{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T11:01:36Z","timestamp":1790938896496,"version":"4.1.0"},"reference-count":43,"publisher":"AIP Publishing","issue":"13","funder":[{"name":"Advanced Materials-National Science and Technology Major Project","award":["2024ZD0606900"],"award-info":[{"award-number":["2024ZD0606900"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12274171"],"award-info":[{"award-number":["12274171"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12674296"],"award-info":[{"award-number":["12674296"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2023YFA1406200"],"award-info":[{"award-number":["2023YFA1406200"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2023YFB3003001"],"award-info":[{"award-number":["2023YFB3003001"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CHE-2154760"],"award-info":[{"award-number":["CHE-2154760"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["OAC-2321103"],"award-info":[{"award-number":["OAC-2321103"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,10,7]]},"abstract":"<jats:p>We present a machine-learning framework, density-independent mapping for exchange\u2013correlation, for incorporating XC effects into density functional theory via a density-independent mapping from the external potential to the XC potential. By predicting the ground-state XC potential in a one-shot manner and holding it fixed throughout the self-consistent field (SCF) procedure, the approach entirely eliminates the need to evaluate the XC potential on the iteratively updated electron density, thereby enhancing numerical stability and efficiency. The model is implemented using kernel ridge regression and trained on a set of small neutral closed-shell molecular systems, representative of common chemical bonding motifs, achieving the predictive accuracy of hybrid functionals\u2014with energy errors on the order of 10\u22123 kcal\/mol\u2014while bypassing expensive, iterative density-dependent XC evaluations during SCF. Further validation through infrared spectral predictions, molecular dynamics simulations, and structural perturbation tests demonstrates robust performance and reasonable transferability. This work establishes that machine-learned density-independent mapping represents a practical pathway for designing stable and transferable XC potentials.<\/jats:p>","DOI":"10.1063\/5.0341316","type":"journal-article","created":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T10:50:14Z","timestamp":1790938214000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Stable and transferable exchange\u2013correlation potentials via machine-learned density-independent mapping"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-2992-8411","authenticated-orcid":false,"given":"Min","family":"Chen","sequence":"first","affiliation":[{"name":"Key Laboratory of Material Simulation Methods & Software of Ministry of Education, College of Physics, Jilin University 1 , Changchun 130012,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7782-5428","authenticated-orcid":false,"given":"Yu","family":"Xie","sequence":"additional","affiliation":[{"name":"Key Laboratory of Material Simulation Methods & Software of Ministry of Education, College of Physics, Jilin University 1 , Changchun 130012,","place":["China"]},{"name":"Key Laboratory of Physics and Technology for Advanced Batteries of Ministry of Education, Jilin University 2 , Changchun 130012,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8294-7481","authenticated-orcid":false,"given":"Michele","family":"Pavanello","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Rutgers University 3 , Newark, New Jersey 07102,","place":["USA"]},{"name":"Department of Physics, Rutgers University 4 , Newark, New Jersey 07102,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1612-5292","authenticated-orcid":false,"given":"Wenhui","family":"Mi","sequence":"additional","affiliation":[{"name":"Key Laboratory of Material Simulation Methods & Software of Ministry of Education, College of Physics, Jilin University 1 , Changchun 130012,","place":["China"]},{"name":"State Key Laboratory of High Pressure and Superhard Materials, College of Physics, Jilin University 5 , Changchun 130012,","place":["China"]},{"name":"International Center of Future Science, Jilin University 6 , Changchun 130012,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2215-0926","authenticated-orcid":false,"given":"Xuecheng","family":"Shao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Material Simulation Methods & Software of Ministry of Education, College of Physics, Jilin University 1 , Changchun 130012,","place":["China"]},{"name":"State Key Laboratory of High Pressure and Superhard Materials, College of Physics, Jilin University 5 , Changchun 130012,","place":["China"]},{"name":"International Center of Future Science, Jilin University 6 , Changchun 130012,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,2]]},"reference":[{"key":"2026100206500723100_c1","doi-asserted-by":"publisher","first-page":"1253","DOI":"10.1103\/revmodphys.71.1253","article-title":"Nobel Lecture: Electronic structure of matter\u2014Wave functions and density functionals","volume":"71","year":"1999","journal-title":"Rev. Mod. Phys."},{"key":"2026100206500723100_c2","doi-asserted-by":"publisher","first-page":"A1133","DOI":"10.1103\/physrev.140.a1133","article-title":"Self-consistent equations including exchange and correlation effects","volume":"140","year":"1965","journal-title":"Phys. Rev."},{"key":"2026100206500723100_c3","doi-asserted-by":"publisher","first-page":"13244","DOI":"10.1103\/physrevb.45.13244","article-title":"Accurate and simple analytic representation of the electron-gas correlation energy","volume":"45","year":"1992","journal-title":"Phys. Rev. B"},{"key":"2026100206500723100_c4","doi-asserted-by":"publisher","first-page":"8800","DOI":"10.1103\/PhysRevB.33.8800","article-title":"Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation","volume":"33","year":"1986","journal-title":"Phys. Rev. B"},{"key":"2026100206500723100_c5","doi-asserted-by":"publisher","first-page":"3865","DOI":"10.1103\/physrevlett.77.3865","article-title":"Generalized gradient approximation made simple","volume":"77","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"2026100206500723100_c6","doi-asserted-by":"publisher","first-page":"3098","DOI":"10.1103\/physreva.38.3098","article-title":"Density-functional exchange-energy approximation with correct asymptotic behavior","volume":"38","year":"1988","journal-title":"Phys. Rev. A"},{"key":"2026100206500723100_c7","doi-asserted-by":"publisher","first-page":"036402","DOI":"10.1103\/physrevlett.115.036402","article-title":"Strongly constrained and appropriately normed semilocal density functional","volume":"115","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"2026100206500723100_c8","doi-asserted-by":"publisher","first-page":"8208","DOI":"10.1021\/acs.jpclett.0c02405","article-title":"Accurate and numerically efficient r2SCAN meta-generalized gradient approximation","volume":"11","year":"2020","journal-title":"J.\u00a0Phys. Chem. Lett."},{"key":"2026100206500723100_c9","doi-asserted-by":"publisher","first-page":"244103","DOI":"10.1063\/1.3521275","article-title":"Nonlocal van der Waals density functional: The simpler the better","volume":"133","year":"2010","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100206500723100_c10","doi-asserted-by":"publisher","first-page":"041005","DOI":"10.1103\/physrevx.6.041005","article-title":"Versatile van der waals density functional based on a meta-generalized gradient approximation","volume":"6","year":"2016","journal-title":"Phys. Rev. X"},{"key":"2026100206500723100_c11","doi-asserted-by":"publisher","first-page":"5648","DOI":"10.1063\/1.464913","article-title":"Density-functional thermochemistry. III. The role of exact exchange","volume":"98","year":"1993","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100206500723100_c12","doi-asserted-by":"publisher","first-page":"6158","DOI":"10.1063\/1.478522","article-title":"Toward reliable density functional methods without adjustable parameters: The PBE0 model","volume":"110","year":"1999","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100206500723100_c13","doi-asserted-by":"publisher","first-page":"11623","DOI":"10.1021\/j100096a001","article-title":"Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields","volume":"98","year":"1994","journal-title":"J.\u00a0Phys. Chem."},{"key":"2026100206500723100_c14","doi-asserted-by":"publisher","first-page":"034108","DOI":"10.1063\/1.2148954","article-title":"Semiempirical hybrid density functional with perturbative second-order correlation","volume":"124","year":"2006","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100206500723100_c15","doi-asserted-by":"publisher","first-page":"2315","DOI":"10.1080\/00268976.2017.1333644","article-title":"Thirty years of density functional theory in computational chemistry: An overview and extensive assessment of 200 density functionals","volume":"115","year":"2017","journal-title":"Mol. Phys."},{"key":"2026100206500723100_c16","doi-asserted-by":"publisher","first-page":"28700","DOI":"10.1039\/d2cp02827a","article-title":"DFT exchange: Sharing perspectives on the workhorse of quantum chemistry and materials science","volume":"24","year":"2022","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026100206500723100_c17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1063\/1.1390175","article-title":"Jacob\u2019s ladder of density functional approximations for the exchange-correlation energy","volume":"577","year":"2001","journal-title":"AIP Conf. Proc."},{"key":"2026100206500723100_c18","unstructured":"G.\n            Luise\n          , C.-W.Huang, T.Vogels, D. P.Kooi, S.Ehlert, S.Lanius, K. J. H.Giesbertz, A.Karton, D.Gunceler, M.Stanley, W. P.Bruinsma, L.Huang, X.Wei, J. G.Torres, A.Katbashev, R. C.Zavaleta, B.M\u00e1t\u00e9, S.-O.Kaba, R.Sordillo, Y.Chen, D. B.Williams-Young, C. M.Bishop, J.Hermann, R.van den Berg, and P.Gori-Giorgi, \u201cAccurate and scalable exchange-correlation with deep learning,\u201d arXiv:2506.14665 (2025)."},{"key":"2026100206500723100_c19","doi-asserted-by":"publisher","first-page":"1385","DOI":"10.1126\/science.abj6511","article-title":"Pushing the frontiers of density functionals by solving the fractional electron problem","volume":"374","year":"2021","journal-title":"Science"},{"key":"2026100206500723100_c20","doi-asserted-by":"publisher","first-page":"126403","DOI":"10.1103\/physrevlett.127.126403","article-title":"Learning the exchange-correlation functional from nature with fully differentiable density functional theory","volume":"127","year":"2021","journal-title":"Phys. Rev. Lett."},{"key":"2026100206500723100_c21","doi-asserted-by":"publisher","first-page":"eady8962","DOI":"10.1126\/sciadv.ady8962","article-title":"Learning local and semi-local density functionals from exact exchange-correlation potentials and energies","volume":"11","year":"2025","journal-title":"Sci. Adv."},{"key":"2026100206500723100_c22","doi-asserted-by":"publisher","first-page":"036401","DOI":"10.1103\/physrevlett.126.036401","article-title":"Kohn\u2013Sham equations as regularizer: Building prior knowledge into machine-learned physics","volume":"126","year":"2021","journal-title":"Phys. Rev. Lett."},{"key":"2026100206500723100_c23","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1038\/s41467-020-20471-y","article-title":"Pure non-local machine-learned density functional theory for electron correlation","volume":"12","year":"2021","journal-title":"Nat. Commun."},{"key":"2026100206500723100_c24","doi-asserted-by":"publisher","first-page":"2540","DOI":"10.1021\/acs.jpclett.2c00371","article-title":"How well does Kohn\u2013Sham regularizer work for weakly correlated systems?","volume":"13","year":"2022","journal-title":"J.\u00a0Phys. Chem. Lett."},{"key":"2026100206500723100_c25","doi-asserted-by":"publisher","first-page":"3509","DOI":"10.1038\/s41467-020-17265-7","article-title":"Machine learning accurate exchange and correlation functionals of the electronic density","volume":"11","year":"2020","journal-title":"Nat. Commun."},{"key":"2026100206500723100_c26","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1038\/s41524-020-0310-0","article-title":"Completing density functional theory by machine learning hidden messages from molecules","volume":"6","year":"2020","journal-title":"npj Comput. Mater."},{"key":"2026100206500723100_c27","doi-asserted-by":"publisher","first-page":"2180","DOI":"10.1021\/acs.jctc.1c00904","article-title":"CIDER: An expressive, nonlocal feature set for machine learning density functionals with exact constraints","volume":"18","year":"2022","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026100206500723100_c28","doi-asserted-by":"publisher","first-page":"075130","DOI":"10.1103\/physrevb.110.075130","article-title":"Nonlocal machine-learned exchange functional for molecules and solids","volume":"110","year":"2024","journal-title":"Phys. Rev. B"},{"key":"2026100206500723100_c29","doi-asserted-by":"publisher","first-page":"11306","DOI":"10.1038\/s41467-025-66450-z","article-title":"Real-space machine learning of correlation density functionals","volume":"16","year":"2025","journal-title":"Nat. Commun."},{"key":"2026100206500723100_c30","doi-asserted-by":"publisher","first-page":"241737","DOI":"10.1063\/1.5029279","article-title":"Neural-network Kohn\u2013Sham exchange-correlation potential and its out-of-training transferability","volume":"148","year":"2018","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100206500723100_c31","doi-asserted-by":"publisher","first-page":"872","DOI":"10.1038\/s41467-017-00839-3","article-title":"Bypassing the Kohn\u2013Sham equations with machine learning","volume":"8","year":"2017","journal-title":"Nat. Commun."},{"key":"2026100206500723100_c32","doi-asserted-by":"publisher","first-page":"6281","DOI":"10.1038\/s41467-023-41953-9","article-title":"Machine learning electronic structure methods based on the one-electron reduced density matrix","volume":"14","year":"2023","journal-title":"Nat. Commun."},{"key":"2026100206500723100_c33","doi-asserted-by":"publisher","first-page":"034119","DOI":"10.1063\/5.0332678","article-title":"Machine learning of electronic structure and atomistic properties from the external potential","volume":"165","year":"2026","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100206500723100_c34","doi-asserted-by":"publisher","first-page":"3764","DOI":"10.1103\/physrevb.53.3764","article-title":"Generalized Kohn\u2013Sham schemes and the band-gap problem","volume":"53","year":"1996","journal-title":"Phys. Rev. B"},{"key":"2026100206500723100_c35","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1103\/physrev.81.385","article-title":"A simplification of the Hartree\u2013Fock method","volume":"81","year":"1951","journal-title":"Phys. Rev."},{"key":"2026100206500723100_c36","doi-asserted-by":"publisher","first-page":"1200","DOI":"10.1139\/p80-159","article-title":"Accurate spin-dependent electron liquid correlation energies for local spin density calculations: A critical analysis","volume":"58","year":"1980","journal-title":"Can. J. Phys."},{"key":"2026100206500723100_c37","doi-asserted-by":"publisher","first-page":"785","DOI":"10.1103\/physrevb.37.785","article-title":"Development of the Colle\u2013Salvetti correlation-energy formula into a functional of the electron density","volume":"37","year":"1988","journal-title":"Phys. Rev. B"},{"key":"2026100206500723100_c38","doi-asserted-by":"publisher","first-page":"e1340","DOI":"10.1002\/wcms.1340","article-title":"PySCF: The Python-based simulations of chemistry framework","volume":"8","year":"2018","journal-title":"WIREs Comput. Mol. Sci."},{"key":"2026100206500723100_c39","doi-asserted-by":"publisher","first-page":"724","DOI":"10.1063\/1.1674902","article-title":"Self-consistent molecular-orbital methods. IX. An extended Gaussian-type basis for molecular-orbital studies of organic molecules","volume":"54","year":"1971","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100206500723100_c40","doi-asserted-by":"publisher","first-page":"2257","DOI":"10.1063\/1.1677527","article-title":"Self-consistent molecular orbital methods. XII. Further extensions of Gaussian-type basis sets for use in molecular orbital studies of organic molecules","volume":"56","year":"1972","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100206500723100_c41","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1109\/5992.998641","article-title":"An object-oriented scripting interface to a legacy electronic structure code","volume":"4","year":"2002","journal-title":"Comput. Sci. Eng."},{"key":"2026100206500723100_c42"},{"key":"2026100206500723100_c43","doi-asserted-by":"publisher","first-page":"027101","DOI":"10.1088\/0256-307x\/40\/2\/027101","article-title":"A time-dependent random state approach for large-scale density functional calculations","volume":"40","year":"2023","journal-title":"Chin. Phys. Lett."}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0341316\/21159815\/134113_1_5.0341316.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0341316\/21159815\/134113_1_5.0341316.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T10:50:17Z","timestamp":1790938217000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/165\/13\/134113\/3405830\/Stable-and-transferable-exchange-correlation"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,2]]},"references-count":43,"journal-issue":{"issue":"13","published-print":{"date-parts":[[2026,10,7]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0341316","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,10,7]]},"published":{"date-parts":[[2026,10,2]]},"article-number":"134113"}}