Time-dependent survival probability in diffusion-controlled reactions in a polymer chain: beyond the Wilemski-Fixman theory

Brownian dynamics simulation results of the time-dependent survival probability (Sp(t)) of a donor-acceptor pair embedded at the two ends of a Rouse chain are compared with two different theories, one of which is the well-known Wilemski-Fixman (WF) theory. The reaction studied is fluorescence energy transfer via the Forster mechanism, which has a R-6 distance (R) dependence of the reaction rate. It has been reported earlier [G. Srinivas, A. Yethiraj, and B. Bagchi, J. Chem. Phys. 114, 9170 (2001)] that while the WF theory is satisfactory for small reaction rates, the agreement was found to become progressively poorer as the rate is increased. In this work, we have generalized the WF theory. We suggest an approximate, reduced propagator technique for three-dimensional treatment (instead of 3N dimensions, where N is the number of monomers in the polymer chain). This equation is solved by combining a Green's function solution with a discretized sink method. The results obtained by this new scheme are in better agreement with the simulation results