Classical variational rate theory portraits of the dynamical stereochemistry of the F+H2→FH+H reaction

A general classical variational theory of reaction rates is applied to the F + H-2 --> FH + H reaction. The variational theory gives the rate as the equilibrium flux of phase points through a trial surface which divides reactants from products and is varied to obtain a least upper bound for the rate. This dividing surface (DS) is defined by a power-series expansion of the H-H internuclear separation (r) in internal coordinates R and theta, i.e., r = F(R, theta) where R is the approach coordinate and theta is the orientation angle. The downhill simplex algorithm is used to search the space of 6 and 10 variational parameters of second- and third-order expansions of the DS and obtain minimum values for the canonical rate constant or, in the microcanonical formulation of the theory, the energy-dependent mean reaction cross section. The presence of angle-dependent terms in the DS makes it possible to describe the dynamical stereochemistry of atom-diatom reactions in a new and useful manner. Portraits of the dynamical stereochemistry are obtained by plotting contours of the density of reaction systems on the DS; such plots are reactivity relief maps of the DS. Reactivity relief maps show how the field of reactivity which surrounds the diatomic reactant molecule expands with increasing temperature and energy. Results are presented here for a new power series formulation of the DS which obeys a condition: partial derivative F(R, theta)/partial derivative theta = 0 at theta = pi/2 which is appropriate for reaction of a homonuclear diatomic molecule. The relationship between reactivity relief maps obtained using quadratic and cubic formulations of the new DS and the locations of angle-dependent energy barriers for reaction is described. Variational and classical mechanical trajectory results are used to show how energy-dependent factors, which correct the variational mean reaction cross section for trajectories which cross and recross the DS, depend on the orientation angle.