What is it about?

Transition-state and minimum-energy-path methods are routine. The usual plot is energy against a cumulative displacement or an image number. That one-dimensional profile hides the geometry and depends on the history of the run, so two methods can be compared only by force-call counts, wall time, and the final saddle. This method maps each configuration onto a plane whose axes are the permutation-corrected root-mean-square deviation (RMSD) to the reactant and to the product. Energy is drawn as a colour-mapped surface interpolated from every optimization step with a gradient-enhanced Gaussian process. Posterior-variance contours mark regions the data support. A rotated frame splits the plane into reaction progress and distance off that line. On a cycloaddition, a machine-learned-potential saddle and a density-functional-theory reference sit on comparable energy contours even though the geometries differ. The same map is checked on a Grignard rearrangement and a conrotatory bicyclobutane ring opening.

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Why is it important?

A 1D profile cannot say whether two paths visit the same structural neighborhood. That is the question when a machine-learned potential is compared to a DFT reference, or when two optimizers stall in different places. The RMSD plane plus variance contours show where the interpolant is backed by samples and where it is guessing. The rotated frame separates progress along the reaction from sideways drift, so a kink or a stall is a geometric feature rather than a wiggle in energy. The code is not a new saddle search. It reads a standard NEB history and writes the projection (https://rgpycrumbs.rgoswami.me, https://chemparseplot.rgoswami.me).

Perspectives

I could not tell, from a 1D profile, whether a machine-learned potential and a DFT reference were walking the same path or two different ones that happened to have similar barriers. Thin-plate splines in the thesis (https://arxiv.org/abs/2510.21368) were a first attempt. The permutation-corrected RMSD plane plus a gradient-enhanced Gaussian process is the version that survived: atom labels no longer matter, and the variance contours stop me from reading structure into empty parts of the plane. The cycloaddition case is the one I wanted. The two saddles are displaced in geometry but sit on comparable energy contours. The Grignard and bicyclobutane checks are there so the plot is not a one-reaction trick.

Rohit Goswami
University of Iceland

Read the Original

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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