Nudged Elastic Band Calculations Accelerated with Gaussian Process Regression Based on Inverse Interatomic Distances

Abstract

Calculations of minimum energy paths for atomic rearrangements using the nudged elastic band method can be accelerated with Gaussian process regression to reduce the number of energy and atomic force evaluations needed for convergence. Problems can arise, however, when configurations with large forces due to short distance between atoms are included in the data set. Here, a significant improvement to the Gaussian process regression approach is obtained by basing the difference measure between two atomic configurations in the covariance function on the inverted interatomic distances and by adding a new early stopping criterion for the path relaxation phase. This greatly improves the performance of the method in two applications where the original formulation does not work well: a dissociative adsorption of an H 2 molecule on a Cu(110) surface and a diffusion hop of an H 2 O molecule on an ice Ih(0001) surface. Also, the revised method works better in the previously analyzed benchmark application to rearrangement transitions of a heptamer island on a surface, requiring fewer energy and force evaluations for convergence to the minimum energy path.

Automatic discovery of chemical reactions using imposed activation

“…70 Efforts are ongoing in this direction. Additionally, we are currently investigating the use of machine learning methods (such as Gaussian process regression 29,71,72 ) to systematically and robustly refine the transition state guesses obtained using semi-empirical calculations at higher levels of theory.…”

Restricted-Variance Constrained, Reaction Path, and Transition State Molecular Optimizations Using Gradient-Enhanced Kriging

“…Recently an alternative surrogate model -the Kriging model, 15,16 in particular the gradient-enhanced Kriging (GEK) [17][18][19] -has been proposed and explored by a number of research groups for geometry optimizations of equilibrium and transition state structures, and explorations of reactions paths. [20][21][22][23][24][25][26][27][28] These studies have demonstrated the potential of the Kriging procedure as a competitive alternative to the standard. However, these studies have also shown that in order to excel, as compared with commonly used algorithms, a GEK-based method should be based on internal coordinates, 27 but also be able to make use of the empirical and practical knowledge accumulated through decades of use and improvement of second-order methods.…”

“…For the case of constrained optimization in combination with GPR we would like to mention four studies on the use of the nudged elastic band method. 20,24,25,41 In all studies the use of GPR significantly reduced the number of evaluations of the energy and gradient of the parent model. It is also worth to mention that Koistinen and co-workers 41 mention the use of the variance to identify parts of the reaction path which might need further improvement.…”

Active Learning Accelerates Ab Initio Molecular Dynamics on Pericyclic Reactive Energy Surfaces

“…36,37 Particularly in the area of surface catalysis and solid-state diffusion, ML approaches have been proposed to accelerate the location of transition states and exploration of minimum energy paths. [38][39][40] Similarly, high-throughput simulation approaches that have been typically aimed at static properties of single organic molecules [41][42][43][44] are increasingly targeting reactivity. [45][46][47][48][49] Here, we demonstrate the combined application of high-throughput (HT) simulation and ML interatomic potentials to study a complex reactive system dominated by dynamical effects.…”