A random walk to local minima and saddle points on a potential energy surface. A strategy based on simulated annealing

We demonstrate how the Metropolis simulated annealing method, a global stochastic minimizer, can also be used as an all-purpose extremizer capable of locating all the local minima and saddle points on a given surface, in addition to the global minimum. The demonstration is done with reference to the well studied Muller-Brown potential and a one-dimensional spin glass with random nearest-neighbour interaction. The relevance of the present strategy in the construction of reaction paths is discussed.