE FLUORESCENCE ANISOTROPY, The Journal of chemical physics, 105(24), 1996, pp. 10896-10904
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.