A SIMPLE GRADIENT-METHOD FOR LOCATING SADDLES

A gradient method is presented which can be viewed as a continuous-time version of the 'distinguished (reaction) coordinate' method, one of the oldest techniques for finding transition states (saddles of first order). The method offers a simple uniform algorithm for finding saddles of any order, is naturally implemented in terms of both internal and Cartesian coordinates and successfully combines with the Newton-Raphson step in later stages of the search. The probable area of application for this technique is in locating simple imaginable saddles, which are associated with localized rearrangements of atoms, for multiatomic systems. The method is illustrated by application both to a two-dimensional model problem (the Adams potential, locating transition states) and the 13-atom Lennard-Jones cluster (locating saddles of first and second order).