Walking on potential energy surfaces

Abstract

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.

A doubly nudged elastic band method for finding transition states

“…Algorithms to locate transition states can generally be divided into single-ended approaches, which simply require a single starting geometry [11,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55], and double-ended methods, which are usually designed to find a transition state between two endpoints [10,56,57,58,59,60,61,62,…”

A quasiclassical approach to strongly correlated quantum dots

“…A number of computational approaches to this problem has been developed and published [11,12]. In our work we chose to employ the adapted parabolic extrapolation scheme which has proven to be sufficiently stable and efficient when applied to fewelectron quantum dots.…”

Clusters containing open-shell molecules. II. Equilibrium structures of ArnOH Van der Waals clusters (X2Π, n=1 to 15)

“…The geometries of Ar n OH clusters were first optimized by means of simulated annealing, and subsequently refined by a direct minimization scheme using several Newton-Raphson steps. For larger clusters, the CerjanMiller eigenvector-following method 42,43 was used to verify these results, and to check that the simulated annealing did not miss any of the cluster minima.…”