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Analytical gradients for molecular-orbital-based machine learning

Lee, Sebastian J. R. and Husch, Tamara and Ding, Feizhi and Miller, Thomas F., III (2021) Analytical gradients for molecular-orbital-based machine learning. Journal of Chemical Physics, 154 (12). Art. No. 124120. ISSN 0021-9606. doi:10.1063/5.0040782.

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Molecular-orbital-based machine learning (MOB-ML) enables the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. Here, we present the derivation, implementation, and numerical demonstration of MOB-ML analytical nuclear gradients, which are formulated in a general Lagrangian framework to enforce orthogonality, localization, and Brillouin constraints on the molecular orbitals. The MOB-ML gradient framework is general with respect to the regression technique (e.g., Gaussian process regression or neural networks) and the MOB feature design. We show that MOB-ML gradients are highly accurate compared to other ML methods on the ISO17 dataset while only being trained on energies for hundreds of molecules compared to energies and gradients for hundreds of thousands of molecules for the other ML methods. The MOB-ML gradients are also shown to yield accurate optimized structures at a computational cost for the gradient evaluation that is comparable to a density-corrected density functional theory calculation.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Lee, Sebastian J. R.0000-0001-7006-9378
Husch, Tamara0000-0002-2880-2481
Miller, Thomas F., III0000-0002-1882-5380
Additional Information:© 2021 Published under license by AIP Publishing. Submitted: 16 December 2020; Accepted: 2 March 2021; Published Online: 25 March 2021. This work was supported, in part, by 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). S.J.R.L. thanks the Molecular Software Sciences Institute (MolSSI) for a MolSSI investment fellowship. T.H. acknowledges funding through an Early Post-Doc Mobility Fellowship by the Swiss National Science Foundation (Award No. P2EZP2_184234). 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 No. DE-AC02-05CH11231. Data Availability: The data that support the findings of this study are available within the article and its supplementary material. The dataset used in Table I and Fig. 1 is available from Ref. 60. The dataset used in Fig. 2 is available from Ref. 60. The dataset used in Table II and Fig. 3 is available from Ref. 14.
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-12-2-0023
Department of Energy (DOE)DE-SC0019390
Caltech De Logi FundUNSPECIFIED
Camille and Henry Dreyfus FoundationML-20-196
Molecular Software Sciences InstituteUNSPECIFIED
Swiss National Science Foundation (SNSF)P2EZP2_184234
Department of Energy (DOE)DE-AC02-05CH11231
Issue or Number:12
Record Number:CaltechAUTHORS:20210119-161656738
Persistent URL:
Official Citation:Analytical gradients for molecular-orbital-based machine learning. J. Chem. Phys. 154, 124120 (2021); doi: 10.1063/5.0040782
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107580
Deposited By: George Porter
Deposited On:20 Jan 2021 15:02
Last Modified:06 Apr 2021 17:53

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