Quantum transition state theory: featuring ensemble pre-equilibrium approximation

Abstract

In this article, we use an ensemble pre-equilibrium approximation to vindicate the use of Heisenberg Equation of Motion and some other approximation for the rate of the change of quasi-equilibrium state in order to derive, based on the most precise and accurate existing theory of reaction rates to date, a rate law for any given elementary step of a chemical reaction that applies even to the condensed phase. The necessity of such a theory arises because first of all, quantum mechanics must be taken into account, and secondly, other molecules and especially the solvent may play an important role in the transition state of any elementary reaction, and we have devised a theory for doing so. Also, the correct theory for reaction rates critically depends on a complete set of wavefunctions of the transition state representing initially the products and finally the reactants, and we show a simple way for deriving it. We also show that several prevailing formulas in the literature for the cumulative reaction rate within the range of applicability of non-relativistic mechanics to the electrons and nuclei of the reacting systems within the reactor are exactly equivalent to each other, even in the condensed phase, and therefore the present theory is exact within the laws of quantum non-relativistic mechanics.