Discrete master equations can be obtained from the diffusion-Smoluchowski equation in the presence of large barriers separating the potential minima, the treatment being equivalent to the derivation of the Kramers transition rates in the overdamped regime. The one-dimensional problem is considered as a test case to illustrate the projection procedure onto the subspace of localized functions. This method, however, generalizes the Kramers theory to intermediate potentials barriers. The inertial effects are shortly discussed in relation to the numerical solutions for a bistable problem. The coupling between the overall rotation and the conformational transitions is analyzed in a molecule with one torsional degree of freedom. The generalization of the Kramers theory to multi-dimensional diffusion equations is presented with particular emphasis on the frictional coupling between the reactive and non-reactive modes of the potential function. The model system of a linear chain of rotors is used to demonstrate that cooperative transitions during saddle point crossing arise as a consequence of the frictional coupling. The parameterization of the transition rates for an alkyl chain attached to a rigid core is summarized, together with the main results concerning the relaxation of conformer populations and the methylene rotational relaxation.

Models of conformational dynamics

MORO, GIORGIO;FERRARINI, ALBERTA;POLIMENO, ANTONINO;NORDIO, PIER LUIGI
1989

Abstract

Discrete master equations can be obtained from the diffusion-Smoluchowski equation in the presence of large barriers separating the potential minima, the treatment being equivalent to the derivation of the Kramers transition rates in the overdamped regime. The one-dimensional problem is considered as a test case to illustrate the projection procedure onto the subspace of localized functions. This method, however, generalizes the Kramers theory to intermediate potentials barriers. The inertial effects are shortly discussed in relation to the numerical solutions for a bistable problem. The coupling between the overall rotation and the conformational transitions is analyzed in a molecule with one torsional degree of freedom. The generalization of the Kramers theory to multi-dimensional diffusion equations is presented with particular emphasis on the frictional coupling between the reactive and non-reactive modes of the potential function. The model system of a linear chain of rotors is used to demonstrate that cooperative transitions during saddle point crossing arise as a consequence of the frictional coupling. The parameterization of the transition rates for an alkyl chain attached to a rigid core is summarized, together with the main results concerning the relaxation of conformer populations and the methylene rotational relaxation.
Reactive and flexible molecules in liquids
9780792304692
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/2486747
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