Nudged Elastic Band

The nudged elastic band (NEB) is a method for finding saddle points and minimum energy paths between known reactants and products. The method works by optimizing a number of intermediate images along the reaction path. Each image finds the lowest energy possible while maintaining equal spacing to neighboring images. This constrained optimization is done by adding spring forces along the band between images and by projecting out the component of the force due to the potential perpendicular to the band.

Details may be found in Jonsson et al. [NEB_JMJ98], Sheppard and Henkelman [NEB_SH11], and Ásgeirsson and Jónsson [NEB_AsgeirssonJonsson18].

In order to run a nudged elastic band calculation, set job to nudged_elastic_band in the [Main] section. Details of the optimizer can be set as per the Optimizer document.

Tip

Python API. Prefer pyeonclient (Python client API) for in-process NEB: build a list[Matter] from ASE images, then NudgedElasticBand(path, params, pot).compute() — same shape as ASE’s NEB + LBFGS, without a workdir.

For a full walkthrough (ASE NEB vs eOn energy-weighted springs + OCI dimer), see the atomistic-cookbook PET-MAD example.

For a built-in Morse Pt NEB with current rgpycrumbs eon plt-neb 1D/2D figures (full history, 1:1 reaction-valley panel, structure strip), see Morse Pt NEB (built-in potential).

Variants

Added in version 2.0:

Note

eOn, like many other codes after Sheppard et al. [NEB_STH08] uses one optimizer instance for moving the whole band of images.

Added in version 2.8: Via the surrogate potential interface, a native C++ implementation of the Gaussian Process accelerated NEB first described in Koistinen et al. [NEB_KDagbjartsdottirAsgeirsson+17] and Koistinen et al. [NEB_KAsgeirssonVJonsson19].

Added in version 2.12:

  • Onsager-Machlup action-based NEB for minimum action paths.

  • OCINEB (Off-Path Climbing Image NEB) Goswami et al. [NEB_GGJonsson26]: hybrid CI-NEB + Min-Mode Following with hessian eigenmode alignment for automated saddle point refinement.

  • Parallel image force evaluation (requires TBB, -Dwith_parallel_neb=true).

  • IDPP (Image Dependent Pair Potential) path initialization.

  • Modular strategy pattern for tangent, projection, and spring force components.

Onsager-Machlup NEB

The Onsager-Machlup variant replaces the standard spring force with an action-based spring that adapts per-image based on the local force magnitude. Enable with onsager_machlup = true in the NEB section.

OCINEB (hybrid dimer refinement)

OCINEB Goswami et al. [NEB_GGJonsson26] activates a Min-Mode Following (dimer) search on the climbing image after it stabilizes, using hessian eigenmode alignment to refine the saddle point to higher accuracy without additional NEB iterations. Enable with ci_mmf = true.

Parallel evaluation

When compiled with TBB support (-Dwith_parallel_neb=true), image forces are evaluated in parallel. Python-based potentials automatically fall back to serial evaluation.

Configuration

The NEB section can be specified in config.ini:

[Nudged Elastic Band]
images = 7
converged_force = 0.01
climbing_image_method = true

Or programmatically via rgpycrumbs:

from rgpycrumbs.eon.helpers import write_eon_config

config = {
    "Main": {"job": "nudged_elastic_band"},
    "Nudged Elastic Band": {
        "images": 7,
        "converged_force": 0.01,
        "climbing_image_method": True,
    },
}
write_eon_config(config, Path("config.ini"))

See Dictionary-Style Configuration for the full programmatic workflow.

[Nudged Elastic Band]

Outputs

NEB writes the usual results.dat, neb.dat, and the final band neb.con.

With write_movies = true in [Debug], eOn also writes per-iteration neb_path_*.con movie files and neb_maximage.con. These .con outputs now embed structured frame metadata via readcon-core, including fields such as energy, frame_index, neb_bead, optional neb_band, reaction_coordinate, relative_energy, and parallel_force.

The existing neb.dat and neb_*.dat outputs are still written and remain the primary compatibility path for current plotting tools.

Refinement

Added in version 2.0.

Far from the minimum energy path, second order optimizers like those using the LBFGS may not be optimal. In these situations, to traverse uninteresting sections of the potential energy surface rapidly, it is best to use an accelerating optimizer like QuickMin to begin with and transition to LBFGS later. To facilitate this, the [Refine] section has been introduced.

References

[NEB_GGJonsson26] (1,2)

Rohit Goswami, Miha Gunde, and Hannes Jónsson. Enhanced climbing image nudged elastic band method with hessian eigenmode alignment. January 2026. arXiv:2601.12630, doi:10.48550/arXiv.2601.12630.

[NEB_HJonsson00]

Graeme Henkelman and Hannes Jónsson. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. The Journal of Chemical Physics, 113(22):9978–9985, December 2000. doi:10.1063/1.1323224.

[NEB_HUJonsson00]

Graeme Henkelman, Blas P. Uberuaga, and Hannes Jónsson. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. The Journal of Chemical Physics, 113(22):9901–9904, November 2000. doi:10.1063/1.1329672.

[NEB_JMJ98]

Hannes Jonsson, Greg Mills, and Karsten W. Jacobsen. Nudged elastic band method for finding minimum energy paths of transitions. In Classical and Quantum Dynamics in Condensed Phase Simulations, pages 385–404. World Scientific, June 1998. doi:10.1142/9789812839664_0016.

[NEB_KDagbjartsdottirAsgeirsson+17]

Olli-Pekka Koistinen, Freyja B. Dagbjartsdóttir, Vilhjálmur Ásgeirsson, Aki Vehtari, and Hannes Jónsson. Nudged elastic band calculations accelerated with Gaussian process regression. The Journal of Chemical Physics, 147(15):152720, September 2017. doi:10.1063/1.4986787.

[NEB_KAsgeirssonVJonsson19]

Olli-Pekka Koistinen, Vilhjálmur Ásgeirsson, Aki Vehtari, and Hannes Jónsson. Nudged Elastic Band Calculations Accelerated with Gaussian Process Regression Based on Inverse Interatomic Distances. Journal of Chemical Theory and Computation, 15(12):6738–6751, December 2019. doi:10.1021/acs.jctc.9b00692.

[NEB_MJonsson94]

Greg Mills and Hannes Jónsson. Quantum and thermal effects in H 2 dissociative adsorption: Evaluation of free energy barriers in multidimensional quantum systems. Physical Review Letters, 72(7):1124–1127, February 1994. doi:10.1103/PhysRevLett.72.1124.

[NEB_SMJonsson94]

Gregory K. Schenter, Gregory Mills, and Hannes Jónsson. Reversible work based quantum transition state theory. The Journal of Chemical Physics, 101(10):8964–8971, November 1994. doi:10.1063/1.468447.

[NEB_SH11]

Daniel Sheppard and Graeme Henkelman. Paths to which the nudged elastic band converges. Journal of Computational Chemistry, 32(8):1769–1771, 2011. doi:10.1002/jcc.21748.

[NEB_STH08]

Daniel Sheppard, Rye Terrell, and Graeme Henkelman. Optimization methods for finding minimum energy paths. The Journal of Chemical Physics, 128(13):134106, April 2008. doi:10.1063/1.2841941.

[NEB_TW04]

Semen A. Trygubenko and David J. Wales. A doubly nudged elastic band method for finding transition states. The Journal of Chemical Physics, 120(5):2082–2094, February 2004. doi:10.1063/1.1636455.

[NEB_AsgeirssonBB+21]

Vilhjálmur Ásgeirsson, Benedikt Orri Birgisson, Ragnar Bjornsson, Ute Becker, Frank Neese, Christoph Riplinger, and Hannes Jónsson. Nudged Elastic Band Method for Molecular Reactions Using Energy-Weighted Springs Combined with Eigenvector Following. Journal of Chemical Theory and Computation, 17(8):4929–4945, August 2021. doi:10.1021/acs.jctc.1c00462.

[NEB_AsgeirssonJonsson18]

Vilhjálmur Ásgeirsson and Hannes Jónsson. Exploring Potential Energy Surfaces with Saddle Point Searches. In Wanda Andreoni and Sidney Yip, editors, Handbook of Materials Modeling, pages 1–26. Springer International Publishing, Cham, 2018. doi:10.1007/978-3-319-42913-7_28-1.