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arXiv:2610.41523

A Hybrid Message-Passing and Electric-Field Representation for Electrostatic QM/MM Embedding with Machine Learning Interatomic Potentials

Raphael T. Husistein, Shobhit S. Chaturvedi, Thomas Weymuth, Beatriz Piniello, Sélène Forget, Kresten Lindorff-Larsen, Gemma C. Solomon, Markus Reiher

physics.chem-phphysics.bio-phphysics.comp-phquant-phSubmitted Oct 30, 2026• Announced Nov 2, 2026
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Abstract

Within a hybrid quantum mechanics/molecular mechanics approach a small region of a large atomistic system is described quantum mechanically, while the rest of the system is represented by a classical force field. Despite this, the computational cost of the quantum calculation severely limits the accessible simulation and sampling time. Replacing the quantum calculation with a machine learning interatomic potential (MLIP) trained on quantum reference data can greatly increase the accessible simulation time. However, the accuracy and efficiency strongly depend on the specific way in which the MLIP incorporates information about the classical (electrostatic) environment. Here, we demonstrate that existing strategies based purely on features derived from an external electric field fail to distinguish certain environments, ultimately limiting their accuracy. As a solution, we propose an extension to the equivariant TensorNet architecture that mitigates this shortcoming by incorporating classical atoms close to the quantum region into the message-passing scheme, combined with features derived from the electric field for describing the environment farther away. We show that this combination achieves higher accuracy than either approach alone.

AI Summary

The paper addresses how machine-learning interatomic potentials can represent the classical electrostatic environment when replacing the quantum calculation in QM/MM simulations. It extends the equivariant TensorNet architecture by combining explicit message passing through nearby MM atoms with the electrostatic potential, electric field, and field gradient evaluated at QM atoms using all MM charges. Only QM-node features contribute directly to the predicted energy. Symmetric point-charge constructions, evaluated using CCSD(T)/aug-cc-pVQZ calculations for argon, demonstrate that truncated local field descriptors can coincide despite different interaction energies. Explicitly resolving nearby charges can distinguish these environments when they lie inside the graph cutoff. Ablations on capped arginine–glutamate in water, using 8,000 training/validation structures and 931 test structures, show energy/force MAEs of 1.94 kJ/mol and 1.15 kJ/mol/Å for the combined representation, versus 4.69/1.92 for field features alone and 4.32/2.25 for nearby MM atoms alone. Results are averaged over three seeds. Subtracting fixed-charge Coulomb interactions before training and restoring them at inference removes statistically detectable distance-dependent projected-force bias in the reported bins. Benchmarks on solvated benzene and uracil give test energy MAEs of 0.55 and 3.54 kJ/mol, respectively, improving on the reported non-delta-learning comparators. The representation still truncates far-environment field information and explicitly resolves only nearby MM atoms. Direct comparison with FieldMACE is withheld because matching data splits are unavailable; uracil errors change sharply between chronological and random splits, attributed to near-duplicate trajectory frames.

No sign of AI-generated textIncrementalMissing comparison

Error found: The second symmetry probe incorrectly attributes vanishing potential to symmetric placement alone: it also requires the unstated condition q+/d1=−q−/d2, although the electric field does vanish by symmetry.

Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.

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23 pages, 3 figures

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Within a hybrid quantum mechanics/molecular mechanics approach a small region of a large atomistic system is described quantum mechanically, while the rest of the system is represented by a classical force field. Despite this, the computational cost of the quantum calculation severely limits the accessible simulation and sampling time. Replacing the quantum calculation with a machine learning interatomic potential (MLIP) trained on quantum reference data can greatly increase the accessible simulation time. However, the accuracy and efficiency strongly depend on the specific way in which the MLIP incorporates information about the classical (electrostatic) environment. Here, we demonstrate that existing strategies based purely on features derived from an external electric field fail to distinguish certain environments, ultimately limiting their accuracy. As a solution, we propose an extension to the equivariant TensorNet architecture that mitigates this shortcoming by incorporating classical atoms close to the quantum region into the message-passing scheme, combined with features derived from the electric field for describing the environment farther away. We show that this combination achieves higher accuracy than either approach alone.
The paper addresses how machine-learning interatomic potentials can represent the classical electrostatic environment when replacing the quantum calculation in QM/MM simulations. It extends the equivariant TensorNet architecture by combining explicit message passing through nearby MM atoms with the electrostatic potential, electric field, and field gradient evaluated at QM atoms using all MM charges. Only QM-node features contribute directly to the predicted energy.
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Benchmarks on solvated benzene and uracil give test energy MAEs of 0.55 and 3.54 kJ/mol, respectively, improving on the reported non-delta-learning comparators. The representation still truncates far-environment field information and explicitly resolves only nearby MM atoms. Direct comparison with FieldMACE is withheld because matching data splits are unavailable; uracil errors change sharply between chronological and random splits, attributed to near-duplicate trajectory frames.
This study explores the use of equivariant quantum neural networks (QNN) for generating molecular force fields, focusing on the rMD17 dataset. We consider a QNN architecture based on previous research and point out shortcomings in the parametrization of the atomic environments, that limits its expressivity as an interatomic potential and precludes transferability between molecules. We propose a revised QNN architecture that addresses these shortcomings. While both QNNs show promise in force prediction, with the revised architecture showing improved accuracy, they struggle with energy prediction. Further, both QNNs architectures fail to demonstrate a meaningful scaling law of decreasing errors with increasing training data. These findings highlight the challenges of scaling QNNs for complex molecular systems and emphasize the need for improved encoding strategies, regularization techniques, and hybrid quantum-classical approaches.
This study explores the use of equivariant quantum neural networks (QNN) for generating molecular force fields, focusing on the rMD17 dataset. We consider a QNN architecture based on previous research and point out shortcomings in the parametrization of the atomic environments. These shortcomings limit its expressivity as an interatomic potential and precludes transferability between molecules. We propose a revised QNN architecture that addresses these shortcomings. While both QNNs show promise in force prediction, with the revised architecture showing improved accuracy, they struggle with energy prediction. Further, both QNNs architectures fail to demonstrate a meaningful scaling law of decreasing errors with increasing training data. These findings highlight the challenges of scaling QNNs for complex molecular systems and emphasize the need for improved encoding strategies, regularization techniques, and hybrid quantum-classical approaches.
This study applied quantum circuit learning, a commonly used hybrid quantum-classical machine learning algorithm, to a machine learning interatomic potential (MLIP) for predicting the energies of molecules in molecular datasets. We retrained the ANI model using the quantum transfer learning architecture [Mari et al., Quantum, 4:340, 2020] and evaluated numerical accuracy with a quantum circuit simulator. The evaluation confirmed that inserting a quantum circuit into the classical neural network of the MLIP yielded slightly higher accuracy than the fully classical neural network under certain conditions. In particular, the model incorporating a quantum circuit was more effective when the pretraining model had room for improvement in accuracy. These findings may contribute to advancing the application of quantum machine learning for MLIPs.
Allegro is a machine learning interatomic potential model designed to predict atomic properties in molecules using E(3) equivariant neural networks. When training this model, there tends to be a trade-off between accuracy and inference time. For this reason, we apply multi-objective hyperparameter optimization to both objectives. Additionally, we experiment with modified architectures by constructing variants of Allegro: one extended with additional classical layers and one incorporating quantum-classical hybrid layers. We evaluate all models on QM9, rMD17-aspirin, rMD17-benzene, and a self-generated dataset of copper-lithium structures. As results, both variants surpass Allegro in force prediction accuracy across multiple datasets. The classical variant consistently improves over the baseline, while the quantum-classical hybrid variant achieves the best overall force prediction accuracy on the Cu-Li dataset, where it was fully optimized, outperforming the classical variant by approximately 13%. Notably, the hybrid variant also achieves competitive results on the remaining datasets despite using hyperparameters transferred from Cu-Li without dataset-specific optimization, suggesting that quantum-classical hybridization is a promising direction for enhancing MLIP architectures.
We propose a framework for incorporating quantum-computing-based electronic-structure calculations into universal machine-learning interatomic potentials (uMLIPs). Rather than constructing an interatomic potential from scratch, we refine a pretrained DFT-based uMLIP using a small set of accurate reference energies obtained from quantum computing. We demonstrate the approach for three chemically distinct applications: the Menshutkin reaction, water adsorption in the metal-organic framework HKUST-1, and CO hopping on a high-entropy-alloy nanoparticle. For the Menshutkin reaction, fine-tuning on gas-phase configurations improves the transition-state energy inside a carbon nanotube but not the product energy. For water adsorption in HKUST-1, fine-tuning with only 14 reference configurations brings adsorption thermodynamics obtained from millions of configurations sampled by Widom insertion into closer agreement with reference values. For CO hopping on an IrPdPtRhRu nanoparticle, the preference for on-top over bridge adsorption is recovered in the finite-temperature free-energy profile obtained from enhanced-sampling molecular dynamics, even though the reference data contain only energies. These results demonstrate that the proposed framework provides a practical route for incorporating quantum-computing calculations into realistic atomistic simulations and that quantum-computing reference data can improve pretrained uMLIPs.
Machine learning techniques are essential tools to compute efficient, yet accurate, force fields for atomistic simulations. This approach has recently been extended to incorporate quantum computational methods, making use of variational quantum learning models to predict potential energy surfaces and atomic forces from ab initio training data. However, the trainability and scalability of such models are still limited, due to both theoretical and practical barriers. Inspired by recent developments in geometric classical and quantum machine learning, here we design quantum neural networks that explicitly incorporate, as a data-inspired prior, an extensive set of physically relevant symmetries. We find that our invariant quantum learning models outperform their more generic counterparts on individual molecules of growing complexity. Furthermore, we study a water dimer as a minimal example of a system with multiple components, showcasing the versatility of our proposed approach and opening the way towards larger simulations. Our results suggest that molecular force fields generation can significantly profit from leveraging the framework of geometric quantum machine learning, and that chemical systems represent, in fact, an interesting and rich playground for the development and application of advanced quantum machine learning tools.