A climbing image nudged elastic band method for finding saddle points and minimum energy paths

@article{Henkelman2000ACI,
  title={A climbing image nudged elastic band method for finding saddle points and minimum energy paths},
  author={Graeme A Henkelman and Blas Pedro Uberuaga and Hannes J{\'o}nsson},
  journal={Journal of Chemical Physics},
  year={2000},
  volume={113},
  pages={9901-9904}
}
A modification of the nudged elastic band method for finding minimum energy paths is presented. One of the images is made to climb up along the elastic band to converge rigorously on the highest saddle point. Also, variable spring constants are used to increase the density of images near the top of the energy barrier to get an improved estimate of the reaction coordinate near the saddle point. Applications to CH4 dissociative adsorption on Ir~111! and H2 on Si~100! using plane wave based… 

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References

SHOWING 1-10 OF 41 REFERENCES

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

An improved way of estimating the local tangent in the nudged elastic band method for finding minimum energy paths is presented, and examples given where a complementary method, the dimer method, is used to efficiently converge to the saddle point.

Methods for Finding Saddle Points and Minimum Energy Paths

The problem of finding minimum energy paths and, in particular, saddle points on high dimensional potential energy surfaces is discussed. Several different methods are reviewed and their efficiency

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

Transition state theory description of surface self-diffusion: Comparison with classical trajectory results

We have computed the surface self‐diffusion constants on four different crystal faces [fcc(111), fcc(100), bcc(110), and bcc(211)] using classical transition state theory methods. These results can

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