Activated complex theory trajectory calculations

The lifetime of an activated state is too short for one to be certain that there is full quantization throughout the trajectory, except where the reactants are well separated. However, complete neglect of quantization in the activated state does not satisfy the requirement that there must be full quantization in the products of reaction. The calculations of Karplus et al. do indeed lead to the result that the product hydrogen molecule has in general a different vibrational amplitude than corresponds to any quantum level. This is obviously a weakness of the treatment, and there is no reason to believe that the resulting rates are any more reliable than those calculated from activated-complex theory. 

A consideration of these results shows, first of all, that both the simple collision and the activated complex theories require considerable corrections in the whole temperature range investigated, not only in a quantum-mechanical, but also in a semiclassical treatment based on quasiclassical trajectory calculations. 

Rather than calculating trajectories, one can use statistical mechanics in an approximate form. The oldest such approximate theory was pioneered in the 1930s by Eyring and Polanyi, and is called the activated complex theory, or the transition-state theory ... 

Theoretical descriptions of absolute reaction rates in terms of the rate-limiting formation of an activated complex during the course of a reaction. Transition-state theory (pioneered by Eyring "", Pelzer and Wigner, and Evans and Polanyi ) has been enormously valuable, and beyond its application to chemical reactions, the theory applies to a wider spectrum of rate processes (eg., diffusion, flow of liquids, internal friction in large polymers, eta). Transition state theory assumes (1) that classical mechanics can be used to calculate trajectories over po-... 

In transition state theory, dynamic effects are included approximately by including a transmission coefficient in the rate expression [9]. This lowers the rate from its ideal maximum TS theory value, and should account for barrier recrossing by trajectories that reach the TS (activated complex) region but do not successfully cross to products (as all trajectories reaching this point are assumed to do in TS theory). The transmission coefficient can be calculated by activated molecular dynamics techniques, in which molecular dynamics trajectories are started from close to the TS and their progress monitored to find the velocity at which the barrier is crossed and the proportion that go on to react successfully [9,26,180]. It is not possible to study activated processes by standard molecular dynamics because barrier crossing events occur so rarely. One reason for the... 

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