Multiexponential approximations to the torsional time correlation function for one-dimensional systems with many barriers

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Abstract
A multiexponential approximation is derived for the torsional time correlation function of a one‐dimensional system with many barriers. This approximation couples a jump model, governed by a Master equation describing transitions between wells, to a model of diffusional fluctuations within individual wells. The rate constants defining the jump model are calculated using the Kramers approximation or from a more accurate number time correlation approach. These approximations compare very favorably to the exact correlation times for torsional diffusion in a periodic potential with multiple barriers, especially when the more accurate rate constants are used. The importance of the multiexponential fluctuation‐jump model approximation lies in the possibility of extending it to multidimensional systems (of polymers or proteins) where exact solutions to the Smoluchowski dynamics are no longer available.