Comparison of methods for finding saddle points without knowledge of the final states

Different methods for finding saddle points without knowing the final states of transition are discussed. The rational function optimization (RFO) methods which employ an approximate Hessian are found to be efficient in finding the saddle point. But when the force and Hessian can be obtained cheaply, the RFO approach using exact Hessian is the better choice. When the force can be obtained cheaply, the minimum mode following methods are efficient in obtaining the lowest saddle point in a large system.