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 calculation...

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