Classical Monte Carlo Analysis of Four-Body Reactions: K + C2H5I System

Abstract

The analysis of the classical four-body problem as applied by Monte Carlo techniques to chemical reactions of the type A+BCD→AB+CD is reported. Using a modified form of a Blais—Bunker interaction potential surface, the model is applied to the reaction of K with C2H5I by approximating the C2H5 radical as being two carbon atoms, one of mass 14 amu, the other of mass 15 amu. Hamilton's equations are solved numerically, and by Monte Carlo averaging over the initial variables for 1060 different trajectories, various attributes of the reaction are calculated; these include the total reaction cross section, the differential reaction cross section, and the distribution of the heat of reaction among the available degrees of freedom of the products. It is found that the total reaction cross section is 15.9 Å2. This result, which is less than that obtained by similar methods for the (K, CH3I) system, is interpreted as reflecting the increased steric hindrance present in the more bulky system. The differential reaction cross section for C2H5 scattering is peaked at small angles, and an average of about 90% of the available reaction energy finds its way into internal degrees of freedom of the products. These results are in reasonable agreement with the available experimental data. It is also found that the C–C vibrational mode of the ethyl radical is important in absorbing the heat of reaction. On the average it accounts for about 14% of the available energy. Two modes of reaction are observed, one a direct interaction, the second through complex formation. This second mechanism is found to enhance the importance of the organic radical in absorbing the heat of reaction. This is interpreted as being due to the increased opportunity for energy exchange during complex formation.