Beyond Transition-State Theory: A Rigorous Quantum Theory of Chemical Reaction Rates

Transition-state theory (TST),’ as all chemists know, provides a marvelously simple and useful way to understand and estimate the rates of chemical reactions. The fundamental assumption2 of transition-state theory (Le., direct dynamics, no recrossing trajectories; see below), however, is based inherently on classical mechanics, so the theory must be quantized if it is to provide a quantitative description of chemical reaction rates. Unlike classical mechanics, though, there seems to be no way to construct a rigorous quantum mechanical theory that contains as its only approximation the transition-state assumption of “direct dynamics”. Pechukas3 has discussed this quite clearly (and it will be reviewed below): as soon as one tries to rid a quantum mechanical version of transition-state theory of all approximations (e.g., separability of a one-dimensional reaction coordinate) beyond the basic transition-state assumption itself, one is faced with having to solve the full (multidimensional) quantum reaction dynamics problem. But a correct treatment of the full quantum dynamics must yield the exact rate constant and is no longer a transition-state “theory”. Though there is no rigorous quantum prescription for determining the rate constant of a chemical reaction that avoids, in one guise or another, the necessity of solving the Schrodinger equation, there is nevertheless a rigorous theoretical approach4 that avoids having to solve the complete state-to-state reactive scattering problem; one does not avoid solving the Schrddinger equation, but needs to solve it only locally, in the vicinity of the transition state, with no explicit information about reactant and product states being required. After reviewing some of the notions alluded to above, the purpose of this Account is to describe this “direct” theoretical approach for calculating chemical reaction rates, the logical conclusion in the quest for a “rigorous” quantum mechanical version of transition-state theory.