Walking on potential energy surfaces

An algorithm for locating stationary points corresponding to local minima and transition states on potential energy surfaces is developed and analyzed. This method, which represents a substantial extension of an earlier algorithm, utilizes local gradient and Hessian (i.e., first and second energy derivative) information to generate a series of ‘‘steps’’ that are followed to the desired stationary point. By designing the step sequence to move energetically downhill in all coordinates, local minima can be found. By stepping uphill along one local eigenmode of the Hessian while minimizing the energy along all other modes, one locates transition states. A key element of this development is a more efficient parametrization of the step vector in terms of quantities that permit the direction (i.e., uphill or downhill) and length of the step to be carefully controlled. This, in turn, allows ‘‘walks’’ that trace streambeds connecting local minima to transition states and to neighboring local minima more closely than has been found using the earlier methods. Such streambed walks provide information that can be used in subsequent reaction-path dynamics simulations.