Oxidation of 4a,4b-Dihydrophenanthrenes. III. A Theoretical Study of the Large Kinetic Isotope Effect of Deuterium in the Initiation Step of the Thermal Reaction with Oxygen

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Abstract
The large kinetic isotope effect of deuterium that occurs in the reaction of perdeuterio‐4a,4b‐dihydrophenanthrene with O2 is studied by a semiempirical calculation. The large effect is a consequence of two significant effects, the existence of quantum mechanical tunneling and the loss of zero‐point energy. The theoretical study is mainly based on the construction of the potential surface by the method of bond eigen‐functions, and the treatment of the reaction as the solution of a 10‐electron problem. The calculated tunneling effect, which is found by integration of all possible transmission probabilities through the potential barrier, results in factors of 11.8 at 242°K and 8.1 at 263°K. A conformational and normal mode analysis shows that the contribution of the zero‐point energy effect amounts to a factor of 7.6 at 242°K and 6.4 at 263°K.