{"term":{"id":"07056","title":"instability of Hartree–Fock solution","longtitle":"IUPAC Gold Book - instability of Hartree–Fock solution","doi":"10.1351\/goldbook.IT07056","code":"IT07056","status":"current","also defines":"<em>also defines<\/em>: spin-restricted Hartree–Fock, spin-unrestricted Hartree–Fock","mentioned":"<em>mentioned<\/em>: RHF, UHF","definitions":[{"id":1,"text":"Existence of additional solutions to the equations of the Hartree–Fock method occurring usually in the case when potential energy surfaces of different electronic states are drawn close together. Within the spin-restricted Hartree–Fock method (RHF), singlet and triplet instabilities are distinguished. The former involves the existence of another solution with lower energy and the electron distribution of lower symmetry. It may be regarded as an indication that the initially assumed molecular shape needs correction. The triplet instability involves rejection of the condition of double occupancy of molecular orbitals and thus transition to the spin-unrestricted Hartree–Fock method (UHF). The triplet instability is a necessary, but insufficient, condition for the conclusion as to the biradical character of the ground state of a given system.","links":[{"term":"Hartree","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/H02747"},{"term":"biradical","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/B00671"},{"term":"ground state","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/G02704"},{"term":"molecular shape","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/MT06972"}],"sources":["PAC, 1999, 71, 1919. 'Glossary of terms used in theoretical organic chemistry' on page 1946 (https:\/\/doi.org\/10.1351\/pac199971101919)"]}],"altoutputs":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/IT07056\/html","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/IT07056\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/IT07056\/plain"},"citation":"Citation: 'instability of Hartree–Fock solution' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351\/goldbook.IT07056","license":"The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/) for individual terms.","collection":"If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org .","disclaimer":"The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using.","accessed":"2026-05-06T21:31:06+00:00"}}