| In the study of both reaction mechanisms and reaction kinetics, the concept of the reaction path is central. For theoretical studies of mechanisms, it is desirable to follow the lengthy and curved path from the transition state toward the products and back to the reactants with as little computational effort as possible. The same is true for the calculation of rate constants by variational transition state theory, where accurate values for the curvature and frequencies along the path are needed. Reaction paths are notoriously difficult to follow. Many of the traditional algorithms used to follow reaction paths have difficulties in reproducing the correct tangent and curvature vectors along the path and consequently, very small step sizes must be used.;A new reaction path following algorithm in mass-weighted internal coordinates has been developed based on a constrained optimization that is exact when the reaction path is an arc of a circle. This method has been shown to be more efficient than many of the most popular algorithms available in the literature. It can follow extremely curved reaction paths with fairly large step sizes. In the limit of small step size, this algorithm is correct to second order, i.e. it yields the correct tangent and curvature along the path and at the transition state (even though only first energy derivatives are needed).;The reaction path following algorithm described above has been implemented into the GAUSSIAN package of programs and used to compute frequencies, curvature coupling elements, total curvature along the path as well as reaction rate constants by the variational transition state theory for the hydrogen abstraction CH... |
