Computational Implementation of Nudged Elastic Band, Rigid Rotation, and Corresponding Force Optimization.

The nudged elastic band (NEB) algorithm is the leading method of calculating transition states in chemical systems. However, the current literature lacks adequate guidance for users wishing to implement a key part of NEB, namely, the optimization method. Here, we provide details of this implementation for the following six gradient descent algorithms: steepest descent, quick-min Verlet, FIRE, conjugate gradient, Broyden-Fletcher-Goldfarb-Shanno (BFGS), and limited-memory BFGS (LBFGS). We also construct and implement a new, accelerated backtracking line search method in concert with a partial Procrustes superimposition to improve upon existing methods. Validation is achieved through benchmark calculations of two test cases, the isomerization of CNX and BOX (where X ∈ {H, Li, Na}) and the study of a conformational change within an alanine dipeptide. We also make direct comparisons to the well-established codebase known as the atomic simulation environment.