Thermal rate constants in collinear atom transfer reactions by optimizing the position of the reactants/products dividing surface

Abstract

On the basis of Miller–Schwartz–Tromp [J. Chem. Phys. 79, 4889 (1983)] formula for the flux autocorrelation function, and its derivation in hyperspherical coordinates by Park and Light [J. Chem. Phys. 94, 2946 (1991)], we study the sensitivity of the thermal rate constant, k(T), for a collinear transfer reaction calculated within the framework of the finite basis set approximation, to the position of the dividing surface between reactants and products, s0=ρα0. Illustrating 2D numerical examples of calculating k(T) for symmetric, H3, and nonsymmetric, Mu–H2 and Mu–D2, potential surfaces by optimizing the value of α0 are given. In all cases (symmetric and nonsymmetric potential surfaces) the optimal dividing surface has to be chosen such that dk(T)/dα0=0. For symmetric potential surfaces tan(2α0)=(mBM/mAmc)1/2, whereas, for highly nonsymmetric potential surfaces, the optimal dividing surface has to be chosen numerically. It is shown that with very limited basis set this numerical stationary solution may be associated with an inflection point rather than a minimum, and therefore k(T) is not necessarily an upper bound to the true thermal rate.