Machine-Learned Short-Range Repulsive Hamiltonians for Electrostatic QM/MM Embedding
- 1China Pharmaceutical University
- 2School of Science
- 3School of Basic Medicine and Clinical Pharmacy
Abstract
Accurate description of short-range quantum effects between a quantum-mechanical (QM) region and its molecular-mechanical (MM) environment remains a central challenge in electrostatic embedding QM/MM methods. In conventional point-charge embedding, MM atoms polarize the QM wave function through electrostatics but lack an explicit electron density, resulting in an incomplete description of short-range Pauli repulsion and, in unfavorable configurations, electron spill-out and excessive QM-MM attraction. Here we develop EmbR, a physically constrained machine-learning framework that restores this missing short-range quantum response while retaining the simplicity of point-charge embedding. Rather than learning an energy correction alone, EmbR predicts environmentdependent MM-site contributions constrained by the spatial overlap between QM electron density and MM-centered density-like functions. These site contributions are then transformed into explicit atom-centered exponential repulsive potentials and incorporated directly into the QM Hamiltonian. A self-consistent energy-matching procedure further accounts for the density relaxation induced by the added repulsive operator without altering the learned spatial distribution. Across amino-acid–water and amino-acid–water/NaCl model systems, EmbR reduces the interaction-energy errors of conventional electrostatic embedding from 20.21–59.18 kcal/mol to 1.23–2.58 kcal/mol relative to counterpoisecorrected full-QM references, while maintaining strong agreement with the reference interaction energies (𝑅2 = 0.9798–0.9912). Beyond energetic accuracy, EmbR suppresses electron spill-out near positively charged MM sites and reproduces the dominant electrondepletion features associated with interfacial Pauli repulsion. These results demonstrate that physically constrained machine learning can provide an efficient intermediate strategy between conventional point-charge embedding and fully electronic embedding approaches by introducing an environment-dependent short-range quantum operator into QM/MM Hamiltonians.
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BibTeX
@misc{cao2026machinelearned,
title = {{Machine-Learned Short-Range Repulsive Hamiltonians for Electrostatic QM/MM Embedding}},
author = {Minghao Cao and Jinfeng Liu},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15008167/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008167/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Machine-Learned Short-Range Repulsive Hamiltonians for Electrostatic QM/MM Embedding
AU - Minghao Cao
AU - Jinfeng Liu
PY - 2026
DA - 2026/09/01
PB - ChemRxiv
DO - 10.26434/chemrxiv.15008167/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008167/v1
AB - Accurate description of short-range quantum effects between a quantum-mechanical (QM) region and its molecular-mechanical (MM) environment remains a central challenge in electrostatic embedding QM/MM methods. In conventional point-charge embedding, MM atoms polarize the QM wave function through electrostatics but lack an explicit electron density, resulting in an incomplete description of short-range Pauli repulsion and, in unfavorable configurations, electron spill-out and excessive QM-MM attraction. Here we develop EmbR, a physically constrained machine-learning framework that restores this missing short-range quantum response while retaining the simplicity of point-charge embedding. Rather than learning an energy correction alone, EmbR predicts environmentdependent MM-site contributions constrained by the spatial overlap between QM electron density and MM-centered density-like functions. These site contributions are then transformed into explicit atom-centered exponential repulsive potentials and incorporated directly into the QM Hamiltonian. A self-consistent energy-matching procedure further accounts for the density relaxation induced by the added repulsive operator without altering the learned spatial distribution. Across amino-acid–water and amino-acid–water/NaCl model systems, EmbR reduces the interaction-energy errors of conventional electrostatic embedding from 20.21–59.18 kcal/mol to 1.23–2.58 kcal/mol relative to counterpoisecorrected full-QM references, while maintaining strong agreement with the reference interaction energies (𝑅2 = 0.9798–0.9912). Beyond energetic accuracy, EmbR suppresses electron spill-out near positively charged MM sites and reproduces the dominant electrondepletion features associated with interfacial Pauli repulsion. These results demonstrate that physically constrained machine learning can provide an efficient intermediate strategy between conventional point-charge embedding and fully electronic embedding approaches by introducing an environment-dependent short-range quantum operator into QM/MM Hamiltonians.
ER -