On the dynamical foundations of transition state theory: a semiclassical analysis

Classical (S) over bar matrix theory is applied to the description of microcanonical unimolecular rate constants in the chaotic scattering regime. If we postulate that the semiclassical treatment satisfyingly describes the relative values of the final populations when only a few product states are available, we arrive, for processes involving tight transition states (TSs), at the following conclusions: (a) there is no semiclassical transition state theory (TST), a result in agreement with previous findings by Pechukas and Miller; stricto sensus, the exact proportionality between the rate constant k(uni) (E) and the available number N-double dagger (E) of quantum states at the TS is not founded; (b) k(uni)(E) should depend rather smoothly on E, even when tunneling is negligible; and (c) TST, however, provides a very satisfying quantitative description of rate constants when N-double dagger(E) is large, which is mostly the case in practice. (C) 2004 Elsevier Inc. All rights reserved.