Theoretical Analysis on the Kinetic Isotope Effects of Bimolecular Nucleophilic Substitution (S(N)2) Reactions and Their Temperature Dependence

Factors affecting the kinetic isotope effects (KIEs) of the gas-phase S(N)2 reactions and their temperature dependence have been analyzed using the ion-molecule collision theory and the transition state theory (TST). The quantum-mechanical tunneling effects were also considered using the canonical variational theory with small curvature tunneling (CVT/SCT). We have benchmarked a few ab initio and density functional theory (DFT) methods for their performance in predicting the deuterium KIEs against eleven experimental values. The results showed that the MP2/aug-cc-pVDZ method gave the most accurate prediction overall. The slight inverse deuterium KIEs usually observed for the gas-phase S(N)2 reactions at room temperature were due to the balance of the normal rotational contribution and the significant inverse vibrational contribution. Since the vibrational contribution is a sensitive function of temperature while the rotation contribution is temperature independent, the KIEs are thus also temperature dependent. For S(N)2 reactions with appreciable barrier heights, the tunneling effects were predicted to contribute significantly both to the rate constants and to the carbon-13, and carbon-14 KIEs, which suggested important carbon atom tunneling at and below room temperature.