A general small-curvature approximation for transition-state-theory transmission coefficients

We derive an expression for the effective mass along the reaction coordinate in a chemically reacting system. This expression is used in two convenient algorithms for including quantum mechanical effects on the reaction coordinate into transition-state theory or generalized transition-state theory. One algorithm is based on a uniform semiclassical approximation; the other is based on a parabolic approximation to the effective potential. Examples are presented to show that the theory accurately accounts for reaction-path-curvature effects on the tunneling contributions to the reactions H + H₂, D + D₂, and D + H₂. Although the derivation, and hence expected reliability, of the new methods is most valid for systems with small reaction-path curvature, the methods are generally applicable and should provide useful accuracy even for medium-curvature and some large-curvature systems.