Calculation of the least energy path on the energy hypersurface

A doubly nudged elastic band method for finding transition states

“…In the present work we used the nudged elastic band [71,76] (NEB) and eigenvectorfollowing [15,17,18,19,20,23,24,34,53,55,80] (EF) methods for locating and refining transition states. In the NEB approach the path is represented as a set of images {X 1 , X 2 ...X N } that connect the endpoints X 0 and X N +1 , where X i is a vector containing the coordinates of image i (Figure 1) [75].…”

“…In contrast, double-ended methods are usually designed to characterise a particular rearrangement, and often do not produce a tightly converged geometry for the transition state. However, the resulting structures can be further refined using single-ended strategies, particularly eigenvector-following [15,17,18,19,20,23,24,34,35,45,53,55,80], and this approach has been used in several previous studies [75,81,82]. Some recent overviews of the field are available [5,83], and readers are referred to these publications for further discussion.…”

“…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,…”

Evolution of the potential energy surface with size for Lennard-Jones clusters

“…Transition states can be found efficiently using eigenvector-following, [24][25][26] in which the energy is maximized along one direction and simultaneously minimized in all the others. The minima connected to a transition state are defined by the two steepest-descent paths which begin parallel and antiparallel to the unique Hessian eigenvector whose corresponding eigenvalue is negative.…”

Energy landscape of a model protein

“…All the transition states in the present work were located by eigenvector-following, [24][25][26][27][28][29] where the energy is maximized along one direction and simultaneously minimized in all the others. Details of our implementation have been given before.…”