Accuracy of tunneling corrections to transition state theory for thermal rate constants of atom transfer reactions

We consider quantum mechanical effects on transition-state-theory transmission coefficients and on generalized transition-state-theory rate constants for elementary atom-transfer reactions in the gas phase. We examine two treatments of tunneling in the context of conventional transition-state-theory, the lowest order correction of Wigner and the full solution of the one-dimensional scattering problem for the classical potential energy barrier. We also examine two additional methods of including quantum effects on the reaction-coordinate motion in the context of adiabatic transition-state theory. One corresponds to taking the reaction coordinate as the minimum-energy reaction path, and the other uses the Marcus-Coltrin tunneling path. To test the accuracy of these approximate theories we present calculations for four collinear reactions: H + H₂, D + D₂, Cl + H₂, and Cl + T₂. Thermal rate constants are computed using these approximate theories and compared with those calculated using conventional and adiabatic transition state theory in which no quantal correction is made to the separable reaction-coordinate motion. The results are also compared with thermal rate constants obtained from accurate quantal calculations. We find that for the H + H₂ and D + D₂ systems the method using the Marcus-Coltrin path is very accurate, leading to errors less than 17% over a temperature range 300-1500 K. However the simple Wigner transmission coefficient is found to give the best overall agreement for the four systems at low temperature.