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.
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.
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.