Adaptive nudged elastic band approach for transition state calculation

Abstract

The wetting behavior of a liquid on solid substrates is governed by the nature of the effective interaction between the liquid-gas and the solid-liquid interfaces, which is described by the binding or wetting potential g(h) which is an excess free energy per unit area that depends on the liquid film height h. Given a microscopic theory for the liquid, to determine g(h) one must calculate the free energy for liquid films of any given value of h; i.e. one needs to create and analyse out-of-equilibrium states, since at equilibrium there is a unique value of h, specified by the temperature and chemical potential of the surrounding gas. Here we introduce a Nudged Elastic Band (NEB) approach to calculate g(h) and illustrate the method by applying it in conjunction with a microscopic lattice density functional theory for the liquid. We show too that the NEB results are identical to those obtained with an established method based on using a fictitious additional potential to stabilize the non-equilibrium states. The advantages of the NEB approach are discussed.

A doubly nudged elastic band method for finding transition states

“…We were able to obtain stable convergence in NEB/L-BFGS calculations only for simple rearrangements, which confirms that straightforward L-BFGS optimisation of the NEB is unstable [79]. Figure 5 By experimentation we have found that the main source of the instabilities is the complete removal of g ⊥ .…”

“…The NEB/QVV approach has previously been systematically tested on systems with around 100 degrees of freedom, η [79]. However, in the majority of cases these test systems could be divided into a 'core' and a smaller part that actually changes significantly.…”

“…For more complex processes an alternative approach adopted in previous work is simply to supply a better initial guess 'by hand', e.g. construct it from the images with unrelaxed geometries containing no atom overlaps [79]. The 'detour' algorithm described in previous calculations that employ the ridge method could also be used to avoid 'atom-crashing' in the initial interpolation [62].…”

“…In contrast, linear interpolation between the endpoints was found to provide a useful initial guess for a number of simpler cases [71]. For example, it was successfully used to construct the NEB for rearrangements that involve one or two atoms following approximately rectilinear trajectories, and for migration of a single atom on a surface [79]. For more complex processes an alternative approach adopted in previous work is simply to supply a better initial guess 'by hand', e.g.…”

“…They report that use of powerful minimisation methods in conjunction with NEB approach was unsuccessful [79]. These problems were attributed to instabilities with respect to the extra parameters introduced by the springs.…”