Reaction path following by quadratic steepest descent

Abstract.

An efficient steepest descent algorithm for the integration of minimum energy paths, based on local quadratic approximations of the potential energy surface, is presented. The algorithm incorporates a selection procedure for the points at which the second derivatives of the energy are calculated fully or partially, thus minimizing the computational effort while maintaining high accuracy. This makes the method especially well suited for application in variational transition state theory calculations with tunnelling corrections, which have very high accuracy requirements. The performance of the algorithm is illustrated by ab initio calculations for four chemical reactions of differing complexity. The overall computational cost is less than for, or comparable to that of, first- or second-order algorithms published previously.