{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:45:08Z","timestamp":1762177508327,"version":"3.41.2"},"reference-count":94,"publisher":"AIP Publishing","issue":"18","license":[{"start":{"date-parts":[[2022,5,9]],"date-time":"2022-05-09T00:00:00Z","timestamp":1652054400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2022,5,9]],"date-time":"2022-05-09T00:00:00Z","timestamp":1652054400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["772834","957189"],"award-info":[{"award-number":["772834","957189"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2022,5,14]]},"abstract":"<jats:p>We propose the relaxation of geometries throughout chemical compound space using alchemical perturbation density functional theory (APDFT). APDFT refers to perturbation theory involving changes in nuclear charges within approximate solutions to Schr\u00f6dinger\u2019s equation. We give an analytical formula to calculate the mixed second order energy derivatives with respect to both nuclear charges and nuclear positions (named \u201calchemical force\u201d) within the restricted Hartree\u2013Fock case. We have implemented and studied the formula for its use in geometry relaxation of various reference and target molecules. We have also analyzed the convergence of the alchemical force perturbation series as well as basis set effects. Interpolating alchemically predicted energies, forces, and Hessian to a Morse potential yields more accurate geometries and equilibrium energies than when performing a standard Newton\u2013Raphson step. Our numerical predictions for small molecules including BF, CO, N2, CH4, NH3, H2O, and HF yield mean absolute errors of equilibrium energies and bond lengths smaller than 10 mHa and 0.01 bohr for fourth order APDFT predictions, respectively. Our alchemical geometry relaxation still preserves the combinatorial efficiency of APDFT: Based on a single coupled perturbed Hartree\u2013Fock derivative for benzene, we provide numerical predictions of equilibrium energies and relaxed structures of all 17 iso-electronic charge-neutral BN-doped mutants with averaged absolute deviations of \u223c27 mHa and \u223c0.12 bohr, respectively.<\/jats:p>","DOI":"10.1063\/5.0085817","type":"journal-article","created":{"date-parts":[[2022,4,12]],"date-time":"2022-04-12T21:06:33Z","timestamp":1649797593000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":11,"title":["Alchemical geometry relaxation"],"prefix":"10.1063","volume":"156","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0322-8292","authenticated-orcid":false,"given":"Giorgio","family":"Domenichini","sequence":"first","affiliation":[{"name":"Faculty of Physics, University of Vienna 1 , Kolingasse 14-16, 1090 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7419-0466","authenticated-orcid":false,"given":"O. Anatole","family":"von Lilienfeld","sequence":"additional","affiliation":[{"name":"Faculty of Physics, University of Vienna 1 , Kolingasse 14-16, 1090 Vienna, Austria"},{"name":"Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials (MARVEL), Department of Chemistry, University of Basel 2 , Klingelbergstrasse 80, 4056 Basel, Switzerland"},{"name":"Machine Learning Group, Technische Universitaet Berlin 3 , 10587 Berlin, Germany"},{"name":"Berlin Institute for the Foundations of Learning and Data 4 , 10587 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2022,5,9]]},"reference":[{"key":"2023122821080382800_c1","doi-asserted-by":"publisher","first-page":"823","DOI":"10.1038\/432823a","article-title":"Chemical space","volume":"432","year":"2004","journal-title":"Nature"},{"key":"2023122821080382800_c2","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1038\/549445a","article-title":"The drug-maker\u2019s guide to the galaxy","volume":"549","year":"2017","journal-title":"Nature"},{"key":"2023122821080382800_c3","doi-asserted-by":"publisher","first-page":"1676","DOI":"10.1002\/qua.24375","article-title":"First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties","volume":"113","year":"2013","journal-title":"Int. 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