Anharmonic Effect on Unimolecular Reactions with Application to the Photodissociation of Ethylene

Abstract

The importance of anharmonic effect on dissociation of molecular systems, especially clusters, has been noted. In this paper, we shall present a theoretical approach that can carry out the first principle calculations of anharmonic canonical and microcanonical rate constants of unimolecular reactions within the framework of transition state theory. In the canonical case, it is essential to calculate the partition function of anharmonic oscillators; for convenience, the Morse oscillator potential will be used for demonstration in this paper. In the microcanical case, which involves the calculation of the total number of states for the activated complex and the density of states for the reactant, we make use of the fact that both the total number of states and the density of states can be expressed in the inverse Laplace transformation of the partition functions and that the inverse Laplace transformation can in turn be carried out by using the saddle-point method. We shall also show that using the theoretical approach presented in this paper the total number of states and density of states can be determined from thermodynamic properties and the difference between the method used in this paper and the thermodynamic model used by Krems and Nordholm will be given. To demonstrate the application of our theoretical approach, we chose the photodissociation of ethylene at 157 and 193 nm as an example.