AIMNet2-rxn: NNP for Organic Reactions

• AIMNet2-rxn is a neural network potential that delivers near-DFT quality energies and forces for exploring complex organic cyclization mechanisms.
• It employs a multi-stage, graph-inspired architecture to reconstruct chemical environments directly from 3D geometries without explicit connectivity data.
• The model integrates into automated reaction workflows, accelerating transition‐state searches by 3–4× compared to traditional semi‐empirical protocols.

AIMNet2-rxn is a neural network potential (NNP) within the AIMNet2 family, specifically developed for efficient and accurate exploration of complex organic reaction mechanisms, with an emphasis on cyclization processes involving multiple concerted bond transformations. It provides near-density functional theory (DFT) quality energies and forces at a small fraction of the computational cost, thereby enabling high-throughput, automated searching of transition states (TSs) and intermediates in large reactive chemical networks (Casetti et al., 14 Jul 2025, Marks et al., 1 Apr 2026).

1. Model Architecture

AIMNet2-rxn employs a multi-stage, graph-inspired neural network framework with atom-centered, three-dimensional input representations. Each molecular system is fed to the model as a set of Cartesian coordinates and atomic numbers; explicit valence, bond order, or connectivity information is not required, as the network reconstructs chemical environments entirely from 3D geometries. The architecture features:

• Atomic Embeddings: Initial embeddings for each atom that encode its chemical identity and the spatial arrangement of nearby atoms.
• Message-Passing/Interaction Blocks: Multiple stages in which atomic embeddings are updated via interactions with neighbors, including "interaction" modules that allow long-range information flow beyond immediate neighbor shells.
• Pooling and Output: Atomic contributions are summed to yield the total potential energy $E_{\mathrm{NN}}$. Forces on each atom are computed by automatic differentiation: $$F_i^{\mathrm{NN}} = -\partial E_{\mathrm{NN}}/\partial r_i$$.

The network does not output additional properties (such as dipoles or charges) in its application to neutral, closed-shell organic molecules composed of C, H, N, and O, although the broader AIMNet2 class can support such outputs (Casetti et al., 14 Jul 2025, Marks et al., 1 Apr 2026).

2. Training Procedures and Data Regimes

AIMNet2-rxn is trained on ∼2.3 million gas-phase structures (reactants, products, transition states, intermediate conformers) computed at the ωB97M-V/def2-TZVPP level of theory. The dataset exclusively comprises neutral, closed-shell organic compounds (C/H/N/O). It densely samples reactive coordinates—electrocyclizations, cycloadditions, [1,5]-shifts—using interpolations and intrinsic reaction coordinate (IRC) scans, ensuring that TS and near-TS geometries are well-represented.

The training objective is a weighted mean-squared error (MSE) over both energies and forces:

$$\mathcal{L} = \frac{1}{N_{\rm conf}} \sum_{i=1}^{N_{\rm conf}} (E_i^{\mathrm{NN}} - E_i^{\mathrm{ref}})^2 + \lambda\frac{1}{3N_{\rm atoms}} \sum_{i=1}^{N_{\rm conf}} \sum_{j=1}^{N_{\rm atoms}} \|\mathbf{F}_{ij}^{\mathrm{NN}} - \mathbf{F}_{ij}^{\mathrm{ref}}\|^2$$

where the hyperparameter $\lambda$ controls the relative weighting of force against energy errors. Specifics regarding optimizer selection, learning rate scheduling, architecture depth, and other hyperparameters are detailed in the forthcoming dedicated AIMNet2-rxn manuscript (Casetti et al., 14 Jul 2025).

3. Integration into Automated Reaction Path and TS Workflows

AIMNet2-rxn serves as the core potential for multiple high-throughput mechanistic exploration pipelines. Notably, in cyclization mechanism discovery ("RAMP" workflow), it operates as follows:

1. Graph-based Enumeration: All possible bond-editing operations (up to 4 bonds broken/formed per elementary step, "b4f4" space), with stereochemical enumeration, typically yields $10^4$–$10^6$ putative intermediates.
2. 2D MPNN Filtering: A lightweight message-passing neural network prunes graph candidates with high reaction enthalpy ($\Delta E_{\mathrm{rxn}} > 60$ kcal/mol) or predicted instability (1–5 ms per graph).
3. AIMNet2-rxn Optimization: For surviving candidates, AIMNet2-rxn performs rapid 3D geometry optimization (FIRE algorithm) and energy evaluation, downselecting to $\sim10^3$ species.
4. Transition-State Search: Climbing-image nudged elastic band (CI-NEB, 20 images) and TS refinement are carried out on the AIMNet2-rxn surface, further reducing candidates to order $\sim10^2$.
5. Final DFT Refinement: Resulting TSs are reoptimized at DFT ($\omega$B97-X/6-31G), with final single-point energies at a higher basis ($$F_i^{\mathrm{NN}} = -\partial E_{\mathrm{NN}}/\partial r_i$$0B97-X/6-311+G).

In transition-state search workflows outside of the RAMP context, AIMNet2 (including AIMNet2-rxn) interfaces with the Freezing-String Method (FSM) and CI-NEB, providing energies and gradients to chain-of-states optimizers. Standard parameterizations are used: 18 images for FSM with at most 3 line search steps and 2 L-BFGS-B optimization steps per image; 7 images and $$F_i^{\mathrm{NN}} = -\partial E_{\mathrm{NN}}/\partial r_i$$1 eV/Å for NEB. For FSM, the relevant expansion is

$$F_i^{\mathrm{NN}} = -\partial E_{\mathrm{NN}}/\partial r_i$$2

and performance is further improved by performing low-level TS refinement on AIMNet2 prior to high-level DFT optimization, using RS-P-RFO algorithms and a force convergence threshold of $$F_i^{\mathrm{NN}} = -\partial E_{\mathrm{NN}}/\partial r_i$$3 eV/Å (Marks et al., 1 Apr 2026).

4. Performance Metrics and Comparative Analysis

AIMNet2-rxn closely reproduces DFT-level energetics and transition-state geometries for challenging organic reaction benchmarks:

Metric	AIMNet2-rxn	GFN2-xTB
MAE (ΔE$$F_i^{\mathrm{NN}} = -\partial E_{\mathrm{NN}}/\partial r_i$$4) cyclization barriers	2.9 kcal/mol (R²=0.90)	11.2 kcal/mol (R²=0.41)
RMSD (TS geometry, NNP vs DFT)	0.17 Å (most <0.10 Å)	Not stated
Speedup (NEB/TS searches)	3–4×	1×

AIMNet2-rxn resolves subtle selectivities, e.g., predicting a ΔΔG$$F_i^{\mathrm{NN}} = -\partial E_{\mathrm{NN}}/\partial r_i$$5 of 1.1 kcal/mol for a Diels–Alder system (Boltzmann cis/trans ≈ 71:29, matching experiment), and correctly pruning disfavored pathways in tethered fumarate ester cyclizations. For complex cascades such as the endiandric acid C sequence, the model predicts major and minor diastereomeric barriers within 3 kcal/mol of DFT values and occasionally eliminates unlikely TSs that are not realized experimentally (Casetti et al., 14 Jul 2025).

In the context of general small-molecule TS search benchmarks (Baker and Sharada sets), the AIMNet2-FSM workflow achieves 82.8% overall success rate (low-level refinement), with DFT gradient call savings of 36–60% relative to direct DFT optimization. In all-DFT FSM searches, this degree of acceleration corresponds to a ~95% reduction in DFT evaluations (Marks et al., 1 Apr 2026).

5. Chemical Scope and Limitations

AIMNet2-rxn is strictly restricted in scope to neutral, closed-shell C/H/N/O molecular systems. It is not applicable to organometallic systems, open-shell, or ionic species. For systems exceeding 60 atoms, combinatorial growth in candidate intermediates from b4f4 enumeration becomes a bottleneck, although progressive filtering typically reduces the number requiring DFT treatment by an order of magnitude. Full automated workflows, even leveraging AIMNet2-rxn at intermediate steps, still require 100–1000 hours of wall time per case, dominated by the final DFT reoptimization and single-point stages (Casetti et al., 14 Jul 2025).

In MLIP-driven TS searches, limitations arise if the training set does not adequately cover TS-like or highly non-equilibrium geometries. For AIMNet2-rxn, the inclusion of such coordinations in the training set mitigates but does not eliminate the risk of Hessian and imaginary-mode misordering near saddle points. Failures often relate to off-target saddle-point convergence or insufficient coverage of very exotic chemical space. Best practice is to monitor the number of imaginary modes post DFT-refinement and, for new classes of chemistry, to prefer MLIPs explicitly trained on similar reactivity space (Marks et al., 1 Apr 2026).

6. Significance in High-Throughput Reaction Discovery

AIMNet2-rxn has advanced the integration of NNPs into fully automated, high-throughput workflows for complex organic mechanism exploration. Its capacity to deliver DFT-grade barrier heights (MAE ≈ 3 kcal/mol) and TS geometries (RMSD ≈ 0.1 Å), combined with a 3–4-fold computational acceleration over semi-empirical protocols in the NEB/TS stages, enables the practical mapping of multistep cyclization networks central to natural product synthesis and synthetic method development.

Its deployment in the RAMP workflow demonstrates the feasibility of starting from enumerative graph-based chemical space expansion and, through a sequence of filtering, geometry optimization, and TS localization steps, returning energetically ranked, stereochemically relevant mechanistic hypotheses in a fully automated fashion (Casetti et al., 14 Jul 2025).

7. Best Practice Recommendations and Future Directions

For robust application, AIMNet2-rxn should be used within its validated chemical domain (neutral, closed-shell C/H/N/O systems). Automated TS searches should incorporate a low-level refinement stage on the AIMNet2-rxn surface (RS-P-RFO) with force thresholds of $$F_i^{\mathrm{NN}} = -\partial E_{\mathrm{NN}}/\partial r_i$$6 eV/Å to maximize DFT cost reduction without significant loss in success rate. For challenging or out-of-domain reactions, including transition metals or highly charged states, models with explicitly reactive or transition-metal-rich training data (e.g., OMol25-based MLIPs) are preferred.

Ongoing research is expected to expand the element coverage, reactivity types, and the robustness of AIMNet2-like models toward saddle-point vibrational properties and broader chemical spaces (Marks et al., 1 Apr 2026). A plausible implication is that future AIMNet architectures with analytic second-derivative support and more comprehensive reactive datasets will further close the gap between MLIP-accelerated and fully ab initio high-throughput reaction discovery.