  Long distance excitation energy transfer between a donor and an acceptor
embedded in a polymer chain is usually assumed to occur via the Forster
mechanism which predicts a 1/R^6 distance dependence of the transfer rate,
where R is the distance between the donor and the acceptor. In solution R
fluctuates with time. In this work, a Brownian dynamics simulation of a polymer
chain with Forster enregy transfer between the two ends is carried out and the
time dependence of the survival probability S_p(t) is obtained. The latter can
be measured by the flourescence resonance energy transfer (FRET) technique,
which is now widely used to study conformations of biopolymers via the single
molecule spectroscopy. It is found that the suvival probability is
exponential-like when the Forster radius (R_F) is comparable to the root mean
square radius(L) of the polymer chain. The decay is strongly non-exponential
both for small and large (R_F), and also for large k_F. Large deviations from
Wilemski-Fixman theory is obtained when R_F is significantly differnet from L.
