Two-dimensional RMSD projections for reaction path visualization and validation

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 may often be trajectory dependent. This precludes the ability to compare optimization trajectories of different methods beyond the number of calculations, time taken, and final saddle geometry. We present a method mapping trajectories onto a two-dimension surface 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 radial basis functions. This representation highlights optimization trajectories, identifies endpoint basins, and diagnoses convergence concerns invisible in one-dimensional profiles. We validate the framework on a cycloaddition reaction, showing that a machine-learned potential saddle and density functional theory reference lie on comparable energy contours despite geometric displacements.

Figures (1)

• Figure 1: NEB optimization of ethylene + N2O cycloaddition using PET-MAD v1.1 potential. Top: 2D RMSD projection showing interpolated energy landscape (color), sampled structures (black dots), and converged path (open circles). White star indicates ORCA B3LYP-D3 saddle. Bottom left: Energy vs. reaction coordinate. Bottom center: Energy vs. image index. Bottom right: Energy vs. RMSD from reactant. In all panels, colored curves show optimization progression (dark$\to$light = early$\to$late); final path in black. The 2D projection reveals landscape topology and enables reference structure assessment impossible in 1D profiles.