Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Molecular electrostatic potentials from machine learning models for dipole and quadrupole predictions

Kadri Muuga, Lisanne Knijff, Chao Zhang

TL;DR

This work investigates whether machine-learning models can reproduce the molecular electrostatic potential (MEP) by learning multipole moments, focusing on the dipole and quadrupole. Extending the PiNet2 framework, the authors train seven dipole/quadrupole models on QM9 and SPICE and evaluate MEP fidelity by comparing ML-derived charges against MK ESP references, all without direct MEP training. They find that including quadrupole information markedly improves MEP recovery, with the AC-DQ-dw100 variant offering the best balance between dipole and quadrupole accuracy across datasets. The results suggest that the quadrupole moment is a particularly effective, compact target for rapid ML-based access to the MEP, enabling efficient solvent and electrolyte design in large chemical spaces.

Abstract

The molecular electrostatic potential (MEP) is a key quantity for describing and predicting intermolecular and ion-molecule interactions. Here, we assess the ability of machine-learning (ML) models to infer the MEP, based on the equivariant graph-convolutional neural network architecture PiNet2 and trained on dipole and quadrupole moments. For the established QM9 dataset, we find that including the quadrupole contribution in the ML models substantially improves their ability to recover the MEP compared to dipole-only models. This trend is confirmed on the SPICE dataset, which spans a much broader region of organic chemical space. Together, this study underscores the central role of the quadrupole moment as a fitting target for ML models aiming at rapid access to the MEP.

Molecular electrostatic potentials from machine learning models for dipole and quadrupole predictions

TL;DR

This work investigates whether machine-learning models can reproduce the molecular electrostatic potential (MEP) by learning multipole moments, focusing on the dipole and quadrupole. Extending the PiNet2 framework, the authors train seven dipole/quadrupole models on QM9 and SPICE and evaluate MEP fidelity by comparing ML-derived charges against MK ESP references, all without direct MEP training. They find that including quadrupole information markedly improves MEP recovery, with the AC-DQ-dw100 variant offering the best balance between dipole and quadrupole accuracy across datasets. The results suggest that the quadrupole moment is a particularly effective, compact target for rapid ML-based access to the MEP, enabling efficient solvent and electrolyte design in large chemical spaces.

Abstract

The molecular electrostatic potential (MEP) is a key quantity for describing and predicting intermolecular and ion-molecule interactions. Here, we assess the ability of machine-learning (ML) models to infer the MEP, based on the equivariant graph-convolutional neural network architecture PiNet2 and trained on dipole and quadrupole moments. For the established QM9 dataset, we find that including the quadrupole contribution in the ML models substantially improves their ability to recover the MEP compared to dipole-only models. This trend is confirmed on the SPICE dataset, which spans a much broader region of organic chemical space. Together, this study underscores the central role of the quadrupole moment as a fitting target for ML models aiming at rapid access to the MEP.
Paper Structure (16 sections, 8 equations, 5 figures, 8 tables)

This paper contains 16 sections, 8 equations, 5 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. ML dipole and quadrupole models
  4. The QM9 dataset and model training
  5. The SPICE dataset and model training
  6. Assessing MEP from ML models
  7. Results
  8. Performance of ML models for dipole and quadrupole predictions on QM9
  9. Inference of atomic charges on QM9
  10. Inference of electrostatic potentials on QM9
  11. Extension to the SPICE dataset
  12. Conclusion and outlook
  13. Traceless quadrupole definitions
  14. Network parameters
  15. Error metrics for the charge distribution comparisons
  16. ...and 1 more sections

Figures (5)

  • Figure 1: Density distributions of atomic charges predicted by different PiNet2-based ML models on the QM9 validation set.
  • Figure 2: Electrostatic potential of propylene carbonate calculated on the 0.001 a.u. density isosurface. The bottom panel shows the potential from atomic charges predicted with PiNet2-based dipole and quadrupole models.
  • Figure 3: Electrostatic potential of fluoropropylene carbonate calculated on the 0.001 a.u. density isosurface. The bottom panel shows the potential from atomic charges predicted with PiNet2-based dipole and quadrupole models.
  • Figure 4: a) Embedding of the QM9 and SPICE datasets using Morgan structural fingerprints. The validation sets are lighter in colour and were mapped on top. Molecules were mapped according to similarity, with more similar structures clustered together; b) The comparison of the molecular weights (MWs) between two datasets; c) The comparison of the total dipole distributions between these two datasets; c) The comparison of the total quadrupole distributions between these two datasets.
  • Figure D1: The correlation of (a) dipole and (b) quadrupole magnitudes obtained from MK ESP charges with DFT reference values for the QM9 dataset. The dipole and quadrupole moments were calculated from ESP charges using Equations \ref{['mu']} and \ref{['Q']}, respectively. All properties are reported at the same level of theory as used in the original QM9 dataset. The per-tensor-component dipole MAE from ESP charges is 0.020 D and that for quadrupole is 0.323 D$\cdot$Å.