{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T19:45:17Z","timestamp":1792784717374,"version":"4.5.0"},"reference-count":65,"publisher":"American Chemical Society (ACS)","issue":"41","license":[{"start":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T00:00:00Z","timestamp":1791158400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T00:00:00Z","timestamp":1791158400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T00:00:00Z","timestamp":1791158400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-045"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["22233001"],"award-info":[{"award-number":["22233001"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"crossref"}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["22473082"],"award-info":[{"award-number":["22473082"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"crossref"}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["22595405"],"award-info":[{"award-number":["22595405"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,10,15]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Basis set extrapolation is an important strategy for reducing basis set incompleteness error (BSIE) in correlation energy calculations. However, extrapolating correlation energies from double-\u03b6\/triple-\u03b6 (DZ\/TZ) levels to the complete basis set (CBS) limit remains challenging. To address this challenge, we apply the sure independence screening and sparsifying operator (SISSO), a symbolic regression method, to discover formulas for the correction from TZ correlation energies to the near-CBS limit based on information from DZ and TZ calculations. In short, a subset of QM9 containing 834 small molecules with no more than 10 atoms was first constructed for subsequent training and test. After that, eight different input feature sets were constructed by combining the TZ\/DZ correlation energy difference (\u0394ETD) with the basis-function increment (\u0394NBasis-TD), the effective atom count (Neff), and the angular-momentum-resolved shell increments (\u0394Ns,p,d and \u0394Nf), followed by a systematic comparison of the models trained using these feature sets. Among them, the formula obtained using \u0394ETD, \u0394NBasis-TD, and Neff as input features achieved the best balance between internal accuracy and external test set performance. These results demonstrate that symbolic regression can generate compact and interpretable formulas for complete basis set extrapolation of correlation energies, while input features with clear physical interpretation improve the accuracy and transferability of basis set extrapolation.<\/jats:p>","DOI":"10.1021\/acs.jpclett.6c02741","type":"journal-article","created":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T03:01:16Z","timestamp":1791255676000},"page":"11792-11800","source":"Crossref","is-referenced-by-count":0,"title":["Extrapolating\nMolecular Correlation Energies to the\nComplete Basis Set Limit with Symbolic Regression"],"prefix":"10.1021","volume":"17","author":[{"given":"Jia-Yu","family":"Dong","sequence":"first","affiliation":[{"name":"Beijing Normal University , , ,","place":["Beijing, China, 100875"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dong-Yi","family":"Xiao","sequence":"additional","affiliation":[{"name":"Beijing Normal University , , ,","place":["Beijing, China, 100875"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8043-222X","authenticated-orcid":true,"given":"Xiang-Yang","family":"Liu","sequence":"additional","affiliation":[{"name":"Sichuan Normal University , , ,","place":["Chengdu, China, 610068"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1668-465X","authenticated-orcid":true,"given":"Wei-Hai","family":"Fang","sequence":"additional","affiliation":[{"name":"Beijing Normal University , , ,","place":["Beijing, China, 100875"]},{"name":"Beijing Normal University , , ,","place":["Beijing, China, 100875"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9752-1659","authenticated-orcid":true,"given":"Ganglong","family":"Cui","sequence":"additional","affiliation":[{"name":"Beijing Normal University , , ,","place":["Beijing, China, 100875"]},{"name":"Beijing Normal University , , ,","place":["Beijing, China, 100875"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,10,5]]},"reference":[{"key":"2026101508221310900_cit1","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1103\/RevModPhys.79.291","article-title":"Coupled-Cluster Theory in Quantum Chemistry","volume":"79","author":"Bartlett","year":"2007","journal-title":"Rev. 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Phys."},{"key":"2026101508221310900_cit5","doi-asserted-by":"publisher","DOI":"10.1063\/1.3265857","article-title":"Extrapolating MP2\nand CCSD Explicitly Correlated Correlation Energies to the Complete\nBasis Set Limit with First and Second Row Correlation Consistent Basis\nSets","volume":"131","author":"Hill","year":"2009","journal-title":"J. Chem. Phys."},{"key":"2026101508221310900_cit6","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1007\/BF00527669","article-title":"r\n            12-Dependent\nTerms in the Wave Function as Closed Sums\nof Partial Wave Amplitudes for Large\u202fl","volume":"68","author":"Kutzelnigg","year":"1985","journal-title":"Theor. Chim. Acta."},{"key":"2026101508221310900_cit7","doi-asserted-by":"publisher","first-page":"1985","DOI":"10.1063\/1.459921","article-title":"Wave Functions with Terms Linear in the Interelectronic\nCoordinates to Take Care of the Correlation Cusp. I. 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Evolvable Mach."},{"key":"2026101508221310900_cit36","doi-asserted-by":"crossref","first-page":"1562","DOI":"10.1145\/3377929.3398099","article-title":"Operon C++: An\nEfficient Genetic Programming Framework for Symbolic Regression","volume-title":"Proceedings of the 2020 Genetic and Evolutionary Computation\nConference Companion","author":"Burlacu","year":"2020"},{"key":"2026101508221310900_cit37","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2305.01582","article-title":"Interpretable\nMachine Learning for Science with PySR and SymbolicRegression.jl","author":"Cranmer","year":"2023","journal-title":"arXiv"},{"key":"2026101508221310900_cit38","doi-asserted-by":"publisher","first-page":"3932","DOI":"10.1073\/pnas.1517384113","article-title":"Discovering Governing\nEquations from\nData by Sparse Identification of Nonlinear Dynamical Systems","volume":"113","author":"Brunton","year":"2016","journal-title":"Proc. Natl. Acad. Sci. U. S. 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