Reorienting off-path Nudged Elastic Bands (RONEB) via Minimum Mode Following

TL;DR

RONEB introduces an adaptive hybrid between Nudged Elastic Band and Minimum Mode Following to accelerate and stabilize transition-state searches. By dynamically triggering local MMF refinement based on mode alignment and maintaining robustness through stability latches and restoration, the method reduces gradient evaluations while preserving accuracy. Benchmarking on Baker-Chan transitions with a PET-MAD interatomic potential and on Pt(111) surface diffusion demonstrates substantial speedups (approximately 46% overall) and reliable saddle-point identification. This approach enables efficient, high-throughput TS discovery on complex PESs, including those described by machine-learned potentials, and offers practical guidelines for parameter choices in blind searches.

Abstract

Accurate determination of transition states remains central to understanding reaction kinetics. Double-ended methods like the Nudged Elastic Band (NEB) ensure relevant transition states and paths, but incur high computational costs and suffer stagnation on flat or rough potential energy surfaces. Conversely, single-ended eigenmode-following techniques offer efficiency but cannot often be constrained between specific states. Here, we present the Reorienting Off-path Nudged Elastic Bands (RONEB), an adaptive hybrid algorithm that integrates the double ended nature of the NEB with the acceleration of single ended Min-Mode Following methods. RONEB provides stability based on the history of the path optimization, relative force triggering, and an alignment-based back-off penalty to dynamically decouple the climbing image from the elastic band constraints. We benchmark the method against the standard Climbing Image NEB (CI-NEB) across the Baker-Chan transition state test set using the PET-MAD machine-learned potential and the OptBench Pt(111) heptamer island surface diffusion set. A Bayesian analysis of the performance data quantifies a median reduction in gradient calls of 46.3% [95% CrI: -54.7%, -36.9%] relative to the baseline, while surface diffusion tests reveal a 28% reduction across 59 metallic rearrangement mechanisms. These results establish RONEB as a highly effective tool for high-throughput automated chemical discovery.

Figures (11)

• Figure 1: Comparative computational cost for the test set of transition configurationsbakerLocationTransitionStates1996. The "dumbbell" spans illustrate the reduction in gradient evaluations (left) and wall-clock time (right) achieved by RONEB (teal) relative to CINEB (coral).
• Figure 2: Algorithmic robustness profile modeled via Bayesian negative binomial regression. The plot tracks the predicted computational cost (gradient calls, log scale) as a function of the initial structural displacement from the final transition state. Shaded regions indicate 95% credible intervals. Both methods show a log-linear rise in cost with distance, but RONEB (teal) maintains a consistent efficiency advantage over CINEB (coral), demonstrating that the local MMF acceleration effectively lowers the computational overhead across the search space.
• Figure 3: Dataset Characterization and Drivers of Cost. (A) Distribution of barrier heights in the test set. (B) Accuracy of RONEB compared to CINEB saddle points; the density peaks below 0.1 Å, confirming correct convergence. (C) Scatter plot of Computational Cost vs. Barrier Height. The lack of a strong trend contrasts with the clear scaling seen in Figure \ref{['fig:brms_pes']}, indicating that initial structural guess quality drives cost more than the energetics of the reaction.
• Figure 4: Saddle Point Equivalence on the Flat HNCCS Landscape.(A) A 2D projection of the potential energy surface. We utilize the denser CINEB trajectory points to generate the background contour, visualizing the extended ridge connecting the reactant and product basins goswamiTwodimensionalRMSDProjections2025. The white square denotes the CINEB saddle, while the blue star indicates the RONEB result. (B) The baseline CINEB struggles to resolve regions of vanishing gradients, requiring nearly 4000 evaluations. (C) RONEB snaps to the saddle region early, terminating on the same energy isocontour with reduced computational effort.
• Figure 5: Ablation study for HCONH3+ fragmentation.(A) A 2D projection of the potential energy surface illustrates the path evolution goswamiTwodimensionalRMSDProjections2025, confirming the numerical equivalence of the converged saddle points. (B-C) Convergence histories for the RONEB protocols. The aggressive configuration (B) initiates premature convergence, resulting in path oscillations. Conversely, the strict protocol (C) stabilizes the search by enforcing rigorous alignment tolerances.