Nudged-elastic band method with two climbing images: Finding transition states in complex energy landscapes

Abstract

The nudged-elastic band (NEB) method is modified with concomitant two climbing images (C2-NEB) to find a transition state (TS) in complex energy landscapes, such as those with a serpentine minimal energy path (MEP). If a single climbing image (C1-NEB) successfully finds the TS, then C2-NEB finds it too. However, improved stability of C2-NEB makes it suitable for more complex cases, where C1-NEB misses the TS because the MEP and NEB directions near the saddle point are different. Generally, C2-NEB not only finds the TS, but also guarantees, by construction, that the climbing images approach it from the opposite sides along the MEP. In addition, C2-NEB provides an accuracy estimate from the three images: the highestenergy one and its climbing neighbors. C2-NEB is suitable for fixed-cell NEB and the generalized solid-state NEB. KeywordsMaterials Science and Engineering, Density functional theory, Nickel, Shape memory effect, Optimization, Band structure DisciplinesEngineering Physics | Metallurgy The nudged-elastic band (NEB) method is modified with concomitant two climbing images (C2-NEB) to find a transition state (TS) in complex energy landscapes, such as those with a serpentine minimal energy path (MEP). If a single climbing image (C1-NEB) successfully finds the TS, then C2-NEB finds it too. However, improved stability of C2-NEB makes it suitable for more complex cases, where C1-NEB misses the TS because the MEP and NEB directions near the saddle point are different. Generally, C2-NEB not only finds the TS, but also guarantees, by construction, that the climbing images approach it from the opposite sides along the MEP. In addition, C2-NEB provides an accuracy estimate from the three images: the highest-energy one and its climbing neighbors. C2-NEB is suitable for fixed-cell NEB and the generalized solid-state NEB. C 2015 AIP Publishing LLC.[http://dx

Coexistence pressure for a martensitic transformation from theory and experiment: Revisiting the bcc-hcp transition of iron under pressure

“…In addition, we use the generalized solid-state nudged elastic band (GSS-NEB) method 184,185 to find the transformation path at P 0 within the shear-shuffle model, 6 see Fig. 3.…”

Magneto-structural transformations via a solid-state nudged elastic band method: Application to iron under pressure

“…It can safely replace the climbing-image algorithm C1-NEB 32 in all cases, where C1-NEB is applicable, and can be generalized for complex energy landscapes. 28 However, the SSNEB convergence malfunctions if any image gets an excited electronic state with intermediate magnetization (Fig. 6).…”

“…We use the bcc-hcp transition in iron as a prototype for the quantitative description of magnetic systems via the SSNEB method 4 and its modifications. 28 For a magneto-structural transformation, we show that the TS is a cusp on the potential energy surface (PES) and is not a single electronic state, but a duality of a non-magnetic (NM) and magnetic states with the same atomic and cell coordinates, the same enthalpy, but different electronic structure. As a result of the coherency stress between those two electronic states, a pressure discontinuity at the TS exists, which can be related to the experimental scatter in the coexistence pressures of magnetic and non-magnetic phases.…”

“…18 While the pressure-induced bcc-hcp transformation in iron has been extensively studied, its complete theoretical description accounting for all relevant DoF is still needed. Recall that the traditional SSNEB method 4 can search the entire phase space, but requires a continuous and differentiable PES with the TS in the form of a saddle (e.g., as in Li 30 ), which can be addressed by the available codes 31 with one 32 or (more stable) two 28 climbing images, while for a magnetostructural transformation, the TS is a cusp on the PES with a discontinuity of atomic forces and stress components, where a climbing image will not stop. We extend the unrestricted SSNEB formalism (the Appendix) and apply it to the bcc-hcp transformation in iron under pressure.…”

Method for finding mechanism and activation energy of magnetic transitions, applied to skyrmion and antivortex annihilation

“…The nudged elastic band (NEB) method [13,16] and variations thereof [17][18][19][20], are commonly used to find MEPs of transitions involving atomic rearrangements. The method involves specifying a discrete representation of some initial path between the two minima and then using an iterative algorithm to bring the discretization points to the nearest MEP.…”