What is it about?
Transition states, the high-energy bottlenecks between chemical configurations, decide how fast reactions go. Two families of methods dominate the calculation. The climbing image nudged elastic band (CI-NEB) starts from two known endpoints and identifies the minimum energy path between them. The minimum mode following (MMF) method starts from a single geometry and walks uphill along the softest curvature direction. CI-NEB is reliable but expensive. MMF is cheap but can drift off onto saddle points that have nothing to do with the transition of interest. We built an adaptive hybrid that runs CI-NEB until the climbing image has locked onto the right basin, then hands off to MMF to walk the rest of the way to the saddle. On the Baker-Chan benchmark with the PET-MAD machine-learned potential, the hybrid cuts energy and force calculations by a median of 57 percent (95 percent credible interval: 50 to 64 percent) relative to CI-NEB. On 59 heptamer island transitions on Pt(111), the reduction is 31 percent. A naive switch at a fixed force cutoff of 0.5 eV per angstrom costs 46 percent more force evaluations than the adaptive version.
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Why is it important?
High-throughput catalysis and materials screening need many saddle searches per run. A method that halves force evaluations at the saddle stage compounds across thousands of transitions. The hybrid also inherits the reliability of CI-NEB without paying the full CI-NEB convergence cost: the climbing image still determines which saddle is relevant. The adaptive switching criterion, rather than a hand-tuned force threshold, is the piece that matters. Every system has its own scale for when CI-NEB has done its job and MMF can take over. The Bayesian analysis in the paper shows the adaptive criterion dominates fixed thresholds across both test sets, and the posterior rules out a lucky-sample explanation.
Perspectives
Saddle searches were the slow step in every project I ran. CI-NEB is my default because it finds the right saddle, but the final climb to the peak is almost always the most expensive stage. MMF should in principle finish faster from a nearby geometry, yet it only works if you are already in the right basin. The obvious answer was to use each method where it is strong and hand off between them. The harder question was when. The adaptive criterion grew out of watching how the CI-NEB force profile evolves. By the time the climbing image is within a short distance of the saddle, MMF can walk in from there for a fraction of the cost. The Bayesian analysis was essential: with 46 BC transitions and 59 heptamer transitions, a mean comparison would have been misleading. The posterior shows the gain is real, not a lucky sample. If you run high-throughput transition searches with an ML potential, this hybrid should drop into your pipeline without retuning.
Rohit Goswami
University of Iceland
Read the Original
This page is a summary of: Enhanced climbing image nudged elastic band method with Hessian eigenmode alignment, Frontiers in Chemistry, May 2026, Frontiers,
DOI: 10.3389/fchem.2026.1807063.
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