Nudged elastic band method

The nudged elastic band method is designed to improve upon the elastic band method. This method is best introduced by considering how a set of images can be adjusted to move them toward the MEP. For each image, we can use DFT to compute the force acting on the system, F, = VE(r,-). From the cur- 

This definition is appropriate for using the elastic band method. 

If all the images in the calculation lie on an MEP, then this update force is zero for every image and the calculation has converged. 

The mathematical definition of the NEB method is important, but the main features of this method can be stated without these details. These include  

The aim of an NEB calculation is to define a series of atomic coordinates (images) that define an MEP connecting two minima on the energy surface. 

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Figure 9.11 Several minimum energy paths for O2 dissociation on PtsCo) 11) (labeled by respective initial states), generating ML of atomic O, compared with equilibrium and 2% compressed Pt(lll). The points on each path are the images or states used to discretize the path with the climbing-image nudged elastic band method. The zero of the energy axis corresponds to an O2 molecule and the respective clean surfaces at infinite separation. The points located on the right vertical axis represent atomic O at ML. (Reproduced with permission from Xu et al. [2004].)...

Henkelman G, Jdnsson H. 2000. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J Chem Phys 113 9978-9985. 

Henkelman G, Uberuaga BP, Jonsson H. 2000. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J Chem Phys 113 9901-9904. 

Jonsson H, Mills G, Jacobsen K (1998) In Berne BJ, Ciccotti G, Coker DF (eds) Nudged Elastic Band Method , in Classical and quantum dynamics in condensed phase simulations, World Scientific, Singapore, pp 387 101... 

H. Jonsson, G. Mills and K. W. Jaeobsen, Nudged Elastic Band Method for Finding Minimum Energy Paths of Transitions , in Classical and Quantum Dynamics in Condensed Phase Simulations , ed. B. J. Berne. G. Ciccotti andD. F. Coker, page 385 (World Scientific, 1998). 

Figure 2 The Climbing Image Nudged Elastic Band method, CI-NEB. An elastic band is...

To estimate the activation energy (Efor the given reagents and products, one can use methods for searching of saddle points for given stationary points, such as the nudged elastic band method (NEB) [83],... 

The calculation of the thermal stability requires the estimation of transition rates between stable equilibrium states of the magnet. The calculation of transition rates needs a detailed characterization of the energy landscape along the most probable path which is taken by the system from its initial state to a final state. Henkelman and Jonsson [20] proposed the nudged elastic band method to calculate minimum energy paths. Starting from an... 

String Methods. - A recently proposed approach that is closely related to the nudged elastic-band method of the preceding section is the string method of E et al.136 (see also 137). We shall here briefly outline the basics of the method and, thereby, also draw the connection to the nudged elastic-band method, following the presentation of Kanai et al.131... 

For the nudged elastic-band method, (b) represents the system images along the path joining initial and final states. Moreover, in that case one seeks only a discrete set of those, i.e., only the structures for a finite, discrete set of b values. 

Alternatively, applying the same steepest-descent approach within the nudged elastic-band method leads to... 

Also Chu et al 34 presented results of an improved version of the nudged elastic-band method. They applied the method on more different systems, including an a-helix to re-helix transition of an alanine decapeptide and the oxidation of dimethyl sulfide. 

Sarkar et al 39 used the nudged elastic-band method in studying the stability of core/shell nanoparticles consisting of a core of one semiconductor covered with a shell of another semiconductor. In this case the two semiconductors were CdS and CdSe, and it was investigated whether processes, where a S and a Se... 

For the first situation, the last decade or so has seen the development of accurate and reliable methods based on chains-of-states methods or extensions hereof (most notably, the nudged elastic-band method). On the other hand, the second situation remains to be a challenge, and also here it shall be remembered... 

Sheppard D, Xiao P, Chemelewski W, Johnson DD, Henkelman G (2012) A generalized solid-state nudged elastic band method. J Chem Phys 136 074103... 

Henkelman G, Jdnsson H (2000) Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J Chem Phys 113 9978-9985 173. E W, Ren W, Vanden Eijnden E (2002) String method for the study of rare events. Phys Rev B 66 052301-1/4... 

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