A growing string method for determining transition states: Comparison to the nudged elastic band and string methods

Abstract

Interpolation methods such as the nudged elastic band and string methods are widely used for calculating minimum energy pathways and transition states for chemical reactions. Both methods require an initial guess for the reaction pathway. A poorly chosen initial guess can cause slow convergence, convergence to an incorrect pathway, or even failed electronic structure force calculations along the guessed pathway. This paper presents a growing string method that can find minimum energy pathways and transition states without the requirement of an initial guess for the pathway. The growing string begins as two string fragments, one associated with the reactants and the other with the products. Each string fragment is grown separately until the fragments converge. Once the two fragments join, the full string moves toward the minimum energy pathway according to the algorithm for the string method. This paper compares the growing string method to the string method and to the nudged elastic band method using the alanine dipeptide rearrangement as an example. In this example, for which the linearly interpolated guess is far from the minimum energy pathway, the growing string method finds the saddle point with significantly fewer electronic structure force calculations than the string method or the nudged elastic band method.

Sampling reactive pathways with random walks in chemical space: Applications to molecular dissociation and catalysis

“…18,19 Over the last few decades, a wide variety of computational strategies have been developed specifically with the purpose of determining reaction pathways and the associated energetic barriers. For example, the Nudged Elastic Band (NEB) method 20,21 and related approaches, [22][23][24] the zero-and finite-temperature string (FTS) methods, 25,26 and the growing string approach 27 all aim to search for a reaction path given an initial guess path connecting specified reactant and product configurations; the constraint of generating a good initial guess is removed in methods such as Gradient Extremal Following (GEF), 28,29 Scaled Hypersphere Searching (SHS [30][31][32], and reduced gradient following (RGF). 33 Rather than focussing on the search for single reaction paths, methods such as transition path sampling [34][35][36][37][38][39][40][41][42][43] and Onsager-Machlup path sampling 44,45 can instead generate ensembles of reaction pathways; subsequent analysis of the path ensemble, for example, by calculation of commitor probabilities, allows further identification of important features associated with transition states (TSs).…”

Nonequilibrium ab initio molecular dynamics determination of Ti monovacancy migration rates in B1 TiN

“…Ab initio density functional theory (DFT) calculations combined with the nudged elastic band (NEB) [34,35] or the string method [36,37] are typically employed to estimate minimum energy paths and migration energies at 0 K [38][39][40][41][42][43]. Kinetic properties are extrapolated to finite temperatures using transition state theory (TST) [44] by assuming essentially fully harmonic lattice vibrations, or employing quasiharmonic approximations [45,46].…”

Self-Elongation with Sequential Folding of a Filament of Bacterial Cells

“…Theoretical investigations can be found in the literature [29,30,31,32]. We hope that this experimental evaluations of parameters controlling the folding processes, which are described as l 1 → l 2 , l 2 → l 4 , and l 1 + l 2 → l 3 using our variables, will be useful for testing the validity of a possible theoretical consideration in the future.…”