Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points

@article{Henkelman2000ImprovedTE,
  title={Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points},
  author={Graeme A Henkelman and Hannes J{\'o}nsson},
  journal={Journal of Chemical Physics},
  year={2000},
  volume={113},
  pages={9978-9985}
}
An improved way of estimating the local tangent in the nudged elastic band method for finding minimum energy paths is presented. In systems where the force along the minimum energy path is large compared to the restoring force perpendicular to the path and when many images of the system are included in the elastic band, kinks can develop and prevent the band from converging to the minimum energy path. We show how the kinks arise and present an improved way of estimating the local tangent which… 

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References

SHOWING 1-10 OF 33 REFERENCES

A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives

The problem of determining which activated (and slow) transitions can occur from a given initial state at a finite temperature is addressed. In the harmonic approximation to transition state theory

Location of Energy Barriers. I. Effect on the Dynamics of Reactions A + BC

The dynamics of exchange reactions A+BC→AB+C have been examined on two types of potential‐energy hypersurfaces that differed in the location of the energy barrier along the reaction coordinate. On

Shadowing, rare events, and rubber bands. A variational Verlet algorithm for molecular dynamics

We present a variational implementation of the Verlet algorithm for molecular dynamics which is both conceptually and computationally attractive. Given an approximate path, this variational Verlet

Atomistic Determination of Cross-Slip Pathway and Energetics

The mechanism for cross slip of a screw dislocation in Cu is determined by atomistic simulations that only presume the initial and final states of the process. The dissociated dislocation constricts

Self-Consistent Equations Including Exchange and Correlation Effects

From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high

Density Functional Theory of Electronic Structure

Density functional theory (DFT) is a (in principle exact) theory of electronic structure, based on the electron density distribution n(r), instead of the many-electron wave function Ψ(r1,r2,r3,...).

Soft self-consistent pseudopotentials in a generalized eigenvalue formalism.

  • Vanderbilt
  • Physics
    Physical review. B, Condensed matter
  • 1990
Novel features are that the pseudopotential itself becomes charge-state dependent, the usual norm-conservation constraint does not apply, and a generalized eigenproblem is introduced.