Calculation of product energy distributions for the reaction OH + D yields OD + H

An interesting approach to the study of a chemical reaction is the exploration of the elementary chemical act, i.e. the events and energy distributions which occur immediately before and after the reaction. This can be done experimentally using molecular beam apparatus and other methods, or theoretically. One theoretical method for examining product energy distributions (PEDs), called the theory of quantum transitions, has been developed by V. Z. Kresin and W. A. Lester, Jr. [Chem. Phys. 90 (1984) 335-346] This approach uses techniques such as the Born-Oppenheimer Approximation and first-order time-dependent perturbation theory (Fermi's Golden Rule) to treat the chemical reaction as a quantum transition from reactants to products. This method provides a theoretical basis to explain product energy distributions obtained from molecular beam experiments. This method for study of the elementary chemical act, before the redistribution of product energy, can provide valuable insight into the nature of reactions in any field of chemistry and biochemistry. In this paper a simple model is derived using Kresin and Lester's method of quantum transitions to calculate PEDs for any reaction AB + C yields A + BC with heavy center B, from any initial vibrational state (within the harmonic approximation) of reactant AB. The resulting equations are applied to the reaction OH + D yields OD + H to obtain product energy distributions. The distributions for this reaction with a maximum final vibrational state of v max = 5, with initial v of 1-3, differ from that calculated by Kresin and Lester from the reactant (i) ground vibrational state with v max = 5 [3]. Thus it is demonstrated that PEDs depend on the initial vibrational state of the reactants. Computer calculations are done with constant total energy, and also with constant initial momentum.