A gradient-only algorithm for tracing a reaction path uphill to the saddle of a potential energy surface

We propose a procedure to follow the weakest ascent along a valley using gradient-only calculations. The device allows one to search for saddles starting somewhere near a minimum provided that the saddle is connected with the minimum by a valley. We define a local criterion for a minimum energy path by comparison of gradients. The algorithm is a predictor-corrector method using two parameters: step length and tolerance. There is no need for a guess of the saddle point region. We calculate valley pathways on 2D test examples, on the HCN surface, and on a 12D potential of an argon 4-cluster.