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Learn.: Sci. Technol."],"published-print":{"date-parts":[[2022,3,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>State-of-the-art machine learning (ML) interatomic potentials use local representations of atomic environments to ensure linear scaling and size-extensivity. This implies a neglect of long-range interactions, most prominently related to electrostatics. To overcome this limitation, we herein present a ML framework for predicting charge distributions and their interactions termed kernel charge equilibration (kQEq). This model is based on classical charge equilibration (QEq) models expanded with an environment-dependent electronegativity. In contrast to previously reported neural network models with a similar concept, kQEq takes advantage of the linearity of both QEq and Kernel Ridge Regression to obtain a closed-form linear algebra expression for training the models. 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As a first application, we show that kQEq can be used to generate accurate and highly data-efficient models for molecular dipole moments.<\/jats:p>","DOI":"10.1088\/2632-2153\/ac568d","type":"journal-article","created":{"date-parts":[[2022,2,18]],"date-time":"2022-02-18T17:11:37Z","timestamp":1645204297000},"page":"015032","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":35,"title":["Kernel charge equilibration: efficient and accurate prediction of molecular dipole moments with a machine-learning enhanced electron density model"],"prefix":"10.1088","volume":"3","author":[{"given":"Carsten G","family":"Staacke","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Simon","family":"Wengert","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Kunkel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G\u00e1bor","family":"Cs\u00e1nyi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karsten","family":"Reuter","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0862-5289","authenticated-orcid":true,"given":"Johannes T","family":"Margraf","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2022,3,11]]},"reference":[{"key":"mlstac568dbib1","doi-asserted-by":"publisher","first-page":"10073","DOI":"10.1021\/acs.chemrev.1c00022","article-title":"Gaussian process regression for materials and molecules","volume":"121","author":"Deringer","year":"2021","journal-title":"Chem. 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