Diffusion coefficients, effects dynamical friction

In this limit, the dynamic solvent effect can also be treated as a diffusion process using the Smoluchowski equation. This emphasizes the fact that the friction leads to multiple crossings of the Gibbs energy barrier. The diffusion coefficient associated with this process is given by... 

We would be remiss if we did not comment on isomerization dynamics in liquids, since they form a very important and widely studied class of reactions. There have been many theoretical models for isomerization reactions in liquids. In Section III.C we briefly outlined Kramers approach to this problem. Since that time much more extensive studies of such barrier-crossing problems have been carried out. These studies have been concerned mainly with obtaining expressions for the rates in the transition region between the low- and high-friction cases, or with effects arising from the nonlocality of the diffusion coefficient in the context of Smoluchowski equation descriptions, applications to polymeric systems, and so on." ... 

Stochastic dynamics The stochastic dynamics (SD) method is a further extension of the original molecular dynamics method. A space-time trajectory of a molecular system is generated by integration of the stochastic Langevin equation which differs from the simple molecular dynamics equation by the addition of a stochastic force R and a frictional force proportional to a friction coefficient g. The SD approach is useful for the description of slow processes such as diffusion, the simulation of electrolyte solutions, and various solvent effects. 

In the sections below a brief overview of static solvent influences is given in A3.6.2, while in A3.6.3 the focus is on the effect of transport phenomena on reaction rates, i.e. diffusion control and the influence of friction on intramolecular motion. In A3.6.4 some special topics are addressed that involve the superposition of static and transport contributions as well as some aspects of dynamic solvent effects that seem relevant to understanding the solvent influence on reaction rate coefficients observed in homologous solvent series and compressed solution. More comprehensive accounts of dynamics of condensed-phase reactions can be found in chapter A3.8, chapter A3.13. chapter B3.3, chapter C3.1. chapter C3.2 and chapter C3.5. 

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