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