Six different methods for walking from a minimum on a potential energy surface to a transition structure are tested on the Lennard-Jones surface for a cluster of eight argon atoms. The six methods consist of two Newton-Raphson-type algorithms using augmented Hessians, two methods for following gradient extremals, one following the intrinsic reaction coordinate on the image potential, and a constrained optimization technique. Only if the lowest mode of a given symmetry is followed can these methods locate transition structures in a stable manner. Optimizations along the higher modes display erratic or no convergence. The analysis shows that this is due to two factors: Hessian eigenvectors in general provide a poor direction for the uphill walk, and the presence of bifurcations along the path.
