Implementation of Distortion Symmetry for the Nudged Elastic Band Method

The nudged elastic band (NEB) method is an effective approach for calculating minimum energy pathways of kinetic processes. However, the final paths obtained by the algorithm rely heavily on the initially chosen path. This often necessitates running multiple calculations with different initial conditions in order to obtain reliable results. Recently, this problem has been reformulated using the language of distortion symmetry, which consists of combining static spatial symmetries with a new operation called distortion reversal, and has the property of only being conserved or raised by the NEB optimization [1]. Using this knowledge, symmetry-adapted perturbations to an initial path can be generated and used to systematically lower its symmetry. By doing so, the exploration of other low-energy pathways that may exist is enabled. The group and representation theory details behind this new approach are presented and implemented in standalone software (DiSPy). The algorithm is then demonstrated by applying it to the calculation of ferroelectric switching pathways in LiNbO₃. Previously reported pathways are recovered, with new paths that involve a higher degree of atomic coordination also being discovered.

[1] Munro, J. M. et al. Phys. Rev. B. 98, 085107 (2018).