Two-dimensional RMSD projections for reaction path visualization and validation

This record contains the complete optimization trajectories, potential model, and analysis data for the Nudged Elastic Band (NEB) calculation of the ethylene + N$_2$O cycloaddition, a Grignard rearrangement, and a bicyclobutane  reaction. This dataset supports the accompanying manuscript "Two-dimensional RMSD projections for reaction path visualization and validation" and enables the full reproduction of the reported 2D RMSD landscapes and 1D energy profiles.

Transition state or minimum energy path finding methods constitute a routine component of the computational chemistry toolkit. Standard analysis involves
trajectories conventionally plotted in terms of the relative energy to the initial state against a cumulative displacement variable, or the image number.
These dimensional reductions obscure structural rearrangements in high dimensions and are often history dependent. This precludes the ability to
compare optimization histories of different methods beyond the number of calculations, time taken, and final saddle geometry. We present a method mapping
trajectories onto a two-dimensional projection defined by a permutation corrected root mean square deviation from the reactant and product configurations. Energy
is represented as an interpolated color-mapped surface constructed from all optimization steps using a gradient-enhanced Gaussian Process with the inverse
multiquadric kernel, whose posterior variance contours delineate data-supported regions from extrapolated ones. A rotated coordinate frame decomposes the RMSD
plane into reaction progress and orthogonal distance. We show the utility of the framework on a cycloaddition reaction, where a machine-learned potential
saddle and density functional theory reference lie on comparable energy contours despite geometric displacements, along with the ratification of the
visualization for more complex reactions, a Grignard rearrangement, and a conrotatory bicyclobutane ring opening.

The provided data encompasses the entire computational workflow: from the pre-trained PET-OMAT machine-learned potential and initial endpoint geometries to the intermediate NEB optimization steps and the final converged reaction path.