Title: Methods to locate Saddle Points in Complex Landscapes,
Abstract: 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 Müller-Brown surface we find that the algorithm always
finds the correct saddle point. For the modified Müller-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.