{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T20:01:40Z","timestamp":1787169700454,"version":"build-2736575974"},"reference-count":90,"publisher":"AIP Publishing","issue":"21","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CHE-13-61293"],"award-info":[{"award-number":["CHE-13-61293"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-14-1-0295"],"award-info":[{"award-number":["FA9550-14-1-0295"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2015,6,7]]},"abstract":"<jats:p>The nuclear-electronic orbital (NEO) approach treats select nuclei quantum mechanically on the same level as the electrons and includes nonadiabatic effects between the electrons and the quantum nuclei. The practical implementation of this approach is challenging due to the significance of electron-nucleus dynamical correlation. Herein, we present a general extension of the previously developed reduced NEO explicitly correlated Hartree-Fock (RXCHF) approach, in which only select electronic orbitals are explicitly correlated to each quantum nuclear orbital via Gaussian-type geminal functions. Approximations of the electronic exchange between the geminal-coupled electronic orbitals and the other electronic orbitals are also explored. This general approach enables computationally tractable yet accurate calculations on molecular systems with quantum protons. The RXCHF method is applied to the hydrogen cyanide (HCN) and FHF\u2212 systems, where the proton and all electrons are treated quantum mechanically. For the HCN system, only the two electronic orbitals associated with the CH covalent bond are geminal-coupled to the proton orbital. For the FHF\u2212 system, only the four electronic orbitals associated with the two FH covalent bonds are geminal-coupled to the proton orbital. For both systems, the RXCHF method produces qualitatively accurate nuclear densities, in contrast to mean field-based NEO approaches. The development and implementation of the RXCHF method provide the framework to perform calculations on systems such as proton-coupled electron transfer reactions, where electron-proton nonadiabatic effects are important.<\/jats:p>","DOI":"10.1063\/1.4921303","type":"journal-article","created":{"date-parts":[[2015,6,4]],"date-time":"2015-06-04T14:02:10Z","timestamp":1433426530000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":36,"title":["Quantum treatment of protons with the reduced explicitly correlated Hartree-Fock approach"],"prefix":"10.1063","volume":"142","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2353-311X","authenticated-orcid":false,"given":"Andrew","family":"Sirjoosingh","sequence":"first","affiliation":[{"name":"University of Illinois at Urbana-Champaign Department of Chemistry, , 600 South Mathews Ave., Urbana, Illinois 61801, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael V.","family":"Pak","sequence":"additional","affiliation":[{"name":"University of Illinois at Urbana-Champaign Department of Chemistry, , 600 South Mathews Ave., Urbana, Illinois 61801, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kurt R.","family":"Brorsen","sequence":"additional","affiliation":[{"name":"University of Illinois at Urbana-Champaign Department of Chemistry, , 600 South Mathews Ave., Urbana, Illinois 61801, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sharon","family":"Hammes-Schiffer","sequence":"additional","affiliation":[{"name":"University of Illinois at Urbana-Champaign Department of Chemistry, , 600 South Mathews Ave., Urbana, Illinois 61801, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2015,6,4]]},"reference":[{"key":"2023080404222881500_c1","doi-asserted-by":"publisher","first-page":"1325","DOI":"10.1126\/science.2646716","volume":"243","year":"1989","journal-title":"Science"},{"key":"2023080404222881500_c2","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1126\/science.275.5301.817","volume":"275","year":"1997","journal-title":"Science"},{"key":"2023080404222881500_c3","doi-asserted-by":"publisher","first-page":"8992","DOI":"10.1021\/ja0351995","volume":"125","year":"2003","journal-title":"J. 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