Predicting molecular dipole moments by combining atomic partial charges and atomic dipoles

Abstract

The molecular dipole moment ($\mathbf{\mu }$) is a central quantity in chemistry. It is essential in predicting infrared and sum-frequency generation spectra, as well as induction and long-range electrostatic interactions. Furthermore, it can be extracted directly from high-level quantum mechanical calculations, making it an ideal target for machine learning (ML). In this work, we choose to represent this quantity with a physically inspired ML model that captures two distinct physical effects: local atomic polarization is captured within the symmetry-adapted Gaussian process regression (SA-GPR) framework, which assigns a (vector) dipole moment to each atom, while movement of charge across the entire molecule is captured by assigning a partial (scalar) charge to each atom. The resulting "MuML" models are fitted together to reproduce molecular $\mathbf{\mu }$ computed using high-level coupled-cluster theory (CCSD) and density functional theory (DFT) on the QM7b dataset. The combined model shows excellent transferability when applied to a showcase dataset of larger and more complex molecules, approaching the accuracy of DFT at a small fraction of the computational cost. We also demonstrate that the uncertainty in the predictions can be estimated reliably using a calibrated committee model. The ultimate performance of the models depends, however, on the details of the system at hand, with the scalar model being clearly superior when describing large molecules whose dipole is almost entirely generated by charge separation. These observations point to the importance of simultaneously accounting for the local and non-local effects that contribute to $\mathbf{\mu }$; further, they define a challenging task to benchmark future models, particularly those aimed at the description of condensed phases.

arXiv comment16 pages, 7 figures, plus supplementary information; added Materials Cloud link and corrected values in Table I. To be published in the Journal of Chemical Physics

References in corpus (28)

• Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons
• Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
• SchNet - a deep learning architecture for molecules and materials
• PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments and Partial Charges
• Machine Learning Unifies the Modelling of Materials and Molecules
• Machine Learning of Molecular Electronic Properties in Chemical Compound Space
• A beginner's guide to the modern theory of polarization
• Machine Learning Molecular Dynamics for the Simulation of Infrared Spectra
• How van der Waals interactions determine the unique properties of water
• Machine learning a general purpose interatomic potential for silicon
• Alchemical and structural distribution based representation for improved QML
• Symmetry-Adapted Machine-Learning for Tensorial Properties of Atomistic Systems
• Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network
• How accurate is density functional theory at predicting dipole moments? An assessment using a new database of 200 benchmark values
• Automatic Selection of Atomic Fingerprints and Reference Configurations for Machine-Learning Potentials
• Chemical Shifts in Molecular Solids by Machine Learning
• Minimal Basis Iterative Stockholder: Atoms in Molecules for Force-Field Development
• Accurate Interatomic Force Fields via Machine Learning with Covariant Kernels
• Incorporating long-range physics in atomic-scale machine learning
• Accurate molecular polarizabilities with coupled-cluster theory and machine learning
• Non-covalent interactions across organic and biological subsets of chemical space: Physics-based potentials parametrized from machine learning
• Fast and Accurate Uncertainty Estimation in Chemical Machine Learning
• Feature Optimization for Atomistic Machine Learning Yields A Data-Driven Construction of the Periodic Table of the Elements
• Operators in Machine Learning: Response Properties in Chemical Space
• Using Gaussian Process Regression to Simulate the Vibrational Raman Spectra of Molecular Crystals
• Equation of state of fluid methane from first principles with machine learning potentials
• Inexpensive modelling of quantum dynamics using path integral generalized Langevin equation thermostats
• Use of the complete basis set limit for computing highly accurate ab initio dipole moments

Cited by in corpus (37)

• Physics-inspired structural representations for molecules and materials
• Machine learning for electronically excited states of molecules
• Learning the electronic density of states in condensed matter
• A Deep Dive into Machine Learning Density Functional Theory for Materials Science and Chemistry
• Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry
• SchNetPack 2.0: A neural network toolbox for atomistic machine learning
• Thermodynamics and dielectric response of ${\text{BaTiO}}_3$ by data-driven modeling
• Deep Learning for UV Absorption Spectra with SchNarc: First Steps Towards Transferability in Chemical Compound Space
• Physically inspired deep learning of molecular excitations and photoemission spectra
• Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties
• Infrared spectra at coupled cluster accuracy from neural network representations
• Fully First-Principles Surface Spectroscopy with Machine Learning
• An equivariant graph neural network for the elasticity tensors of all seven crystal systems
• NENCI-2021 Part I: A Large Benchmark Database of Non-Equilibrium Non-Covalent Interactions Emphasizing Close Intermolecular Contacts
• Tensorial properties via the neuroevolution potential framework: Fast simulation of infrared and Raman spectra
• Accurate Molecular-Orbital-Based Machine Learning Energies via Unsupervised Clustering of Chemical Space
• Modeling electronic response properties with an explicit-electron machine learning potential
• Impact of the characteristics of quantum chemical databases on machine learning predictions of tautomerization energies
• A Universal Framework for Accurate and Efficient Geometric Deep Learning of Molecular Systems
• Predicting the Electronic Density Response of Condensed-Phase Systems to Electric Field Perturbations
• Exploring the design space of machine-learning models for quantum chemistry with a fully differentiable framework
• Mean-Field Density Matrix Decompositions
• A chemical bond-based machine learning model for dipole moment: Application to dielectric properties of liquid methanol and ethanol
• Predicting hot-electron free energies from ground-state data
• Machine Learning Inference of Molecular Dipole Moment in Liquid Water
• Predicting second virial coefficients of organic and inorganic compounds using Gaussian Process Regression
• Machine learning based modeling of disordered elemental semiconductors: understanding the atomic structure of a-Si and a-C
• Molecular Dipole Moment Learning via Rotationally Equivariant Gaussian Process Regression with Derivatives in Molecular-orbital-based Machine Learning
• Decomposed Mean-Field Simulations of Local Properties in Condensed Phases
• A Bond-Based Machine Learning Model for Molecular Polarizabilities and A Priori Raman Spectra
• Transferability of the chemical bond-based machine learning model for dipole moment: the GHz to THz dielectric properties of liquid propylene glycol and polypropylene glycol
• Unified theory of atom-centered representations and message-passing machine-learning schemes
• General Learning of the Electric Response of Inorganic Materials
• What is the diatomic molecule with the largest dipole moment?
• Learning Atomic Multipoles: Prediction of the Electrostatic Potential with Equivariant Graph Neural Networks
• Learning electron densities in the condensed phase
• Machine learning of electronic structure and atomistic properties from the external potential