Transferable Learning of Reaction Pathways from Geometric Priors

TL;DR

MEPIN introduces a transferable, endpoint-based framework for predicting minimum-energy reaction paths without requiring transition-state data during training. By combining a parametrized path with an energy-based MaxFlux objective and two initialization strategies—geodesic-based pre-training (MEPIN-L) and geodesic initialization (MEPIN-G)—the approach achieves accurate alignment with reference intrinsic reaction coordinates across diverse reactions. Demonstrations on Transition1x and [3+2] cycloaddition datasets show robust generalization to unseen reactions and faster downstream TS refinement, enabling scalable exploration of large reaction spaces. The method reduces dependency on costly TS data and paves the way for data-driven, large-scale reaction-path discovery and optimization in computational chemistry.

Abstract

Identifying minimum-energy paths (MEPs) is crucial for understanding chemical reaction mechanisms but remains computationally demanding. We introduce MEPIN, a scalable machine-learning method for efficiently predicting MEPs from reactant and product configurations, without relying on transition-state geometries or pre-optimized reaction paths during training. The task is defined as predicting deviations from geometric interpolations along reaction coordinates. We address this task with a continuous reaction path model based on a symmetry-broken equivariant neural network that generates a flexible number of intermediate structures. The model is trained using an energy-based objective, with efficiency enhanced by incorporating geometric priors from geodesic interpolation as initial interpolations or pre-training objectives. Our approach generalizes across diverse chemical reactions and achieves accurate alignment with reference intrinsic reaction coordinates, as demonstrated on various small molecule reactions and [3+2] cycloadditions. Our method enables the exploration of large chemical reaction spaces with efficient, data-driven predictions of reaction pathways.

Figures (6)

• Figure 1: Schematic of the MEPIN (MEP Inference Network) training and inference. The model leverages an implicit reaction path parametrized by a neural network to transfer knowledge of the reaction path learned during training to unseen reactant-product pairs. It learns the difference between the minimum energy path and initial interpolation, derived from either geodesic (MEPIN-G) or linear (MEPIN-L) interpolations. The linear-initialized model may also benefit from geometric pre-training on geodesic interpolation. The proposed approach speeds up reaction path finding by reducing the need for costly energy evaluations at inference time.
• Figure 2: Symmetry considerations for the reaction path model. (a) Two-dimensional example showing a symmetric potential landscape and linear interpolation path with respect to reflection $\sigma$, while the MEP is asymmetric. The NN model $\phi$, which learns the deviation between the initial interpolation and the MEP (scale factor $t(1-t)$ and argument $a$ are omitted), must be non-equivariant with respect to $\sigma$ to properly break the symmetry. (b) Conversion between triazole tautomers 1 and 2. (c) Projections of the intrinsic reaction coordinates (IRCs) and reaction paths on the $x$--$y$ and $x$--$z$ planes learned by an SE(3)- and E(3)-equivariant neural networks for the reaction shown in panel (b). Curves and markers denote the positions of migrating hydrogen atoms, with the ring atoms aligned. The E(3) model fails to capture the out-of-plane atomic displacement.
• Figure 3: Geodesic interpolation. (a) Vectors with equal "length" under the metric $\frac{\partial U}{\partial x^1} \frac{\partial U}{\partial x^2}$, plotted on a two-dimensional potential $U(x^1, x^2)$. The length scale contracts compared to Cartesian coordinates as the position rises on the potential surface, making the MEP the shortest path on this metric. (b) Illustration of internal coordinates used to define the "length" in the geodesic interpolation scheme (\ref{['eq:internal_coordinates']}) for C--C interactions. Converting to internal coordinates prioritizes changes in bonded pairs over long-range non-bonded pairs. (c) Pre-training with geodesic loss (\ref{['eq:geodesic_loss']}) reduces the initial flux loss (\ref{['eq:flux_loss']}) significantly, accelerating the overall training time (including pre-training).
• Figure 4: Results reaction path learning on the Transition1x reaction set schreiner2022transition1x. (a) Example reaction from the Transition1x dataset, comprising molecules with up to seven heavy atoms (C, N, O). (b) Distribution of atom count and reaction activation energy at the GFN1-xTB level grimme2017robust for test set reactions. (c) Comparison of discrete Fréchet distance (\ref{['eq:frechet_distance']}) to the IRC based on potential energy difference and RMSD of different interpolation methods and reaction path models (MEPIN-L and G). (d) Potential energy difference and RMSD between predicted and actual TS (highest energy configuration on the path), evaluated for various interpolation methods and reaction path models. The white horizontal lines represent median values.
• Figure 5: Results for reaction path learning on the [3+2] cycloaddition reaction set stuyver2023reaction. (a) General reaction scheme for [3+2] cycloadditions, where dipole 3 and dipolarophile 4 undergo 1,3-cycloaddition to form cycloadduct 5. An example reaction from the dataset is shown in the lower panel, with the reactive five-atom moieties highlighted. (b) Distribution of atom count and reaction activation energy at the GFN1-xTB level grimme2017robust for test set reactions. (c) Comparison of discrete Fréchet distance (\ref{['eq:frechet_distance']}) to the IRC based on energy difference and RMSD of different interpolation methods and reaction path models (MEPIN-L and G). (d) Energy difference and RMSD between predicted and actual TS (highest energy configuration on the path), evaluated for various interpolation methods and reaction path models. The white horizontal lines represent median values.