The coupling between librational motions and conformational transitions in chain molecules. II. The rotor chain represented by the master equation for site distributions

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Abstract
The model system of the rotor chain is considered in order to analyze the coupling between conformation transitions and the librational motions, i.e., the small amplitude displacements within the energy wells of the stable states. The master equation for site (conformer) distributions (MESD) on the torsional angle displacements is the suitable formalism which allows one to describe at the same time both types of motions. While in the previous work the MESD was proposed on a phenomenological ground, the formal derivation of the MESD is now provided by means of a projection procedure. The ingredients of the MESD, in particular the coordinate-dependent rate kernel, are determined unambiguously in this way. A reduced equation without site indeces is recovered by applying the MESD to the rotor chain with equivalent potential minima. A new procedure based on the Gaussian approximation for the site distribution is introduced to solve the reduced equation. This allows one to calculate rather easily correlation functions for different observables. A good agreement is found in the comparison with the available Brownian molecular; dynamics simulations on the same system. The behavior of the orientational correlation functions is examined in detail in order to disentangle in the overall relaxation the contributions of the conformational dynamics from the effects of the librationa