Tunneling in bimolecular reactions

The estimation of the tunneling fraction of bimolecular reaction from the empirical rate equation has been made by using the Laplace transform relation between the rate equation and the cumulative reaction probability on the knowledge of the reaction barrier height. The tunneling fractions of the D + H2 → HD + H reaction were found to be 95%, 65%, 24%, and 2.4% at the temperatures of 200, 300, 500, and 1000 K, respectively. Similar estimations were made for several reactions including the reactions of F-atoms with H2 and its isotopes, the reactions of O-atoms and OH-radicals with H2 and D2, the reactions of H-atoms and Mu (muonium) with F2, and the methoxy radical decomposition reaction. For most reactions containing H2 as the reactant, the tunneling fractions exceeded 50% at 300 K, while for the reactions containing D2 in place of H2, found were about a half of those for the reactions containing H2. Exception was found in the reactions of F-atoms with H2 and its isotopes. The tunneling fraction of the F + H2 reaction at 300 K was found to be 14%. The value is much smaller than those of other hydrogen atom transfer reactions calculated in this paper. The reason is probably the fact that the barriers of the F atom-reactions are flat and their heights are very low. Although there are some uncertainties on the accuracy of barrier heights, the Mu + F2 reaction seems to occur thoroughly through tunneling at 300 K, and the methoxy radical decomposition also seems to occur through tunneling at the temperatures up to 1000 K. Finally, an example of the application of the present method to the analysis other than the estimation of tunneling fraction was presented.