Importance of nonseparability in quantum mechanical transition-state theory

A discussion of classical transition state theory shows that the fundamental dynamical assumption in transition state theory is that the reaction mechanism is "direct", and for reactions with activation barriers it is reasoned that this is a good approximation for the threshold of the reactive cross section. Examples are presented which show that this is indeed true within the framework of classical mechanics. Analogous comparisons that have been made quantum mechanically, however, show transition state theory to be significantly poorer than in the classical case, and it is argued that this is a result of the fact that the conventional quantum mechanical version of transition state theory involves the assumption that motion along some reaction coordinate is separable from that of the other degrees of freedom. (This separability approximation is known to be poor in the threshold region. ) It is then shown how a more general_ definition of quantum mechanical transition state theory can be constructed, which does not necessitate the assumption of separability, and sample calculations show this to be in good agreement with (exact) quantum scattering theory.