One of the most common operations in computational chemistry is finding stationary points in energy surfaces based on local gradients and curvatures. In 1989, a group of researchers published a paper describing a computationaly efficent algorithm for exploring energy surfaces [doi: 10.1063/1.458435]. The most important thing to remember with walking on surfaces is that we only have local information about the energy surface. Therefore every calculation and step must take place within a set distance of the initial location. One trick employed to reduce required computation is the local quadratic approximation.
Another variable to consider is the step size. A short step size will require more iterations to cover the same distance as a longer step, but will be more accurate. Long step sizes tend to overshoot the target location. While this makes sense, some mathematical justification would improve the quality of the paper.
To conclude the paper the authors provide an example application. They implement their algorithm and show that it matches the experimental results conducted in a chemistry lab. This step is important to show the feasibility of their method.
This paper is cited in most transition path papers, including Eric Vanden-Eijnden's paper String Method for the Study of Rare Events.