Quadratic steepest descent on potential energy surfaces. III. Minima seeking along steepest descent lines

Abstract

A simplified quadratic steepest descent method, based on the availability of energies and gradients, is formulated for use in minimum searching. It requires only a fraction of the computational effort needed for the previously developed accurate steepest descent procedures and, typically, involves less work than standard quasi-Newton minimum searches. At the same time, it follows the true steepest descent curves reasonably closely and reaches the closest minima. This is in contrast to quasi-Newton procedures which cannot be relied upon to do so. The performance is documented by applications to a variety of searches on the Müller–Brown surface.