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| Nudged Elastic Band | |
|---|---|
| Name | Nudged Elastic Band |
| Type | Computational method |
| Field | Physical chemistry, Materials science, Computational chemistry |
| Introduced | 1990s |
| Developer | Henrik Jónsson, G. Mills, K. J. Richardson |
| Related | Transition state theory, Molecular dynamics, Density functional theory |
Nudged Elastic Band
The Nudged Elastic Band (NEB) method is a computational technique for finding minimum energy paths between known initial and final states in multidimensional potential energy landscapes, widely used in Physical chemistry, Materials science, and Surface science. It constructs a discrete chain of images connecting endpoints and optimizes them to reveal saddle points and reaction pathways, complementing Transition state theory and aiding studies involving Density functional theory and Molecular dynamics. NEB links to practical workflows in software developed by groups at institutions such as Argonne National Laboratory, Lawrence Berkeley National Laboratory, and universities including University of Iceland.
NEB addresses the problem of locating transition states along reaction coordinates between specified endpoints in complex potential surfaces encountered in Computational chemistry and Materials science. The method builds on earlier concepts from Transition state theory, Reaction rate theory, and string methods used in Statistical mechanics and Chemical kinetics. NEB produces a discretized path of "images" that are optimized under forces derived from the system's potential and spring terms, enabling connection to techniques like Maximum likelihood estimation in parameter spaces of models used by research groups at NASA Ames Research Center and Oak Ridge National Laboratory.
The theoretical foundation combines variational principles from Classical mechanics with constrained optimization as used in algorithms pioneered by researchers at Sandia National Laboratories and in the context of Quantum chemistry calculations at institutions like California Institute of Technology. Each image in the chain experiences the true force projected perpendicular to the local path tangent and artificial spring forces along the tangent, reducing corner cutting and kinks. The approach complements Eigenvalue following and the dimer method for saddle point localization developed by researchers affiliated with ETH Zurich and Université de Genève. NEB supports incorporation into Density functional theory codes originating from groups at Cornell University and Princeton University.
Multiple variants extend the original formulation by G. Mills, Henrik Jónsson, and K. J. Richardson, inspired by algorithms from Numerical analysis and optimization research at Stanford University and Massachusetts Institute of Technology. Examples include the climbing image NEB (CI-NEB) which converges an image to the saddle by inverting parallel force components, parallels to developments in the String method by teams at Los Alamos National Laboratory and CEA Saclay. Adaptive spring constants, improved tangent definitions, and incorporation of quasi-Newton optimizers connect to methods from SIAM communities and optimization packages used at University of Cambridge. Hybridizations with the dimer method and constrained minimization link to work at Max Planck Society institutes.
NEB implementations are available in major electronic structure packages and molecular dynamics engines developed at institutions such as Oak Ridge National Laboratory, Argonne National Laboratory, Lawrence Livermore National Laboratory, Fritz Haber Institute, and research groups at University of California, Berkeley. Practical considerations include choice of image count, spring constants, and convergence criteria, as well as integration with force evaluations from Density functional theory and empirical potentials used by teams at Sandia National Laboratories and Los Alamos National Laboratory. Parallelization strategies draw on techniques from high-performance computing centers including National Energy Research Scientific Computing Center and Argonne Leadership Computing Facility, while preconditioning and Hessian approximations benefit from work at Imperial College London and École Polytechnique Fédérale de Lausanne.
NEB has been applied to chemical reactions studied at Harvard University and Yale University, diffusion processes in materials researched at MIT and Northwestern University, defect migration in semiconductors of interest to Intel Corporation and IBM research labs, and catalytic surface reactions investigated at California Institute of Technology and Scripps Research. It supports modeling of battery materials explored by Toyota Research Institute and Toyota Motor Corporation, phase transitions relevant to Max Planck Institute for Iron Research, and protein conformational changes studied at Stanford University and Rockefeller University. NEB-derived barriers inform microkinetic models used by teams at University of Chicago and Columbia University.
Challenges include high-dimensional scaling that burdens resources at supercomputing centers such as Oak Ridge National Laboratory and sensitivity to endpoint selection as noted by researchers at University of Oxford and University of Groningen. The method may miss multiple competing pathways studied in Chemical physics and requires careful selection of images and optimization parameters as emphasized by groups at University of Tokyo and Seoul National University. Combining NEB with enhanced sampling techniques developed at Princeton University and University of Illinois Urbana-Champaign can mitigate sampling limitations, while integration with machine-learned potentials from teams at Google DeepMind and Flatiron Institute is an active area.
NEB evolved from earlier chain-of-states and elastic band ideas formalized by G. Mills, Henrik Jónsson, and K. J. Richardson in the 1990s, with climbing image and related variants developed through collaborations among researchers at University of Iceland, Sandia National Laboratories, and Pacific Northwest National Laboratory. Foundational concepts tie to Transition state theory work by figures associated with University of Cambridge and Princeton University, and continuous method analogues like the string method were advanced at Los Alamos National Laboratory and CEA Saclay. Key software implementations have been produced by teams at Argonne National Laboratory, Lawrence Berkeley National Laboratory, and Oak Ridge National Laboratory, and subsequent methodological refinements continue in groups across North America, Europe, and Asia.
Category:Computational chemistry methods