Abstract
.We present a class of simple algorithms that allows to find the reaction path in systems with a complexpotential energy landscape. The approach does not need any knowledge on the product state and doesnot require the calculation of any second derivatives. The underlying idea is to use two nearby points inconfiguration space to locate the path of slowest ascent. By introducing a weak noise term, the algorithmis able to find even low-lying saddle points that are not reachable by means of a slowest ascent path. Sincethe algorithm makes only use of the value of the potential and its gradient, the computational effort to findsaddles is linear in the number of degrees of freedom, if the potential is short-ranged. We test the performanceof the algorithm for two potential energy landscapes. For the M¨uller-Brown surface we find that the algorithmalways finds the correct saddle point. For the modified M¨uller-Brown surface, which has a saddle point thatis not reachable by means of a slowest ascent path, the algorithm is still able to find this saddle point withhigh probability