‘‘Direct’’ calculation of quantum mechanical rate constants via path integral methods: Application to the reaction path Hamiltonian, with numerical test for the H+H2 reaction in 3D

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Abstract
The method recently proposed by Miller, Schwartz, and Tromp for determining Boltzmann rate constants ‘‘directly’’—by the path integral evaluation of a reactive flux correlation function—is developed within the framework of the reaction path Hamiltonian model for a general polyatomic reaction. The expression for the correlation function, the time integral of which is the rate constant, is reduced to a single path integral over only one degree of freedom (the reaction coordinate). Effects of tunneling, ‘‘frictional’’ effects on the reaction coordinate due to coupling to other degrees of freedom, and the effects of recrossing the transition state dividing surface are all correctly accounted for in the approach. Numerical tests of the formulas for the 3D version of the H+H2 reaction (on the Porter–Karplus potential surface) gives excellent agreement with the (known) accurate results for this system.