A Caltech Library Service

Molecular dipole moment learning via rotationally equivariant derivative kernels in molecular-orbital-based machine learning

Sun, Jiace and Cheng, Lixue and Miller, Thomas F. (2022) Molecular dipole moment learning via rotationally equivariant derivative kernels in molecular-orbital-based machine learning. Journal of Chemical Physics, 157 (10). Art. No. 104109. ISSN 0021-9606. doi:10.1063/5.0101280.

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item:


This study extends the accurate and transferable molecular-orbital-based machine learning (MOB-ML) approach to modeling the contribution of electron correlation to dipole moments at the cost of Hartree–Fock computations. A MOB pairwise decomposition of the correlation part of the dipole moment is applied, and these pair dipole moments could be further regressed as a universal function of MOs. The dipole MOB features consist of the energy MOB features and their responses to electric fields. An interpretable and rotationally equivariant derivative kernel for Gaussian process regression (GPR) is introduced to learn the dipole moment more efficiently. The proposed problem setup, feature design, and ML algorithm are shown to provide highly accurate models for both dipole moments and energies on water and 14 small molecules. To demonstrate the ability of MOB-ML to function as generalized density-matrix functionals for molecular dipole moments and energies of organic molecules, we further apply the proposed MOB-ML approach to train and test the molecules from the QM9 dataset. The application of local scalable GPR with Gaussian mixture model unsupervised clustering GPR scales up MOB-ML to a large-data regime while retaining the prediction accuracy. In addition, compared with the literature results, MOB-ML provides the best test mean absolute errors of 4.21 mD and 0.045 kcal/mol for dipole moment and energy models, respectively, when training on 110 000 QM9 molecules. The excellent transferability of the resulting QM9 models is also illustrated by the accurate predictions for four different series of peptides.

Item Type:Article
Related URLs:
URLURL TypeDescription ItemDiscussion Paper
Sun, Jiace0000-0002-0566-2084
Cheng, Lixue0000-0002-7329-0585
Miller, Thomas F.0000-0002-1882-5380
Alternate Title:Molecular Dipole Moment Learning via Rotationally Equivariant Gaussian Process Regression with Derivatives in Molecular-orbital-based Machine Learning
Additional Information:We thank Vignesh Bhethanabotla for his help in improving the quality of the manuscript. T.F.M. acknowledges support from the U.S. Army Research Laboratory (Grant No. W911NF-12-2-0023), the U.S. Department of Energy (Grant No. DE-SC0019390), the Caltech DeLogi Fund, and the Camille and Henry Dreyfus Foundation (Award No. ML-20-196). Computational resources were provided by the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the DOE Office of Science under contract Grant No. DE-AC02-05CH11231.
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-12-2-0023
Department of Energy (DOE)DE-SC0019390
Caltech DeLogi FundUNSPECIFIED
Camille and Henry Dreyfus FoundationML-20-196
Department of Energy (DOE)DE-AC02-05CH11231
Issue or Number:10
Record Number:CaltechAUTHORS:20221010-454096500.3
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117290
Deposited By: Research Services Depository
Deposited On:14 Oct 2022 22:24
Last Modified:17 Oct 2022 14:22

Repository Staff Only: item control page