Variable reaction coordinate transition state theory: Analytic results and application to the C2H3+H→C2H4 reaction

A novel derivation is provided for the canonical, microcanonical, and energy E and total angular momentum J resolved reactive flux within the variable reaction coordinate transition state theory (VRC-TST) formalism. The use of an alternative representation for the reaction coordinate velocity yields a new expression for the kinematic factor which better illustrates its dependence on the pivot point location, and which can be straightforwardly evaluated. Also, the use of a geometric approach in place of an earlier algebraic one clarifies the derivation as does the use of Lagrange multiplier methodology for the analytic integration over the total angular momentum. Finally, a quaternion representation for the fragment and line-of-centers orientations is employed in place of the Euler angle or internal/external rotational coordinates used in prior studies. The result is an efficient, and particularly easy to implement, methodology for performing variable reaction coordinate transition state theory calculations. Furthermore, the simplicity of the derivation allows for the straightforward generalization to alternative forms for the dividing surface, as is illustrated by deriving the expressions for the cases of elliptical and planar dividing surfaces. Application to the C2H3+H reaction yields results for the total rate coefficient that are generally only 15% greater than those obtained from related trajectory simulations, thereby demonstrating the accuracy of the VRC-TST formalism. Meanwhile, results for the two separate addition channels (frontside and backside) illustrate the difficulty of accurately apportioning the total flux and particularly the inadequacy of canonical predictions for the channel specific optimized dividing surfaces.