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While recent machine learning (ML) integrations have accelerated determinant selection, existing regression and classification approaches suffer from a fundamental objective-loss mismatch: they evaluate the importance of determinants in isolation without explicitly accounting for their relative importance ranking. Here, we introduce ranking configuration interaction (RCI), a novel ML-supported SCI framework that reframes determinant selection as a pairwise ranking problem. Building upon a Transformer-based architecture to capture complex, nonlocal orbital dependencies, RCI progressively optimizes the partial ordering of determinants. By doing so, RCI aligns the training objective more closely with the intrinsic ranking nature of SCI. Extensive benchmarks across both plane-wave and Gaussian basis sets, including the molecules N2, CO, H2O, NH3, and C2, demonstrate the efficiency of RCI. Compared to previously reported classification baselines, RCI consistently accelerates convergence\u2500reducing overall computational time by 23% to over 50% depending on the system and requiring only 55% of the determinant count in representative cases such as N2 and CO. Furthermore, RCI exhibits robust performance and reaches chemical accuracy on the highly challenging iron\u2013sulfur cluster using only 12% of the full CI space. Notably, RCI outperforms recent regression-based SCI methods by delivering a more than 15% improvement in accuracy at comparable determinant counts. RCI also demonstrates higher efficiency than heat-bath CI on the strongly correlated chromium dimer, yielding a compact and accurate wave function. This pairwise learning-to-rank model provides a lightweight and modular plugin that can be seamlessly incorporated into other supervised learning frameworks.<\/jats:p>","DOI":"10.1021\/acs.jctc.6c00937","type":"journal-article","created":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T17:01:58Z","timestamp":1787245318000},"page":"8797-8812","source":"Crossref","is-referenced-by-count":0,"title":["Learning to Rank\nfor Selected Configuration Interaction"],"prefix":"10.1021","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0590-6608","authenticated-orcid":true,"given":"Wan","family":"Nie","sequence":"first","affiliation":[{"name":"City University of Hong Kong , , ,","place":["Hong Kong SAR, China, 999077"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2374-3977","authenticated-orcid":true,"given":"Songwei","family":"Liu","sequence":"additional","affiliation":[{"name":"The Chinese University of Hong Kong , , ,","place":["Hong Kong SAR, China, 999077"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9452-0298","authenticated-orcid":true,"given":"Yingying","family":"Yu","sequence":"additional","affiliation":[{"name":"City University of Hong Kong , , ,","place":["Hong Kong SAR, China, 999077"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhiwen","family":"Wang","sequence":"additional","affiliation":[{"name":"City University of Hong Kong , , ,","place":["Hong Kong SAR, China, 999077"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8701-9297","authenticated-orcid":true,"given":"Jun","family":"Yang","sequence":"additional","affiliation":[{"name":"The University of Hong Kong , , ,","place":["Hong Kong SAR, China, 999077"]},{"name":"Hong Kong Quantum AI Lab Limited , ,","place":["Hong Kong SAR, China, 999077"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,8,20]]},"reference":[{"key":"2026090808100120600_cit1","doi-asserted-by":"publisher","first-page":"5745","DOI":"10.1063\/1.1679199","article-title":"Iterative perturbation calculations\nof ground and excited state energies from multiconfigurational zeroth-order\nwavefunctions","volume":"58","author":"Huron","year":"1973","journal-title":"J. Chem. Phys."},{"key":"2026090808100120600_cit2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4955109","article-title":"A deterministic\nalternative to the full configuration interaction quantum Monte Carlo\nmethod","volume":"145","author":"Tubman","year":"2016","journal-title":"J. Chem. Phys."},{"key":"2026090808100120600_cit3","doi-asserted-by":"publisher","first-page":"2139","DOI":"10.1021\/acs.jctc.8b00536","article-title":"Modern approaches to exact diagonalization and selected\nconfiguration interaction with the adaptive sampling CI method","volume":"16","author":"Tubman","year":"2020","journal-title":"J. Chem. Theory Comput."},{"key":"2026090808100120600_cit4","doi-asserted-by":"publisher","first-page":"1561","DOI":"10.1021\/acs.jctc.5b01170","article-title":"Efficient heat-bath\nsampling in Fock\nspace","volume":"12","author":"Holmes","year":"2016","journal-title":"J. Chem. Theory Comput."},{"key":"2026090808100120600_cit5","doi-asserted-by":"publisher","first-page":"3674","DOI":"10.1021\/acs.jctc.6b00407","article-title":"Heat-bath\nconfiguration interaction:\nAn efficient selected configuration interaction algorithm inspired\nby heat-bath sampling","volume":"12","author":"Holmes","year":"2016","journal-title":"J. Chem. Theory Comput."},{"key":"2026090808100120600_cit6","doi-asserted-by":"publisher","first-page":"1595","DOI":"10.1021\/acs.jctc.6b01028","article-title":"Semistochastic\nheat-bath configuration interaction method: Selected configuration\ninteraction with semistochastic perturbation theory","volume":"13","author":"Sharma","year":"2017","journal-title":"J. Chem. Theory Comput."},{"key":"2026090808100120600_cit7","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1016\/0009-2614(92)80863-7","article-title":"Direct selected configuration interaction\nusing a hole-particle\nformalism","volume":"188","author":"Caballol","year":"1992","journal-title":"Chem. Phys. Lett."},{"key":"2026090808100120600_cit8","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1002\/qua.560020603","article-title":"An application of perturbation\ntheory ideas in configuration\ninteraction calculations","volume":"2","author":"Gershgorn","year":"1968","journal-title":"Int. J. Quantum Chem."},{"key":"2026090808100120600_cit9","doi-asserted-by":"publisher","DOI":"10.1063\/1.4869192","article-title":"Adaptive\nmulticonfigurational wave functions","volume":"140","author":"Evangelista","year":"2014","journal-title":"J. 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Synthesis\nand properties of complexes containing the iron sulfide (Fe2S2) core\nand the structures of bis[o-xylyl-.alpha.,.alpha.\u2019-dithiolato-.mu.-sulfido-ferrate(III)]\nand bis[p-tolylthiolato-.mu.-sulfido-ferrate(III)] dianions","volume":"97","author":"Mayerle","year":"1975","journal-title":"J. Am. Chem. Soc."},{"key":"2026090808100120600_cit53","doi-asserted-by":"publisher","first-page":"927","DOI":"10.1038\/nchem.2041","article-title":"Low-energy spectrum\nof iron-sulfur clusters directly from many-particle quantum mechanics","volume":"6","author":"Sharma","year":"2014","journal-title":"Nat. Chem."},{"key":"2026090808100120600_cit54","doi-asserted-by":"publisher","first-page":"2681","DOI":"10.1021\/acs.jctc.7b00270","article-title":"Spin-projected matrix product states: Versatile tool\nfor strongly correlated systems","volume":"13","author":"Li","year":"2017","journal-title":"J. Chem. Theory\nComput."},{"key":"2026090808100120600_cit55","doi-asserted-by":"publisher","DOI":"10.1063\/1.5055390","article-title":"Fast semistochastic\nheat-bath configuration interaction","volume":"149","author":"Li","year":"2018","journal-title":"J. Chem.\nPhys."},{"key":"2026090808100120600_cit56","unstructured":"Zhang, H.; Otten, M.\n          From random determinants to\nthe ground state. arXiv preprint arXiv:2511.14734 2025."},{"key":"2026090808100120600_cit57","article-title":"Absorbing Many-Body Correlations\ninto Core-Optimized Orbitals","author":"Zhang","year":"2026"},{"key":"2026090808100120600_cit58","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.012015","article-title":"Accurate many-body\nelectronic structure near the basis\nset limit: Application to the chromium dimer","volume":"2","author":"Li","year":"2020","journal-title":"Phys. Rev. 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