The Choice of Origin: Evaluating Variational Hirshfeld Atomic Multipoles for Machine Learning Electrostatics
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Authors
van Zyl, Maximilian
Date
2025-07-03
Type
thesis
Language
eng
Keyword
Computational chemistry , Machine learning , Multipole expansion of the electrostatic potential , Graph convolutional neural networks , Message passing neural networks , Atomic multipole moments , Molecular multipole moments , Atoms-in-molecules partitioning schemes , Learning atomic multipole moments
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Abstract
Accurately modelling molecular electrostatics is essential for simulating chemical systems and understanding their interactions. Traditional fixed-charge force fields (FFs), while computationally efficient, are unable to capture conformational dependence or anisotropic effects. Their limited accuracy in studying biologically and pharmaceutically relevant systems has motivated the development of physics-based approaches to electrostatic modelling. In these efforts, machine learning (ML) models offer a promising alternative by learning from quantum mechanical data to make accurate, yet computationally efficient, predictions of chemical properties. However, the performance of ML-based models strongly depends on the quality and diversity of the reference data used for training. This thesis systematically evaluates atomic multipole moments from several variational Hirshfeld partitioning schemes to identify reliable and transferable reference data for ML models that improve the long-range electrostatic treatment of FFs.
Through a detailed analysis of datasets spanning organic, inorganic, and protein fragment molecules, this work demonstrates that atomic multipoles from the Additive Variational Hirshfeld (AVH) method outperform those from the popular Iterative Hirshfeld (HI) and Minimal Basis Iterative Stockholder (MBIS) schemes in reproducing both molecular moments and approximating electrostatic potentials (ESPs). Our work challenges the assumption that the method producing the “best” atomic charges is also the most suitable when approximating the ESP using dipoles and quadrupoles with an atom-centred multipole expansion. These results establish AVH as a suitable reference scheme for modelling electrostatics beyond atomic charges alone.
Based on these findings, state-of-the-art equivariant message passing neural networks were trained on atomic multipole moments directly from molecular geometry. Reference atomic moments were obtained from the AVH, HI, and MBIS partitioning schemes. Comparative analysis again revealed that models trained on AVH-derived multipoles consistently outperformed those trained on HI or MBIS data, achieving superior accuracy in ESP predictions both within and beyond the training domain, even when using only atomic charges. These results establish AVH’s atomic density and its corresponding multipole moments as a reliable training target for developing transferable ML models.
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Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.