Protocol for Directing Nudged Elastic Band Calculations to the Minimum Energy Pathway: Nurturing Errant Calculations Back to Convergence.

Abstract

The combination of density functional theory (DFT) and the nudged elastic band (NEB) method offers a practical tool for the discovery of underlying reaction mechanisms related to the synthesis of functional materials. However, in practice, the lack of a standardized protocol for minimum energy pathway determination too often leads to an inefficient and computationally intensive design process. To that end, we define a verifiable DFT+NEB protocol for efficiently locating and confirming the transition state of a reaction. To test this assertion, we curate 226 unique reactions within 14 classes of reactions and investigate their performance in terms of the number of NEB iterations they require to locate the transition state and an estimate of the associated mean absolute error. Leveraging this protocol, we demonstrate its application for an initial set of parameters: number of frames, Nframes = 11; maximum step size, Smax = 0.04 Å; optimizer = LBFGS; and spring constant, kspr = 0.1 eV/Å2. We report a convergence rate of 73% and find that a root-mean-square force (FRMS) of 0.01 eV/Å provides a "rule of thumb" below which NEB simulations are likely to converge. Venturing beyond this baseline enquiry, we delineate the effect on performance of altering the number of frames, maximum step size, choice of optimizer and spring constant. We find improvements in performance with increasing Nframes and Smax, ostensibly approaching some asymptotic limit. We also see substantial improvement in efficiency with the LBFGS optimizer and a clear minimum in performance for the spring constant value of 0.1 eV/Å2. Finally, we provide five case studies that demonstrate typical convergence issues for NEB simulations and suggest methods to overcome them. Our results provide specific and transferable recommendations, offering a transparent and practical tool for beginner and expert researchers alike toward a more rational NEB simulation design.