) is assigned to each image x k . Using NEB, a path is sought where the path direction and the energy gradient of each image are aligned while lowering each image's energy under the constraint of constant inter-image distances. Although NEB adds force corrections, each image prefers to minimize V (x k ; k/(N -1)), and the distances of each image tend to approach d ij (k/(N -1)) (or +∞ in some cases). When w(r) emphasizes short distances, pairs with short distances, such as covalent bonds, are prioritized. Thus, for example, the pairs forming bonds at both ends of the path are expected to be preserved along the optimized path.