HOW TO FIND A SADDLE-POINT

This paper explains a method for finding saddle points on a multidimensional surface and shows how it may be used to define saddle‐point seeking curves that have properties similar to well‐known orthogonal trajectories. It is shown that a gradient extremal is a special case of one of these curves, and its chemical significance as the path, defined by local criteria, which starts from a stable structure and leads to a transition state, is discussed briefly in relation to the intrinsic reaction coordinate. It is emphasized that this theory gives a natural method for locating points that have Hessians of similar structure to those of transition states. Copyright © 1990 John Wiley & Sons, Inc.