Stochastic reduction for dynamics of reactions with complex formation

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Abstract
We present a method for evaluating the distribution of products in chemical reactions which proceed by complex formation. The method consists of separating the degrees of freedom into strong modes, which are correlated directly with the reactiondynamics and weak modes. We then treat the dynamics of the strong modes explicitly and perform a statistical averaging over the weak degrees of freedom. Our final result [Eq. (5)] for the distribution of products is in the form of a product of three matrices whose sizes are determined by the number of relevant strong modes. The first matrix accounts for the preparation of the complex, the second for the energy redistribution within the complex, and the third for the dissociation of the complex. As one possible course of procedure we evaluate the first and third matrices by applying a normal coordinate transformation of the strong modes from reactants to complex and then to products and then use Franck–Condon factors between the strong states of the complex and fragments (reactants and products); the second matrix is evaluated using a step ladder model. We then apply the formulation to the system F+C2H4 for which deviations from statistical behavior were observed. Nonstatistical behavior may occur in our model from two distinct sources: (1) the Franck–Condon factors which are associated with the dynamics and (2) the finite energy redistribution rate within the complex (relative to the dissociation rate). We discuss the influence of these two effects in F+C2H4 and conclude that the first one is dominant in this case.