Semiclassical theory rate constants

Miller W H 1974 Quantum mechanical transition state theory and a new semiclassical model for reaction rate constants J. Chem. Phys. 61 1823-34... 

The classical (or semiclassical) equation for the rate constant of e.t. in the Marcus-Hush theory is fundamentally an Arrhenius-Eyring transition state equation, which leads to two quite different temperature effects. The preexponential factor implies only the usual square-root dependence related to the activation entropy so that the major temperature effect resides in the exponential term. The quadratic relationship of the activation energy and the reaction free energy then leads to the prediction that the influence of the temperature on the rate constant should go through a minimum when AG is zero, and then should increase as AG° becomes either more negative, or more positive (Fig. 12). In a quantitative formulation, the derivative dk/dT is expected to follow a bell-shaped function [83]. 

Two different theoretical approaches have been used to relate the ET rate constant (k ) to the thermodynamic driving force (AG ) and parameters related to molecular structure. The first approach is the semiclassical treatment derived from the early work by Marcus on ET theory [2-4,45],... 

In this chapter we have reviewed the development of unimolecular reaction rate theory for systems that exhibit deterministic chaos. Our attention is focused on a number of classical statistical theories developed in our group. These theories, applicable to two- or three-dimensional systems, have predicted reaction rate constants that are in good agreement with experimental data. We have also introduced some quantum and semiclassical approaches to unimolecular reaction rate theory and presented some interesting results on the quantum-classical difference in energy transport in classically chaotic systems. There exist numerous other studies that are not considered in this chapter but are of general interest to unimolecular reaction rate theory. 

This is supported by computed rate constants with tunneling contributions using the semiclassical Wentzel-Kramers-Brillouin (WKB) theory. The WKB procedure requires a carefully described intrinsic reaction path, and... 

W. H. Miller, Quantum Mechanical Transition State Theory and a New Semiclassical Model for Reaction Rate Constants, J. Chem. Phys., 61 (1974) 1823. 

The theoretical description of the kinetics of electron transfer reactions starts fi om the pioneering work of Marcus [1] in his work the convenient expression for the free energy of activation was defined. However, the pre-exponential factor in the expression for the reaction rate constant was left undetermined in the framework of that classical (activate-complex formalism) and macroscopic theory. The more sophisticated, semiclassical or quantum-mechanical, approaches [37-41] avoid this inadequacy. Typically, they are based on the Franck-Condon principle, i.e., assuming the separation of the electronic and nuclear motions. The Franck-Condon principle... 

X. Sun, H. B. Wang, and W. H. Miller (1998) On the semiclassical description of quantum coherence in thermal rate constants. J. Chem,. Phys. 109, p. 4190 X. Sun, H. B. Wang, and W. H. Miller (1998) Semiclassical theory of electronically nonadaibatic molecular dynamics Results of a linearized approximation to the initial value representation. J. Chem. Phys. 109, p. 7064... 

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