Using the Reaction Path Concept to Obtain Rate Constants From ab initio Calculations

Abstract

Even after so many years of progress in theoretical chemistry, the accurate first-principles description of chemical reactions still poses a major challenge. Under the BornOppenheimer approximation, the dynamics of an elementary chemical reaction are determined by the sum of the electronic energy plus the internuclear coulomb repulsion energy as a function of the nuclear geometry, i.e., the potential energy surface (PES). (Although we shall restrict the present section to bimolecular elementary gas-phase reactions occurring on a single PES, the concepts and methodologies discussed below are applicable to unimolecular reactions as well as to processes occurring in condensed phases or at phase interfaces; for some examples of such applications, see [1].) For example, given the entire PES for a particular reaction, the thermal rate constant can be obtained through a Boltzmann average of the reaction cross section [2,3], which can be approximated with classical trajectory [3-5] or quantum mechanical coupled-channel calculations [6,7]. More recently, a discrete variable representation approach [8] to the calculation of the cumulative reaction probability has also shown great promise. However, since such methods require a great deal of information about the PES, and, in addition, are generally not practical for three-dimensional studies of reactions involving more than three (or, perhaps, four) atoms, the most common approach for calculating thermal rate constants is transition state theory.