Two-dimensional RMSD projections for reaction path visualization and validation

TL;DR

This paper introduces a novel two-dimensional RMSD projection method for visualizing and validating reaction pathways, providing clearer insights into structural changes and energy landscapes during chemical reactions.

Contribution

The authors develop a permutation-corrected RMSD projection combined with Gaussian Process energy interpolation, enabling detailed comparison of reaction pathways beyond traditional energy vs. displacement plots.

Findings

Effective visualization of reaction paths in complex reactions.

Comparable energy contours for machine-learned and DFT potentials.

Validation of the method on multiple chemical reactions.

Abstract

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.