Variational transition state theory, vibrationally adiabatic transmission coefficients, and the unified statistical model tested against accurate quantal rate constants for collinear F+H₂, H+F₂, and isotopic analogs

We test several approximate theories of thermal rate constants against accurate quantal equilibrium rate constants for collinear bimolecular reactions governed by given potential energy surfaces. The systems considered are F+H ₂ and F+D₂ for the Muckerman potential energy surface no. 5 at 200-1200 K and H+F₂, D+F₂, and T+F₂ for potential surface II of Jonathan, Okuda, and Timlin at 233-1260 K. For F+H ₂, conventional transition state theory overestimates the accurate rate constant by factors of 2.9-3.4, with the largest errors at the lowest and highest temperatures. Vibrationally adiabatic transmission coefficients or variational transition state theory decrease the error to factors of 1.2-1.3 at the lowest temperature and to a factor of 3.2 at the highest temperature. The unified statistical model reduces the errors to a factor of 1.1 at the lowest temperature and a factor of 2.7 at the highest temperature. For F+D₂ the trends are similar but the errors in all the methods are smaller at all temperatures. For H+F₂ conventional transition state theory underestimates the rate constants by a factor of 0.56 at the lowest temperature with the error decreasing to 2% at the highest temperature. Various formulations of vibrationally adiabatic transmission coefficients, in conjunction with either conventional or variational transition state theory, reduce the error to factors of 0.84-0.96 at the lowest temperature while not destroying the good agreement at the highest temperature. The unified statistical theory seems to overestimate the recrossing correction for this reaction, though only by about 10%. The results are similar for D+F₂ and T+F₂ except that the low-temperature underestimates of the calculations without tunneling are not as severe. The best theory, improved canonical variational theory with the Marcus-Coltrin path semiclassical adiabatic ground-state transmission coefficient, reproduces the accurate quantal results for H+F₂, D+F₂, and T+F₂ within 5% or better in every case for the whole temperature range.