What is it about?

Computational chemists locate transition states and reaction paths to understand chemical reactions, of which path methods are very popular, like the Nudged Elastic Band or NEB. Standard visualization plots energy along a one-dimensional "reaction coordinate" that hides structural details and makes method comparisons difficult. This work introduces a two-dimensional projection that maps each molecular configuration onto a plane defined by its distances from reactant and product structures. Algorithms compute these distances with a measure that works regardless of how researchers label the atoms. A statistical model utilizing energy and force data interpolates the energy surface across this plane; a rotation separates progress along the reaction from sideways deviations. The resulting plot shows the complete optimization history, reveals whether different algorithms or machine-learning potentials produce similar barrier regions, and distinguishes numerical artifacts from physical features. The method works for any double-ended saddle-search algorithm (NEB, string methods) and easily applies to single-ended searches or molecular dynamics trajectories.

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Why is it important?

One-dimensional energy profiles discard geometric context, making it hard to validate whether a computed transition state represents a correct structure or a numerical artifact. Researchers spend days inspecting structures or repeating calculations. This two-dimensional projection provides a standardized, geometry-aware visual framework that: - Enables direct comparison of different saddle-search algorithms and machine-learning potentials. - Reveals when two paths look geometrically similar despite differences in atom positions. - Identifies numerical instability (e.g., "kinks" in the path) invisible in 1D plots. - Supplies reliability contours from the uncertainty estimates, showing where data tightly constrains the interpolated surface. The method proves timely because researchers increasingly use machine-learned interatomic potentials for saddle-point searches, and the field requires robust validation tools to trust their results. We implemented the projection in an open-source Python project (https://rgpycrumbs.rgoswami.me with https://chemparseplot.rgoswami.me) so users can incorporate it into existing workflows with minimal effort.

Perspectives

As a computational chemist who routinely runs hundreds of saddle-point searches, I developed this visualization as a refinement to an approach using thin plate splines during my PhD thesis (https://arxiv.org/pdf/2510.21368) to solve a practical problem: I could not easily tell whether a new machine-learning potential gave a similar reaction path to a density-functional theory reference, nor could I quickly diagnose where an optimization stalled and how different methods and surfaces vary in their predicted saddles. The 2D RMSD projection answers those questions at a glance and provides a common language for discussing path quality across research groups. The rotated (s,d) frame, inspired by path collective variables in enhanced sampling, gives a physically intuitive coordinate system where "progress along the reaction" and "deviation from the ideal path" function as separate axes. This representation supplements traditional energy profiles for benchmarking new algorithms or potentials. The code runs efficiently and interoperates smoothly with standard tools; it reads standard NEB output files and produces publication-ready figures with one command.

Rohit Goswami
University of Iceland

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This page is a summary of: Two-dimensional RMSD projections for reaction path visualization and validation, MethodsX, March 2026, Elsevier,
DOI: 10.1016/j.mex.2026.103851.
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