In this review article, we present a systematic comparison of the theoretical rate constants for a range of bimolecular reactions that are calculated by using three different classes of theoretical methods: quantum dynamics (QD), quasi-classical trajectory (QCT), and transition state theory (TST) approaches. The study shows that the difference of rate constants between TST results and those of the global dynamics methods (QD and QCT) are seen to be related to a number of factors including the number of degrees-of-freedom (DOF), the density of states at transition state (TS), etc. For reactions with more DOF and higher density of states at the TS, it is found that the rate constants from TST calculations are systematically higher than those obtained from global dynamics calculations, indicating large recrossing effect for these systems. The physical insight of this phenomenon is elucidated in the present review.

We present variational transition state theory (VTST) calculations for the H 2 + CN → HCN + H (R1) and D 2 + CN → DCN + D (R2) reactions and their reverses based on a global many-body expansion potential energy surface (PES) for ground-state H 2 CN (ter Horst MA, Schatz GC, Harding LB, J Chem Phys105:558, 1996). It is found that the tunneling effects are negligible over the 200–2000 K temperature range and non-negligible over 100–200 K for R1 and R2 reactions. The C–N bond acts almost as a spectator for both reactions. The present VTST rate constants are in good agreement with the available experimental results and the previous theoretical predictions for R1 and R2 reactions except for the overestimation of rate constants by VTST at lower temperatures that may be caused by recrossing effect. Additionally, the kinetic isotope effects are important for the forward R1 and R2 reactions, but not for the reverses of R1 and R2.

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