Enhanced climbing image nudged elastic band method with Hessian eigenmode alignment

Accurate determination of the transition states is central to an understanding of reaction kinetics. Double-endpoint methods where both the initial and final states are specified, such as the climbing image nudged elastic band (CI-NEB), identify the minimum energy path between the two and thereby the saddle point on the energy surface that is relevant for the given transition, thus providing an estimate of the transition state within the harmonic transition state theory. Such calculations can, however, incur high computational costs and may suffer stagnation on exceptionally flat or rough energy surfaces. Conversely, methods that only require the specification of an initial set of atomic coordinates, such as the minimum mode following (MMF) method, offer efficiency but can converge on saddle points that are not relevant for the transition of interest. Here, we present an adaptive hybrid algorithm that switches between the CI-NEB and the MMF methods so as to achieve faster convergence to the relevant saddle point. The method is benchmarked On for the Baker-Chan (BC) saddle point test set using the PET-MAD machine-learned potential, along with 59 transitions of a heptamer island on Pt (111) from the OptBench set. A Bayesian analysis of the performance shows a median reduction of energy and force calculations by 57% [95% CrI: 64%, -50%] relative to CI-NEB for the BC set, while a 31% reduction is found for the transitions of the heptamer island. Calculations of the BC set, where a simple switch from the CI-NEB to the MMF method is made when the magnitude of the atomic forces decreases below 0.5 eV/Å, requires 46% more force calculations than the OCI-NEB algorithm. These results show that an adaptive hybrid method mixing CI-NEB and MMF can be a highly efficient tool for high-throughput automated chemical discovery of atomic rearrangements.