A climbing string method for saddle point search.

The string method originally proposed for the computation of minimum energy paths (MEPs) is modified to find saddle points around a given minimum on a potential energy landscape using the location of this minimum as only input. In the modified method the string is evolved by gradient flow in path space, with one of its end points fixed at the minimum and the other end point (the climbing image) evolving towards a saddle point according to a modified potential force in which the component of the potential force in the tangent direction of the string is reversed. The use of a string allows us to monitor the evolution of the climbing image and prevent its escape from the basin of attraction of the minimum. This guarantees that the string always converges towards a MEP connecting the minimum to a saddle point lying on the boundary of the basin of attraction of this minimum. The convergence of the climbing image to the saddle point can also be accelerated by an inexact Newton method in the late stage of the computation. The performance of the numerical method is illustrated using the example of a 7-atom cluster on a substrate. Comparison is made with the dimer method.