Nudged Elastic Band
The nudged elastic band (NEB) method finds a minimum energy path between a known initial and final state by relaxing a chain of intermediate images connected by springs, keeping only the force components perpendicular to the path (plus the spring force along it). With the climbing image variant, the highest image is driven to the saddle point, giving the transition state and activation energy. Each NEB requires many force evaluations on every image, so with DFT it is among the most expensive routine calculations in computational catalysis, which motivates surrogate and machine-learned accelerations.
NEB and dimer implementations in ASE (2017)
The ASE review describes its NEB module, which applies spring and tangent-projected forces on top of any ASE optimizer and calculator, illustrated with Au diffusion on Al(001) (Hjorth Larsen et al. 2017). Extensions include climbing image, initial paths from the image dependent pair potential (IDPP), NEB-TR to remove overall rotation and translation for nanoparticles, and AutoNEB, which adds images dynamically where gaps or energy slopes are largest and was reported to reduce cost by 50 to 70% relative to standard NEB in benchmarks. A dimer method implementation finds saddle points starting from a single minimum. Summary: hjorthlarsen2017.
Neural network ensemble surrogates for climbing-image NEB (2021)
Yang, Jiménez-Negrón and Kitchin used an ensemble of 10 SingleNN networks as an active learning surrogate, sending a configuration to the reference calculator only when the ensemble energy variance exceeded a multiple of the largest training set variance. In two climbing-image NEB tests, Pt heptamer rearrangement on Pt(111) with EMT and acetylene hydrogenation on Pd(111) with DFT, the transition states matched the reference with activation energy errors of 6 meV and 4 meV while using 9 instead of 596 EMT calls and 30 instead of 1109 VASP calls. Because convergence was checked only on the highest energy image, intermediate image energies along the DFT band did not all match the reference (Yang et al. 2021). Summary: yang2021.
Alchemical barrier predictions from a single reference NEB (2021)
Griego, Kitchin and Keith applied first-order alchemical perturbation DFT image by image to a single DFT NEB for CH4* dehydrogenation to CH3* + H* on Pt(111), generating reaction energy profiles for 32 hypothetical Pt-Au and Pt-Ir alloys without new NEB calculations. Au substitution generally raised the barrier and Ir lowered it. The largest barrier errors against single-point DFT were about 0.3 eV, for the cases with the largest alchemical derivatives, with most predictions more accurate, which the authors consider good enough to guide screening of which barriers merit full calculations (Griego et al. 2020). Summary: griego2021.
Zero-shot NEBs with pretrained Open Catalyst potentials (2025)
Wander, Shuaibi, Kitchin, Ulissi and Zitnick introduced CatTSunami, a high-throughput framework that enumerates adsorbate placements, builds initial and final frames with an ML potential, and runs NEBs with graph neural network potentials pretrained only on OC20 relaxations. On their OC20NEB benchmark of 932 RPBE DFT NEBs (desorptions, dissociations and transfers), the 153M EquiformerV2 model found activation energies within 0.1 eV of DFT for 98.8%, 89.9% and 83.8% of the three classes when end states were DFT relaxed and the transition state energy was a DFT single point, with about a 28x speedup. Schemes ranged from all-ML (about 2200x faster, 70% success) to an ML pre-relaxed band finished with DFT (about 3x, DFT accuracy, and occasionally lower barriers than pure DFT NEBs) (Wander et al. 2025). Summary: wander2025a.
Hessian-based refinement of ML-NEB transition states (2025)
Refining CatTSunami ML-NEB transition states with the Sella saddle point optimizer, using an EquiformerV2 Hessian recomputed at each step, raised the converged fraction on OC20NEB from 80.2% to 93.0% (65% fewer unconverged cases) with a small rise in energy MAE (0.069 versus 0.060 eV). Keeping only cases where both NEB and Sella converged gave 0.041 eV MAE and 95.2% success at the cost of coverage (Wander et al. 2025). Summary: wander2025.
Bonds-Aware Sella and fine-tuned potentials for saddle searches (2026)
Cheula, Andersen and Kitchin benchmarked single-ended alternatives to NEB on 250 reverse water-gas shift transition states on metal and single-atom alloy surfaces, using universal potentials for the force calls (Cheula et al. 2026). They introduced Bonds-Aware Sella, which lowers the approximate Hessian curvature along the expected bond-forming and bond-breaking direction whenever the lowest eigenmode drifts away from it. With eSEN-OAM it found the intended transition state in 88% of cases versus about 80% for Sella, 74% for Dimer and 68% for ARPESS, and about 97% with up to 20 stochastic restarts. Pre-refining guesses with NEB helped little, since only about 70% of NEBs converged within 500 steps, and the original DFT NEBs had cost roughly 2000 single points per transition state. Summary: cheula2026.