{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/76103"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/76103","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Approximate Spin Extended Hartree-Fock theory","abstract":"An approximate spin-extended method is developed in which the Occupation Numbers of the Natural Orbitals of Charge are varied but the orbitals themselves are frozen. A number of techniques for obtaining appropriate Natural Orbitals of Charge are presented and these techniques are employed in semi-empirical and Ab-Initio studies. The molecules chosen for the Ab-Initio study, O₃, F₂ and C₂, are particularly interesting as Restricted Hartree-Fock (RHF) theory fails to provide an adequate description of these systems at their equilibrium geometries. The results of this work indicate that Approximate SpinExtended Hartree-Fock (ASEHF) theory provides a qualitatively acceptable description of bond dissociation, correctly predicts the symmetry of molecular states where RHF theory fails, and provides an efficient means for obtaining a significant amount of correlation energy in molecular calculations. Moreover, when the Generalized Valence Bond form of the ASEHF wavefunction is employed, a particularly useful description of the molecule is obtained. Specifically, the success or failure of the Woodward-Hoffman becomes transparent when the system is analyzed in terms of this wavefunction.","abstract_html":"An approximate spin-extended method is developed in which the Occupation Numbers of the Natural Orbitals of Charge are varied but the orbitals themselves are frozen. A number of techniques for obtaining appropriate Natural Orbitals of Charge are presented and these techniques are employed in semi-empirical and Ab-Initio studies. The molecules chosen for the Ab-Initio study, O₃, F₂ and C₂, are particularly interesting as Restricted Hartree-Fock (RHF) theory fails to provide an adequate description of these systems at their equilibrium geometries. The results of this work indicate that Approximate SpinExtended Hartree-Fock (ASEHF) theory provides a qualitatively acceptable description of bond dissociation, correctly predicts the symmetry of molecular states where RHF theory fails, and provides an efficient means for obtaining a significant amount of correlation energy in molecular calculations. Moreover, when the Generalized Valence Bond form of the ASEHF wavefunction is employed, a particularly useful description of the molecule is obtained. Specifically, the success or failure of the Woodward-Hoffman becomes transparent when the system is analyzed in terms of this wavefunction.","abstract_has_math":false,"creators":["Lengsfield, Byron H."],"institution":"Virginia Polytechnic Institute and State University","degree_name":"Ph. D.","degree_level":"doctoral","degree_discipline":"Chemistry","degree_department":"Chemistry","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1978,"date_issued":"1978","date_published":"1978","updated_at":"2026-07-22T22:19:33Z","subjects":[],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10919/76103","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Chemistry"]},{"key":"dc:creator","label":"Author","values":["Lengsfield, Byron H."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-03-10T15:15:18Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-03-10T15:15:18Z"]},{"key":"dc:date.issued","label":"Date","values":["1978"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Polytechnic Institute and State University"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Chemistry"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. 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A number of techniques for obtaining appropriate Natural Orbitals of Charge are presented and these techniques are employed in semi-empirical and Ab-Initio studies. The molecules chosen for the Ab-Initio study, O₃, F₂ and C₂, are particularly interesting as Restricted Hartree-Fock (RHF) theory fails to provide an adequate description of these systems at their equilibrium geometries. The results of this work indicate that Approximate SpinExtended Hartree-Fock (ASEHF) theory provides a qualitatively acceptable description of bond dissociation, correctly predicts the symmetry of molecular states where RHF theory fails, and provides an efficient means for obtaining a significant amount of correlation energy in molecular calculations. Moreover, when the Generalized Valence Bond form of the ASEHF wavefunction is employed, a particularly useful description of the molecule is obtained. Specifically, the success or failure of the Woodward-Hoffman becomes transparent when the system is analyzed in terms of this wavefunction."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Approximate Spin Extended Hartree-Fock theory"]}]}],"canonical_facts":{"dc:contributor.department":["Chemistry"],"dc:creator":["Lengsfield, Byron H."],"dc:date.accessioned":["2017-03-10T15:15:18Z"],"dc:date.available":["2017-03-10T15:15:18Z"],"dc:date.issued":["1978"],"dc:description.abstract":["An approximate spin-extended method is developed in which the Occupation Numbers of the Natural Orbitals of Charge are varied but the orbitals themselves are frozen. A number of techniques for obtaining appropriate Natural Orbitals of Charge are presented and these techniques are employed in semi-empirical and Ab-Initio studies. The molecules chosen for the Ab-Initio study, O₃, F₂ and C₂, are particularly interesting as Restricted Hartree-Fock (RHF) theory fails to provide an adequate description of these systems at their equilibrium geometries. The results of this work indicate that Approximate SpinExtended Hartree-Fock (ASEHF) theory provides a qualitatively acceptable description of bond dissociation, correctly predicts the symmetry of molecular states where RHF theory fails, and provides an efficient means for obtaining a significant amount of correlation energy in molecular calculations. Moreover, when the Generalized Valence Bond form of the ASEHF wavefunction is employed, a particularly useful description of the molecule is obtained. Specifically, the success or failure of the Woodward-Hoffman becomes transparent when the system is analyzed in terms of this wavefunction."],"dc:description.degree":["Ph. D."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/76103"],"dc:language.iso":["en"],"dc:publisher":["Virginia Polytechnic Institute and State University"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Approximate Spin Extended Hartree-Fock theory"],"dc:type":["Dissertation"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Chemistry"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph. D."],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:33Z"}