Quadratic steepest descent on potential energy surfaces. II. Reaction path following without analytic Hessians

A second order method is developed for determining steepest descent lines of potential energy surfaces by following steepest curves of successive local quadratic surface approximations. The basic principle is similar to that of a previously developed method where, however, the availability of analytically calculated exact Hessians was assumed wherever needed. By contrast, only the analytically calculated exact values of the energy and its gradient are used here and this difference entails marked changes in strategy. Applications to the Gonzalez–Schlegel and the Müller–Brown surfaces show that the method compares favorably with existing methods.