Miha Gunde

Miha Gunde, Nicolas Salles, Anne Hémeryck et al.

We propose a versatile, parameter-less approach for solving the shape matching problem, specifically in the context of atomic structures when atomic assignments are not known a priori. The algorithm Iteratively suggests Rotated atom-centered reference frames and Assignments (Iterative Rotations and Assignments, IRA). The frame for which a permutationally invariant set-set distance, namely the Hausdorff distance, returns minimal value is chosen as the solution of the matching problem. IRA is able to find rigid rotations, reflections, translations, and permutations between structures with different numbers of atoms, for any atomic arrangement and pattern, periodic or not. When distortions are present between the structures, optimal rotation and translation are found by further applying a standard Singular Value Decomposition-based method. To compute the atomic assignments under the one-to-one assignment constraint, we develop our own algorithm, Constrained Shortest Distance Assignments (CShDA). The overall approach is extensively tested on several structures, including distorted structural fragments. Efficiency of the proposed algorithm is shown as a benchmark comparison against two other shape matching algorithms. We discuss the use of our approach for the identification and comparison of structures and structural fragments through two examples: a replica exchange trajectory of a cyanine molecule, in which we show how our approach could aid the exploration of relevant collective coordinates for clustering the data; and an SiO$_2$ amorphous model, in which we compute distortion scores and compare them with a classical strain-based potential. The source code and benchmark data are available at \url{https://github.com/mammasmias/IterativeRotationsAssignments}.

Rohit Goswami, Miha Gunde, Hannes Jónsson

Accurate determination of transition states remains central to understanding reaction kinetics. Double-ended methods like the Nudged Elastic Band (NEB) ensure relevant transition states and paths, but incur high computational costs and suffer stagnation on flat or rough potential energy surfaces. Conversely, single-ended eigenmode-following techniques offer efficiency but cannot often be constrained between specific states. Here, we present the Reorienting Off-path Nudged Elastic Bands (RONEB), an adaptive hybrid algorithm that integrates the double ended nature of the NEB with the acceleration of single ended Min-Mode Following methods. RONEB provides stability based on the history of the path optimization, relative force triggering, and an alignment-based back-off penalty to dynamically decouple the climbing image from the elastic band constraints. We benchmark the method against the standard Climbing Image NEB (CI-NEB) across the Baker-Chan transition state test set using the PET-MAD machine-learned potential and the OptBench Pt(111) heptamer island surface diffusion set. A Bayesian analysis of the performance data quantifies a median reduction in gradient calls of 46.3% [95% CrI: -54.7%, -36.9%] relative to the baseline, while surface diffusion tests reveal a 28% reduction across 59 metallic rearrangement mechanisms. These results establish RONEB as a highly effective tool for high-throughput automated chemical discovery.