Entropic effects on the dynamical bottleneck location and tunneling contributions for C₂H₄ + H → C₂H₅: Variable scaling of external correlation energy for association reactions

The temperature dependence of the dynamical bottleneck location for the prototype olefin addition process H + C₂H₄ has been studied by variational transition state theory. In addition, a multidimensional tunneling calculation has been carried out. To obtain a reliable potential energy profile, a new way to extrapolate electronic structure calculations to the limit of full configuration mixing and a complete electronic basis set is proposed. The method, called variable scaling of external correlation (VSEC) uses a scale factor that varies with geometry to combine a complete-active-space self-consistent-field (CASSCF) calculation with a calculation including an appreciable amount of the dynamical correlation energy. The parameters in the scaling factor are adjusted to experimental or high-quality theoretical data at critical points. For the title reaction we find excellent agreement with experiment at all temperatures both for the rate constant of the association reaction and also for the rate constant of its reverse dissociation, and we use the resulting model to infer critical details of the dynamics. In particular, we find that dynamical bottlenecks are ∼0.06-0.15 Å tighter than the saddle point, with bending frequencies 1.2-1.8 times higher than at the saddle point. Furthermore, we conclude that tunneling effects account quantitatively for the curvature of the Arrhenius plots.