Two-dimensional RMSD projections for reaction path visualization and validation

2025-12-08

AI Summary

Traditional reaction path visualization methods—e.g., energy–displacement plots—project high-dimensional structural evolution onto a one-dimensional trajectory, obscuring configurational details and impeding cross-algorithm comparison of optimization dynamics. To address this, we propose a two-dimensional projection framework based on permutation-corrected RMSD: the configuration plane is defined by RMSD distances from reactant and product structures; radial basis function interpolation and energy-based coloring yield a continuous, interpretable potential energy surface. This enables simultaneous trajectory visualization, convergence diagnostics, and precise saddle-point localization, facilitating intuitive comparative analysis across optimization algorithms. Validation on cycloaddition reactions shows that machine-learned interatomic potentials predict saddle points with minor geometric deviations, yet these lie within energy contour levels closely matching DFT reference results—demonstrating strong configurational–energetic consistency.

Technology Category

• Machine Learning: Learning with Manifolds
• Planning, Routing, and Scheduling: Activity and Plan Recognition
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Web data visualization

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.

Problem

• Visualize high-dimensional reaction paths in 2D
• Compare different optimization trajectories effectively
• Diagnose convergence issues invisible in 1D profiles

Innovation

• Two-dimensional RMSD projections for path visualization
• Permutation-corrected deviation from reactant and product configurations
• Energy represented as color-mapped surface using radial basis functions