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. 2022 Jan 20;13:414. doi: 10.1038/s41467-022-28041-0

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 1 — a FF vs. QM energies for all the dimers in our training sets. The functional form reproduces the lower energy conformations very well and is designed to permit a larger error in less important high-energy high electron overlap regions. b the distribution of errors for our training dimer sets. The MAE of errors are 0.17 kcal/mol for all, 0.19 kcal/mol for dimers with water (total number of dimers = 36,309), and 0.16 kcal/mol for dimers with alkanes (total number of dimers = 25,986): A specific system (ethanol-water) provides a more detailed illustration of model energies and their correspondence with QM. c, d dissociation curves for primary (c) and secondary (d) minima of the ethanol-water dimer. QM energies are solid lines and FF values are filled circles. The colors designate the energy components: electrostatics (ES), exchange-repulsion (EX), dispersion (DS) and induction (IND). The agreements for the total energy and for each component are excellent. e–g Error distributions for the ethanol-water dimer: e is analogous to a; f is a difference plot offering a more detailed view and is projected onto (g) the error distribution. The MAE for the errors in this system is 0.08 kcal/mol.