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For the electrostatic interactions, point charges (PCs) and machine learning (ML)\u2010based minimally distributed charges (MDCM) fitted to the molecular electrostatic potential are evaluated together with electrostatics based on the Coulomb integral. The impact of explicitly including second\u2010order terms is investigated by adding a fragment molecular orbital (FMO)\u2010derived polarization energy to an existing force field, in this case CHARMM. It is demonstrated that anisotropic electrostatics reduce the RMSE for water (by 1.4 kcal\/mol), CHCl (by 0.8 kcal\/mol) and for solvated Cl clusters (by 0.4 kcal\/mol). An additional polarization term can be neglected for CHCl but further improves the models for pure water (by 1.0 kcal\/mol) and hydrated Cl (by 0.4 kcal\/mol), and is key for solvated K, reducing the RMSE by 2.3 kcal\/mol. A 12\u20106 Lennard\u2010Jones functional form performs satisfactorily with PC and MDCM electrostatics, but is not appropriate for descriptions that account for the electrostatic penetration energy. The importance of many\u2010body contributions is assessed by comparing a strictly 2\u2010body approach with self\u2010consistent reference data. Two\u2010body interactions suffice for CHCl whereas water and solvated K and Cl ions require explicit many\u2010body corrections. Finally, a many\u2010body\u2010corrected dimer potential energy surface exceeds the accuracy attained using a conventional empirical force field, potentially reaching that of an FMO calculation. The present work systematically quantifies which terms improve the performance of an existing force field and what reference data to use for parametrizing these terms in a tractable fashion for ML fitting of pure and heterogeneous systems.<\/jats:p>","DOI":"10.1002\/jcc.27367","type":"journal-article","created":{"date-parts":[[2024,5,2]],"date-time":"2024-05-02T07:46:20Z","timestamp":1714635980000},"page":"1899-1913","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Systematic improvement of empirical energy functions in the era of machine learning"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1561-1635","authenticated-orcid":false,"given":"Mike","family":"Devereux","sequence":"first","affiliation":[{"name":"Department of Chemistry University of Basel  Basel Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eric D.","family":"Boittier","sequence":"additional","affiliation":[{"name":"Department of Chemistry University of Basel  Basel Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7930-8806","authenticated-orcid":false,"given":"Markus","family":"Meuwly","sequence":"additional","affiliation":[{"name":"Department of Chemistry University of Basel  Basel Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2024,5,2]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1187409"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1021\/jp910674d"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jctc.9b00181"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1021\/ct400863t"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.98.146401"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jctc.2c00029"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jctc.0c00121"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/jcc.540040211"},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/jcc.21287"},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0151266"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.104.136403"},{"key":"e_1_2_7_13_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.96.014112"},{"key":"e_1_2_7_14_1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0067565"},{"key":"e_1_2_7_15_1","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpcb.2c04698"},{"key":"e_1_2_7_16_1","volume":"14","author":"Bore S. 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