# Two-dimensional RMSD projections for reaction path visualization and validation

arXiv: https://arxiv.org/abs/2512.07329 · HTML: https://mlsanity.com/paper/2512.07329/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Builds on (most cited first, 7 of 7)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Scaling Gaussian Process Regression with Derivatives](https://mlsanity.com/paper/1810.12283/) (2018)
- [PET-MAD, a lightweight universal interatomic potential for advanced materials modeling](https://mlsanity.com/paper/2503.14118/) (2025)
- [IRA: A shape matching approach for recognition and comparison of generic atomic patterns](https://mlsanity.com/paper/2111.00939/) (2021)
- [Efficient Implementation of Gaussian Process Regression Accelerated Saddle Point Searches with Application to Molecular Reactions](https://mlsanity.com/paper/2505.12519/) (2025)
- [Adaptive Pruning for Increased Robustness and Reduced Computational Overhead in Gaussian Process Accelerated Saddle Point Searches](https://mlsanity.com/paper/2510.06030/) (2025)

## Built on by (most cited first, 2 of 2)

- [Enhanced Climbing Image Nudged Elastic Band method with Hessian Eigenmode Alignment](https://mlsanity.com/paper/2601.12630/) (2026)
- [A Tutorial Review of Bayesian Optimization with Gaussian Processes to Accelerate Stationary Point Searches](https://mlsanity.com/paper/2603.10992/) (2026)

## Abstract (arXiv)

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.