A Quadratically-Converging Nudged Elastic Band Optimizer

Nudged elastic band (NEB) is a well established chain-of-states method to locate the minimum energy path in configuration space. Unfortunately, existing search algorithms suffer from slow convergence. We provide an analytic derivative of the nudged elastic band force, enabling a full Newton–Raphson optimization. For molecular systems, the components of the step belonging to translations and rotations are removed with an efficient algorithm. Minimization of the NEB force is ensured by reversing components for which the Newton–Raphson step would increase the force. We achieve quadratic convergence of this optimizer when applied to simple test cases where analytic Hessians are available: one analytic two-dimensional potential and a system of Lennard-Jones particles.