{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T18:39:21Z","timestamp":1778351961594,"version":"3.51.4"},"reference-count":201,"publisher":"AIP Publishing","issue":"2","funder":[{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-AC02-05CH11231"],"award-info":[{"award-number":["DE-AC02-05CH11231"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2015,1,14]]},"abstract":"<jats:p>Restricted Hartree Fock using complex-valued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and real-valued RHF, and use it to uncover the close relationship between cRHF, unrestricted Hartree Fock, and generalized valence bond perfect pairing. This enables an intuition for cRHF, contrasting with the generally unintuitive nature of complex orbitals. We also describe an efficient computer implementation of cRHF and its corresponding stability analysis. By applying cRHF to the Be + H2 insertion reaction, a Woodward-Hoffmann violating reaction, and a symmetry-driven conical intersection, we demonstrate in genuine molecular systems that cRHF is capable of removing certain potential energy surface singularities that plague real-valued RHF and related methods. This complements earlier work that showed this capability in a model system. We also describe how cRHF is the preferred RHF method for certain radicaloid systems like singlet oxygen and antiaromatic molecules. For singlet O2, we show that standard methods fail even at the equilibrium geometry. An implication of this work is that, regardless of their individual efficacies, cRHF solutions to the HF equations are fairly commonplace.<\/jats:p>","DOI":"10.1063\/1.4905120","type":"journal-article","created":{"date-parts":[[2015,1,10]],"date-time":"2015-01-10T00:09:55Z","timestamp":1420848595000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":35,"title":["Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory"],"prefix":"10.1063","volume":"142","author":[{"given":"David W.","family":"Small","sequence":"first","affiliation":[{"name":"University of California Department of Chemistry, , Berkeley, California 94720, USA and Chemical Sciences Division, , Berkeley, California 94720, USA"},{"name":"Lawrence Berkeley National Laboratory Department of Chemistry, , Berkeley, California 94720, USA and Chemical Sciences Division, , Berkeley, California 94720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eric J.","family":"Sundstrom","sequence":"additional","affiliation":[{"name":"University of California Department of Chemistry, , Berkeley, California 94720, USA and Chemical Sciences Division, , Berkeley, California 94720, USA"},{"name":"Lawrence Berkeley National Laboratory Department of Chemistry, , Berkeley, California 94720, USA and Chemical Sciences Division, , Berkeley, California 94720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Head-Gordon","sequence":"additional","affiliation":[{"name":"University of California Department of Chemistry, , Berkeley, California 94720, USA and Chemical Sciences Division, , Berkeley, California 94720, USA"},{"name":"Lawrence Berkeley National Laboratory Department of Chemistry, , Berkeley, California 94720, USA and Chemical Sciences Division, , Berkeley, California 94720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2015,1,9]]},"reference":[{"key":"2023071706404704600_c1","doi-asserted-by":"publisher","first-page":"084103","DOI":"10.1063\/1.3069296","volume":"130","year":"2009","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c2","doi-asserted-by":"publisher","first-page":"19285","DOI":"10.1039\/c1cp21832h","volume":"13","year":"2011","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023071706404704600_c3","doi-asserted-by":"publisher","first-page":"2027","DOI":"10.1021\/ct500112y","volume":"10","year":"2014","journal-title":"J. Chem. Theory Comput."},{"key":"2023071706404704600_c4","doi-asserted-by":"publisher","first-page":"1394","DOI":"10.1021\/ct300902c","volume":"9","year":"2013","journal-title":"J. Chem. Theory Comput."},{"key":"2023071706404704600_c5","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/j.comptc.2012.09.030","volume":"1003","year":"2013","journal-title":"Comput. Theor. Chem."},{"key":"2023071706404704600_c6","doi-asserted-by":"publisher","first-page":"201106","DOI":"10.1103\/PhysRevB.89.201106","volume":"89","year":"2014","journal-title":"Phys. Rev. B"},{"key":"2023071706404704600_c7","doi-asserted-by":"publisher","first-page":"084101","DOI":"10.1063\/1.3086027","volume":"130","year":"2009","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c8","doi-asserted-by":"publisher","first-page":"024103","DOI":"10.1063\/1.3456001","volume":"133","year":"2010","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c9","doi-asserted-by":"publisher","first-page":"124108","DOI":"10.1063\/1.3643338","volume":"135","year":"2011","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c10","doi-asserted-by":"publisher","first-page":"164109","DOI":"10.1063\/1.4705280","volume":"136","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c11","doi-asserted-by":"publisher","first-page":"214113","DOI":"10.1063\/1.4880819","volume":"140","year":"2014","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c12","doi-asserted-by":"publisher","first-page":"204101","DOI":"10.1063\/1.4876490","volume":"140","year":"2014","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c13","article-title":"Local spin from strongly orthogonal geminal wavefunctions","journal-title":"Mol. Phys."},{"key":"2023071706404704600_c14","doi-asserted-by":"publisher","first-page":"534","DOI":"10.1007\/s10910-011-9849-9","volume":"50","year":"2012","journal-title":"J. Math. Chem."},{"key":"2023071706404704600_c15","doi-asserted-by":"publisher","first-page":"878","DOI":"10.1063\/1.1427918","volume":"116","year":"2002","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c16","doi-asserted-by":"publisher","first-page":"5978","DOI":"10.1063\/1.1503773","volume":"117","year":"2002","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c17","doi-asserted-by":"publisher","first-page":"10385","DOI":"10.1063\/1.1738110","volume":"120","year":"2004","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c18","doi-asserted-by":"publisher","first-page":"5736","DOI":"10.1063\/1.1555983","volume":"118","year":"2003","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c19","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1002\/jcc.20319","volume":"27","year":"2006","journal-title":"J. Comput. Chem."},{"key":"2023071706404704600_c20","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1002\/qua.24045","volume":"113","year":"2013","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c21","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1002\/andp.200310072","volume":"13","year":"2004","journal-title":"Ann. Phys. (Berlin)"},{"key":"2023071706404704600_c22","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/j.comptc.2012.08.022","volume":"1003","year":"2013","journal-title":"Comput. Theor. Chem."},{"key":"2023071706404704600_c23","doi-asserted-by":"publisher","first-page":"244105","DOI":"10.1063\/1.2817602","volume":"127","year":"2007","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c24","doi-asserted-by":"publisher","first-page":"134108","DOI":"10.1063\/1.2983652","volume":"129","year":"2008","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c25","doi-asserted-by":"publisher","first-page":"052502","DOI":"10.1103\/PhysRevA.76.052502","volume":"76","year":"2007","journal-title":"Phys. Rev. A"},{"key":"2023071706404704600_c26","doi-asserted-by":"publisher","first-page":"034107","DOI":"10.1063\/1.4731810","volume":"137","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c27","doi-asserted-by":"publisher","first-page":"203001","DOI":"10.1103\/PhysRevLett.109.203001","volume":"109","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"2023071706404704600_c28","doi-asserted-by":"publisher","first-page":"181101","DOI":"10.1063\/1.4829536","volume":"139","year":"2013","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c29","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1146\/annurev-physchem-032210-103338","volume":"62","year":"2011","journal-title":"Annu. Rev. Phys. Chem."},{"key":"2023071706404704600_c30","doi-asserted-by":"publisher","first-page":"144117","DOI":"10.1063\/1.2883976","volume":"128","year":"2008","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c31","doi-asserted-by":"publisher","first-page":"094104","DOI":"10.1063\/1.3629454","volume":"135","year":"2011","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c32","doi-asserted-by":"publisher","first-page":"4462","DOI":"10.1021\/ct400707k","volume":"9","year":"2013","journal-title":"J. Chem. Theory Comput."},{"key":"2023071706404704600_c33","doi-asserted-by":"publisher","first-page":"2193","DOI":"10.1103\/PhysRevA.30.2193","volume":"30","year":"1984","journal-title":"Phys. Rev. A"},{"key":"2023071706404704600_c34","doi-asserted-by":"publisher","first-page":"4267","DOI":"10.1103\/PhysRevB.30.4267","volume":"30","year":"1984","journal-title":"Phys. Rev. B"},{"key":"2023071706404704600_c35","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/BF01119191","volume":"78","year":"1990","journal-title":"Theor. Chim. Acta"},{"key":"2023071706404704600_c36","doi-asserted-by":"publisher","first-page":"3351","DOI":"10.1103\/PhysRevB.42.3351","volume":"42","year":"1990","journal-title":"Phys. Rev. B"},{"key":"2023071706404704600_c37","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1002\/qua.560420110","volume":"42","year":"1992","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c38","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1002\/qua.560550208","volume":"55","year":"1995","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c39","doi-asserted-by":"publisher","first-page":"4699","DOI":"10.1063\/1.471164","volume":"104","year":"1996","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c40","doi-asserted-by":"publisher","first-page":"114103","DOI":"10.1063\/1.4751485","volume":"137","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c41","doi-asserted-by":"publisher","first-page":"021102","DOI":"10.1063\/1.4813481","volume":"139","year":"2013","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c42","doi-asserted-by":"publisher","first-page":"061101","DOI":"10.1063\/1.4892792","volume":"141","year":"2014","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c43","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/0009-2614(88)80392-0","volume":"150","year":"1988","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c44","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1016\/S0009-2614(00)01137-4","volume":"330","year":"2000","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c45","doi-asserted-by":"publisher","first-page":"2191","DOI":"10.1080\/00268970500131595","volume":"103","year":"2005","journal-title":"Mol. Phys."},{"key":"2023071706404704600_c46","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0065-3276(06)51001-9","volume":"51","year":"2006","journal-title":"Adv. Quantum Chem."},{"key":"2023071706404704600_c47","doi-asserted-by":"publisher","first-page":"224106","DOI":"10.1063\/1.3507876","volume":"133","year":"2010","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c48","doi-asserted-by":"publisher","first-page":"044113","DOI":"10.1063\/1.3615060","volume":"135","year":"2011","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c49","doi-asserted-by":"publisher","first-page":"054114","DOI":"10.1063\/1.3680560","volume":"136","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c50","doi-asserted-by":"publisher","first-page":"6729","DOI":"10.1039\/c2cp40698e","volume":"14","year":"2012","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023071706404704600_c51","doi-asserted-by":"publisher","first-page":"074104","DOI":"10.1063\/1.4791636","volume":"138","year":"2013","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c52","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1002\/qua.560050839","volume":"S5","year":"1971","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c53","doi-asserted-by":"publisher","first-page":"1225","DOI":"10.1063\/1.430637","volume":"62","year":"1975","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c54","doi-asserted-by":"publisher","first-page":"1243","DOI":"10.1002\/qua.560180511","volume":"18","year":"1980","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c55","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/j.chemphys.2007.07.001","volume":"343","year":"2008","journal-title":"Chem. Phys."},{"key":"2023071706404704600_c56","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/j.cplett.2010.05.006","volume":"493","year":"2010","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c57","doi-asserted-by":"publisher","first-page":"2316","DOI":"10.1103\/PhysRevA.24.2316","volume":"24","year":"1981","journal-title":"Phys. Rev. A"},{"key":"2023071706404704600_c58","doi-asserted-by":"publisher","first-page":"2330","DOI":"10.1103\/PhysRevA.24.2330","volume":"24","year":"1981","journal-title":"Phys. Rev. A"},{"key":"2023071706404704600_c59","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/0009-2614(81)80059-0","volume":"80","year":"1981","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c60","doi-asserted-by":"publisher","first-page":"2270","DOI":"10.1063\/1.442288","volume":"75","year":"1981","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c61","doi-asserted-by":"publisher","first-page":"204105","DOI":"10.1063\/1.2387952","volume":"125","year":"2006","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c62","doi-asserted-by":"publisher","first-page":"184109","DOI":"10.1063\/1.3494113","volume":"133","year":"2010","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c63","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1021\/ar800241t","volume":"42","year":"2009","journal-title":"Acc. Chem. Res."},{"key":"2023071706404704600_c64","doi-asserted-by":"publisher","first-page":"064101","DOI":"10.1063\/1.3682325","volume":"136","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c65"},{"key":"2023071706404704600_c66","doi-asserted-by":"publisher","first-page":"3648","DOI":"10.1063\/1.1695775","volume":"42","year":"1965","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c67","first-page":"S17","volume":"43","year":"1965","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c68","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1002\/qua.560020710","volume":"2","year":"1968","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c69","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1002\/qua.560010413","volume":"1","year":"1967","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c70","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/BF00529947","volume":"9","year":"1967","journal-title":"Theor. Chim. Acta"},{"key":"2023071706404704600_c71","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1002\/qua.560020105","volume":"2","year":"1968","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c72","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1016\/0022-2852(68)90033-7","volume":"27","year":"1968","journal-title":"J. Mol. Spectrosc."},{"key":"2023071706404704600_c73","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/0009-2614(69)80241-1","volume":"3","year":"1969","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c74","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1080\/00268977000100651","volume":"18","year":"1970","journal-title":"Mol. Phys."},{"key":"2023071706404704600_c75","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1002\/qua.560050823","volume":"5","year":"1971","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c76","doi-asserted-by":"publisher","first-page":"2994","DOI":"10.1063\/1.1678695","volume":"57","year":"1972","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c77","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/BF00572556","volume":"36","year":"1975","journal-title":"Theor. Chim. Acta"},{"key":"2023071706404704600_c78","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/BF00572557","volume":"36","year":"1975","journal-title":"Theor. Chim. Acta"},{"key":"2023071706404704600_c79","doi-asserted-by":"publisher","first-page":"917","DOI":"10.1002\/qua.560100520","volume":"10","year":"1976","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c80","doi-asserted-by":"publisher","first-page":"3045","DOI":"10.1063\/1.434318","volume":"66","year":"1977","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c81","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/BF00549018","volume":"48","year":"1978","journal-title":"Theor. Chim. Acta"},{"key":"2023071706404704600_c82","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1002\/qua.560340859","volume":"34","year":"1988","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c83","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1002\/qua.560200502","volume":"20","year":"1981","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c84","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1016\/0009-2614(70)80318-9","volume":"7","year":"1970","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c85","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1016\/0009-2614(73)80050-8","volume":"21","year":"1973","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c86","doi-asserted-by":"publisher","first-page":"799","DOI":"10.1002\/qua.560080515","volume":"8","year":"1974","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c87","doi-asserted-by":"publisher","first-page":"1025","DOI":"10.1002\/qua.560100613","volume":"10","year":"1976","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c88","doi-asserted-by":"publisher","first-page":"4535","DOI":"10.1063\/1.436451","volume":"69","year":"1978","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c89","doi-asserted-by":"publisher","first-page":"6531","DOI":"10.1021\/ja00801a003","volume":"95","year":"1973","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c90","doi-asserted-by":"publisher","first-page":"1433","DOI":"10.1143\/PTP.50.1433","volume":"50","year":"1973","journal-title":"Prog. Theor. Phys."},{"key":"2023071706404704600_c91","doi-asserted-by":"publisher","first-page":"1645","DOI":"10.1021\/ja00840a003","volume":"97","year":"1975","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c92","doi-asserted-by":"publisher","first-page":"3402","DOI":"10.1021\/ja00845a021","volume":"97","year":"1975","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c93","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1021\/ja00289a003","volume":"107","year":"1985","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c94","doi-asserted-by":"publisher","first-page":"5449","DOI":"10.1021\/j100377a006","volume":"94","year":"1990","journal-title":"J. Phys. Chem."},{"key":"2023071706404704600_c95","doi-asserted-by":"publisher","first-page":"853","DOI":"10.1080\/00268976.2013.874600","volume":"112","year":"2014","journal-title":"Mol. Phys."},{"key":"2023071706404704600_c96","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1002\/bbpc.19810850806","volume":"85","year":"1981","journal-title":"Ber. Bunsenges. Phys. Chem."},{"key":"2023071706404704600_c97","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1016\/0009-2614(81)85517-0","volume":"83","year":"1981","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c98","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1002\/qua.560240206","volume":"24","year":"1983","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c99","volume-title":"Matrix Analysis","year":"2013","edition":"2nd ed."},{"key":"2023071706404704600_c100","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/978-1-4757-0887-5","volume-title":"Methods of Electronic Structure Theory","author":"Schaefer","year":"1977"},{"key":"2023071706404704600_c101","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1098\/rspa.1961.0175","volume":"263","year":"1961","journal-title":"Proc. R. Soc. London, Ser. A"},{"key":"2023071706404704600_c102","doi-asserted-by":"publisher","first-page":"3172","DOI":"10.1039\/b517914a","volume":"8","year":"2006","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023071706404704600_c103","unstructured":"C.\u2008Sanderson, Armadillo: An open source C++ linear algebra library for fast prototyping and computationally intensive experiments, Technical Report, NICTA, Australia, 2010."},{"key":"2023071706404704600_c104","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1016\/0009-2614(80)80396-4","volume":"73","year":"1980","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c105","doi-asserted-by":"publisher","first-page":"556","DOI":"10.1002\/jcc.540030413","volume":"3","year":"1982","journal-title":"J. Comput. Chem."},{"key":"2023071706404704600_c106","volume-title":"Numerical Optimization","year":"2006","edition":"2nd ed."},{"key":"2023071706404704600_c107","doi-asserted-by":"publisher","first-page":"1713","DOI":"10.1080\/00268970110103642","volume":"100","year":"2002","journal-title":"Mol. Phys."},{"key":"2023071706404704600_c108","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/0021-9991(75)90065-0","volume":"17","year":"1975","journal-title":"J. Comput. Phys."},{"key":"2023071706404704600_c109","doi-asserted-by":"publisher","first-page":"1007","DOI":"10.1063\/1.456153","volume":"90","year":"1989","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c110","doi-asserted-by":"publisher","first-page":"3098","DOI":"10.1103\/PhysRevA.38.3098","volume":"38","year":"1988","journal-title":"Phys. Rev. A"},{"key":"2023071706404704600_c111","doi-asserted-by":"publisher","first-page":"785","DOI":"10.1103\/PhysRevB.37.785","volume":"37","year":"1988","journal-title":"Phys. Rev. B"},{"key":"2023071706404704600_c112","doi-asserted-by":"publisher","first-page":"5648","DOI":"10.1063\/1.464913","volume":"98","year":"1993","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c113","doi-asserted-by":"publisher","first-page":"11623","DOI":"10.1021\/j100096a001","volume":"98","year":"1994","journal-title":"J. Phys. Chem."},{"key":"2023071706404704600_c114","doi-asserted-by":"publisher","first-page":"1910","DOI":"10.1063\/1.443164","volume":"76","year":"1982","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c115","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1016\/S0009-2614(89)87395-6","volume":"157","year":"1989","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c116","doi-asserted-by":"publisher","first-page":"374","DOI":"10.1016\/0009-2614(92)85354-D","volume":"190","year":"1992","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c117","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1016\/0009-2614(92)85710-R","volume":"196","year":"1992","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c118","doi-asserted-by":"publisher","first-page":"771","DOI":"10.1080\/00268977800100581","volume":"35","year":"1978","journal-title":"Mol. Phys."},{"key":"2023071706404704600_c119","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1002\/qua.560170310","volume":"17","year":"1980","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c120","doi-asserted-by":"publisher","first-page":"5803","DOI":"10.1063\/1.455556","volume":"89","year":"1988","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c121","doi-asserted-by":"publisher","first-page":"5682","DOI":"10.1063\/1.445449","volume":"78","year":"1983","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c122","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1002\/9780470142943.ch7","volume":"69","year":"1987","journal-title":"Adv. Chem. Phys."},{"key":"2023071706404704600_c123","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1016\/0301-0104(80)80045-0","volume":"48","year":"1980","journal-title":"Adv. Chem. Phys."},{"key":"2023071706404704600_c124","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/0301-0104(82)87004-3","volume":"71","year":"1982","journal-title":"Chem. Phys."},{"key":"2023071706404704600_c125","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/0301-0104(82)87005-5","volume":"71","year":"1982","journal-title":"Chem. Phys."},{"key":"2023071706404704600_c126","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/0301-0104(82)87006-7","volume":"71","year":"1982","journal-title":"Chem. Phys."},{"key":"2023071706404704600_c127","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1146\/annurev.physchem.49.1.233","volume":"49","year":"1998","journal-title":"Annu. Rev. Phys. Chem."},{"key":"2023071706404704600_c128","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1088\/0031-8949\/21\/3-4\/014","volume":"21","year":"1980","journal-title":"Phys. Scr."},{"key":"2023071706404704600_c129","doi-asserted-by":"publisher","first-page":"2384","DOI":"10.1063\/1.441359","volume":"74","year":"1981","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c130","doi-asserted-by":"publisher","first-page":"1347","DOI":"10.1002\/jcc.540141112","volume":"14","year":"1993","journal-title":"J. Comput. Chem."},{"key":"2023071706404704600_c131"},{"key":"2023071706404704600_c132","doi-asserted-by":"publisher","first-page":"193001","DOI":"10.1103\/PhysRevLett.101.193001","volume":"101","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"2023071706404704600_c133","doi-asserted-by":"publisher","first-page":"144119","DOI":"10.1063\/1.2868768","volume":"128","year":"2008","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c134","doi-asserted-by":"publisher","first-page":"074307","DOI":"10.1063\/1.3298376","volume":"132","year":"2010","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c135","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1016\/S0009-2614(99)00179-7","volume":"302","year":"1999","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c136","doi-asserted-by":"publisher","first-page":"9639","DOI":"10.1063\/1.473863","volume":"106","year":"1997","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c137","doi-asserted-by":"publisher","first-page":"6796","DOI":"10.1063\/1.462569","volume":"96","year":"1992","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c138","doi-asserted-by":"publisher","first-page":"835","DOI":"10.1002\/qua.560230307","volume":"23","year":"1983","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c139","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/S0065-3276(08)60507-9","volume":"30","year":"1998","journal-title":"Adv. Quantum Chem."},{"key":"2023071706404704600_c140","doi-asserted-by":"publisher","first-page":"6171","DOI":"10.1063\/1.478523","volume":"110","year":"1999","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c141","doi-asserted-by":"publisher","first-page":"204108","DOI":"10.1063\/1.4718704","volume":"136","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c142","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1021\/cr2001417","volume":"112","year":"2012","journal-title":"Chem. Rev."},{"key":"2023071706404704600_c143","doi-asserted-by":"publisher","first-page":"224110","DOI":"10.1063\/1.4840097","volume":"139","year":"2013","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c144","doi-asserted-by":"publisher","first-page":"124102","DOI":"10.1063\/1.3692969","volume":"136","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c145","doi-asserted-by":"publisher","first-page":"014108","DOI":"10.1063\/1.4731634","volume":"137","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c146","doi-asserted-by":"publisher","first-page":"194111","DOI":"10.1063\/1.4767052","volume":"137","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c147","doi-asserted-by":"publisher","first-page":"4753","DOI":"10.1039\/c2cp23198k","volume":"14","year":"2012","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023071706404704600_c148","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1002\/qua.24103","volume":"113","year":"2013","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c149","doi-asserted-by":"publisher","first-page":"064105","DOI":"10.1063\/1.4890734","volume":"141","year":"2014","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c150","doi-asserted-by":"publisher","first-page":"7632","DOI":"10.1063\/1.1792071","volume":"121","year":"2004","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c151","doi-asserted-by":"publisher","first-page":"8023","DOI":"10.1063\/1.469000","volume":"102","year":"1995","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c152","doi-asserted-by":"publisher","first-page":"2320","DOI":"10.1039\/b301627g","volume":"5","year":"2003","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023071706404704600_c153","doi-asserted-by":"publisher","first-page":"124509","DOI":"10.1063\/1.3236840","volume":"131","year":"2009","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c154","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1016\/0009-2614(94)01243-1","volume":"231","year":"1994","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c155","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1016\/0009-2614(95)00945-Z","volume":"244","year":"1995","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c156","volume-title":"Organic Chemistry","year":"2011","edition":"3rd ed."},{"key":"2023071706404704600_c157","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1021\/ja01080a054","volume":"87","year":"1965","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c158","doi-asserted-by":"publisher","first-page":"1920","DOI":"10.1021\/ja01009a054","volume":"90","year":"1968","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c159","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1039\/qr9682200338","volume":"22","year":"1968","journal-title":"Q. Rev. Chem. Soc."},{"key":"2023071706404704600_c160","doi-asserted-by":"publisher","first-page":"1839","DOI":"10.1039\/P19740001839","volume":"1974","journal-title":"J. Chem. Soc., Perkin Trans. 1"},{"key":"2023071706404704600_c161","doi-asserted-by":"publisher","first-page":"3859","DOI":"10.1021\/ja00846a075","volume":"97","year":"1975","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c162","doi-asserted-by":"publisher","first-page":"572","DOI":"10.1002\/anie.197705721","volume":"16","year":"1977","journal-title":"Angew. Chem., Int. Ed. Engl."},{"key":"2023071706404704600_c163","doi-asserted-by":"publisher","first-page":"5839","DOI":"10.1021\/ja028963g","volume":"125","year":"2003","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c164","doi-asserted-by":"publisher","first-page":"165305","DOI":"10.1103\/PhysRevB.72.165305","volume":"72","year":"2005","journal-title":"Phys. Rev. B"},{"key":"2023071706404704600_c165","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1038\/nature05681","volume":"446","year":"2007","journal-title":"Nature"},{"key":"2023071706404704600_c166","doi-asserted-by":"publisher","first-page":"6377","DOI":"10.1021\/ja8095834","volume":"131","year":"2009","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c167","doi-asserted-by":"publisher","first-page":"1221","DOI":"10.1021\/ja00317a009","volume":"106","year":"1984","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c168","doi-asserted-by":"publisher","first-page":"8917","DOI":"10.1063\/1.475183","volume":"107","year":"1997","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c169","doi-asserted-by":"publisher","first-page":"6339","DOI":"10.1021\/jp0560011","volume":"110","year":"2006","journal-title":"J. Phys. Chem. A"},{"key":"2023071706404704600_c170","doi-asserted-by":"publisher","first-page":"3710","DOI":"10.1021\/ja00062a042","volume":"115","year":"1993","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c171","doi-asserted-by":"publisher","first-page":"5733","DOI":"10.1063\/1.469304","volume":"102","year":"1995","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c172","doi-asserted-by":"publisher","first-page":"2182","DOI":"10.1021\/jp067614w","volume":"111","year":"2007","journal-title":"J. Phys. Chem. A"},{"key":"2023071706404704600_c173","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/S0009-2614(98)00177-8","volume":"287","year":"1998","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c174","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1016\/S0009-2614(00)00167-6","volume":"319","year":"2000","journal-title":"Chem. Phys. Lett."},{"key":"2023071706404704600_c175","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.chemphys.2007.10.022","volume":"347","year":"2008","journal-title":"Chem. Phys."},{"key":"2023071706404704600_c176","doi-asserted-by":"publisher","first-page":"4116","DOI":"10.1021\/ct400512u","volume":"9","year":"2013","journal-title":"J. Chem. Theory Comput."},{"key":"2023071706404704600_c177","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1021\/jp036792b","volume":"108","year":"2004","journal-title":"J. Phys. Chem. A"},{"key":"2023071706404704600_c178","doi-asserted-by":"publisher","first-page":"5009","DOI":"10.1002\/chem.200601151","volume":"13","year":"2007","journal-title":"Chem. Eur. J."},{"key":"2023071706404704600_c179","doi-asserted-by":"publisher","first-page":"2153","DOI":"10.1063\/1.434152","volume":"66","year":"1977","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c180","doi-asserted-by":"publisher","first-page":"1476","DOI":"10.1021\/j100317a022","volume":"92","year":"1988","journal-title":"J. Phys. Chem."},{"key":"2023071706404704600_c181","doi-asserted-by":"publisher","first-page":"5523","DOI":"10.1021\/j100377a021","volume":"94","year":"1990","journal-title":"J. Phys. Chem."},{"key":"2023071706404704600_c182","doi-asserted-by":"publisher","first-page":"2585","DOI":"10.1021\/ja00295a002","volume":"107","year":"1985","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c183","doi-asserted-by":"publisher","first-page":"2650","DOI":"10.1021\/jp0663661","volume":"111","year":"2007","journal-title":"J. Phys. Chem. A"},{"key":"2023071706404704600_c184","doi-asserted-by":"publisher","first-page":"215102","DOI":"10.1063\/1.2932102","volume":"128","year":"2008","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c185","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/s00706-011-0447-0","volume":"142","year":"2011","journal-title":"Monatsh. Chem."},{"key":"2023071706404704600_c186","doi-asserted-by":"publisher","first-page":"10165","DOI":"10.1039\/b913131k","volume":"11","year":"2009","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023071706404704600_c187","doi-asserted-by":"publisher","first-page":"11965","DOI":"10.1021\/jp806622m","volume":"112","year":"2008","journal-title":"J. Phys. Chem. A"},{"key":"2023071706404704600_c188","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1021\/jp206546g","volume":"116","year":"2012","journal-title":"J. Phys. Chem. A"},{"key":"2023071706404704600_c189","doi-asserted-by":"publisher","first-page":"6398","DOI":"10.1021\/ja016915a","volume":"124","year":"2002","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c190","doi-asserted-by":"publisher","first-page":"034303","DOI":"10.1063\/1.2748049","volume":"127","year":"2007","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c191","doi-asserted-by":"publisher","first-page":"3277","DOI":"10.1002\/qua.24116","volume":"112","year":"2012","journal-title":"Int. J. Quantum Chem."},{"key":"2023071706404704600_c192","doi-asserted-by":"publisher","first-page":"3771","DOI":"10.1021\/ja00508a012","volume":"101","year":"1979","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c193","doi-asserted-by":"publisher","first-page":"10683","DOI":"10.1021\/ja026304y","volume":"124","year":"2002","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c194","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1039\/a808035f","volume":"1","year":"1999","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023071706404704600_c195","doi-asserted-by":"publisher","first-page":"4648","DOI":"10.1021\/ja00195a019","volume":"111","year":"1989","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c196","doi-asserted-by":"publisher","first-page":"5837","DOI":"10.1021\/ja00798a106","volume":"95","year":"1973","journal-title":"J. Am. Chem. Soc."},{"key":"2023071706404704600_c197","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1070\/MC1993v003n03ABEH000242","volume":"3","year":"1993","journal-title":"Mendeleev Commun."},{"key":"2023071706404704600_c198","doi-asserted-by":"publisher","first-page":"164101","DOI":"10.1063\/1.2718952","volume":"126","year":"2007","journal-title":"J. Chem. Phys."},{"key":"2023071706404704600_c199","doi-asserted-by":"publisher","first-page":"3060","DOI":"10.1021\/ct9003299","volume":"5","year":"2009","journal-title":"J. Chem. Theory Comput."},{"key":"2023071706404704600_c200","doi-asserted-by":"publisher","first-page":"2371","DOI":"10.1021\/ct500231c","volume":"10","year":"2014","journal-title":"J. Chem. Theory Comput."},{"key":"2023071706404704600_c201","unstructured":"See supplementary material at http:\/\/dx.doi.org\/10.1063\/1.4905120  for TS coordinates for the WHV reaction and extra PES plots for the polyatomic examples."}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/aip.scitation.org\/doi\/am-pdf\/10.1063\/1.4905120","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/1.4905120\/15489958\/024104_1_online.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/1.4905120\/15489958\/024104_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T06:40:56Z","timestamp":1689576056000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/142\/2\/024104\/605269\/Restricted-Hartree-Fock-using-complex-valued"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,9]]},"references-count":201,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,1,14]]}},"URL":"https:\/\/doi.org\/10.1063\/1.4905120","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2015,1,14]]},"published":{"date-parts":[[2015,1,9]]},"article-number":"024104"}}