Proton transfer in condensed phases beyond the quantum

PROTON TRANSFER IN CONDENSED PHASES BEYOND THE QUANTUM KRAMERS PARADIGM 

Evaluation of quantum rates for multi-dimensional systems, m. Beyond the Langevin equation/quantum Kramers paradigm  

Schwartz (ed), Theoretical Methods in Condensed Phase Chemistry, 69-90, 2000 Kluwer Academic Publishers. Printed in the Netherlands. 

A common approach for the study of activated barrier crossing reactions is the transition state theory (TST), in which the transfer rate over the activation barrier V is given by (ci)R/2jt)e 15 v. where ci)r (the oscillation frequency of the reaction coordinate at the reactant well) is an attempt frequency1 to overcome the activation barrier. For reactions in solution a multi-dimensional version2 of TST is used, in which the transfer rate is given by 

An alternative view of the same physical process is to model the interaction of the reaction coordinate with the environment as a stochastic process through the generalized Langevin equation (GLE) 

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