Positional time correlation function for one-dimensional systems with barrier crossing: Memory function corrections to the optimized Rouse-Zimm approximation

Abstract

The one-variable Smoluchowski equation is used to study the influence of barrier crossing processes on the positional time correlation function. The memory function of this correlation function is evaluated for a 2-4 potential as a function of the barrier height using the Mori continued fraction expansion and an equivalent but more efficient matrix formulation. Higher orders in the expansions are required to obtain numerical convergence as the barrier height increases. An exact integral solution for the correlation time is derived and is compared with the approximations. A biexponential approximation, which describes the independent motion in a potential well and the transition between wells, is found to be very accurate for high barriers. Numerical simulations provide checks on the approximations to the correlation function for a barrier height of 2 kBT. The possibility of including the influence of more rapid barrier crossing processes into the many variable Smoluchowski description of long time polymer and protein dynamics is discussed. © 1993 American Institute of Physics.