{"id":{"repo_id":"umkc","oai_identifier":"oai:mospace.umsystem.edu:10355/45947"},"canonical_url":"https://search.dev.ndltd.org/etd/umkc/oai:mospace.umsystem.edu:10355/45947","repository":{"repo_id":"umkc","name":"University of Missouri - Kansas City","base_url":"https://mospace.umsystem.edu/oai/request"},"display":{"title":"Mathematical Analysis of Compressive/Tensile Molecular and Nuclear Structures","abstract":"Mathematical analysis in chemistry is a fascinating and critical tool to explain experimental observations. In this dissertation, mathematical methods to present chemical bonding and other structures for many-particle systems are discussed at different levels (molecular, atomic, and nuclear). First, the tetrahedral geometry of single, double, or triple carbon-carbon bonds gives an unsatisfying demonstration of bond lengths, compared to experimental trends. To correct this, Platonic solids and Archimedean solids were evaluated as atoms in covalent carbon or nitrogen bond systems in order to find the best solids for geometric fitting. Pentagonal solids, e.g. the dodecahedron and icosidodecahedron, give the best fit with experimental bond lengths; an ideal pyramidal solid which models covalent bonds was also generated. Second, the macroscopic compression/tension architectural approach was applied to forces at the molecular level, considering atomic interactions as compressive (repulsive) and tensile (attractive) forces. Two particle interactions were considered, followed by a model of the dihydrogen molecule (H₂; two protons and two electrons). Dihydrogen was evaluated as two different types of compression/tension structures: a coaxial spring model and a ring model. Using similar methods, covalent diatomic molecules (made up of C, N, O, or F) were evaluated. Finally, the compression/tension model was extended to the nuclear level, based on the observation that nuclei with certain numbers of protons/neutrons (magic numbers) have extra stability compared to other nucleon ratios. A hollow spherical model was developed that combines elements of the classic nuclear shell model and liquid drop model. Nuclear structure and the trend of the “island of stability” for the current and extended periodic table were studied.","abstract_html":"Mathematical analysis in chemistry is a fascinating and critical tool to explain experimental observations. In this dissertation, mathematical methods to present chemical bonding and other structures for many-particle systems are discussed at different levels (molecular, atomic, and nuclear). First, the tetrahedral geometry of single, double, or triple carbon-carbon bonds gives an unsatisfying demonstration of bond lengths, compared to experimental trends. To correct this, Platonic solids and Archimedean solids were evaluated as atoms in covalent carbon or nitrogen bond systems in order to find the best solids for geometric fitting. Pentagonal solids, e.g. the dodecahedron and icosidodecahedron, give the best fit with experimental bond lengths; an ideal pyramidal solid which models covalent bonds was also generated. Second, the macroscopic compression/tension architectural approach was applied to forces at the molecular level, considering atomic interactions as compressive (repulsive) and tensile (attractive) forces. Two particle interactions were considered, followed by a model of the dihydrogen molecule (H₂; two protons and two electrons). Dihydrogen was evaluated as two different types of compression/tension structures: a coaxial spring model and a ring model. Using similar methods, covalent diatomic molecules (made up of C, N, O, or F) were evaluated. Finally, the compression/tension model was extended to the nuclear level, based on the observation that nuclei with certain numbers of protons/neutrons (magic numbers) have extra stability compared to other nucleon ratios. A hollow spherical model was developed that combines elements of the classic nuclear shell model and liquid drop model. Nuclear structure and the trend of the “island of stability” for the current and extended periodic table were studied.","abstract_has_math":false,"creators":["Wang, Dayu"],"institution":"University of Missouri--Kansas City","degree_name":"Ph.D.","degree_level":"Doctoral","degree_discipline":"Chemistry (UMKC)","degree_department":null,"school":null,"contributors":[],"advisors":["Van Horn, J. David"],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-06-19","date_published":"2015-06-19","updated_at":"2026-07-24T05:16:57Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10355/45947","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Van Horn, J. 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David Van Horn","Vita","Includes bibliographic references (pages 166-177)","Thesis (Ph.D.)--Department of Chemistry and Department of Physics and Astronomy. University of Missouri--Kansas City, 2015"]},{"key":"dc:description.abstract","label":"Abstract","values":["Mathematical analysis in chemistry is a fascinating and critical tool to explain experimental observations. In this dissertation, mathematical methods to present chemical bonding and other structures for many-particle systems are discussed at different levels (molecular, atomic, and nuclear). First, the tetrahedral geometry of single, double, or triple carbon-carbon bonds gives an unsatisfying demonstration of bond lengths, compared to experimental trends. To correct this, Platonic solids and Archimedean solids were evaluated as atoms in covalent carbon or nitrogen bond systems in order to find the best solids for geometric fitting. Pentagonal solids, e.g. the dodecahedron and icosidodecahedron, give the best fit with experimental bond lengths; an ideal pyramidal solid which models covalent bonds was also generated. Second, the macroscopic compression/tension architectural approach was applied to forces at the molecular level, considering atomic interactions as compressive (repulsive) and tensile (attractive) forces. Two particle interactions were considered, followed by a model of the dihydrogen molecule (H₂; two protons and two electrons). Dihydrogen was evaluated as two different types of compression/tension structures: a coaxial spring model and a ring model. Using similar methods, covalent diatomic molecules (made up of C, N, O, or F) were evaluated. Finally, the compression/tension model was extended to the nuclear level, based on the observation that nuclei with certain numbers of protons/neutrons (magic numbers) have extra stability compared to other nucleon ratios. A hollow spherical model was developed that combines elements of the classic nuclear shell model and liquid drop model. Nuclear structure and the trend of the “island of stability” for the current and extended periodic table were studied."]},{"key":"dc:title","label":"Title","values":["Mathematical Analysis of Compressive/Tensile Molecular and Nuclear Structures"]}]}],"canonical_facts":{"dc:contributor.advisor":["Van Horn, J. David"],"dc:creator":["Wang, Dayu"],"dc:date.accessioned":["2015-06-19T18:33:41Z"],"dc:date.available":["2015-06-19T18:33:41Z"],"dc:date.issued":["2015-06-19"],"dc:description":["Title from PDF of title page, viewed on July 10, 2015","Dissertation advisor: J. David Van Horn","Vita","Includes bibliographic references (pages 166-177)","Thesis (Ph.D.)--Department of Chemistry and Department of Physics and Astronomy. University of Missouri--Kansas City, 2015"],"dc:description.abstract":["Mathematical analysis in chemistry is a fascinating and critical tool to explain experimental observations. In this dissertation, mathematical methods to present chemical bonding and other structures for many-particle systems are discussed at different levels (molecular, atomic, and nuclear). First, the tetrahedral geometry of single, double, or triple carbon-carbon bonds gives an unsatisfying demonstration of bond lengths, compared to experimental trends. To correct this, Platonic solids and Archimedean solids were evaluated as atoms in covalent carbon or nitrogen bond systems in order to find the best solids for geometric fitting. Pentagonal solids, e.g. the dodecahedron and icosidodecahedron, give the best fit with experimental bond lengths; an ideal pyramidal solid which models covalent bonds was also generated. Second, the macroscopic compression/tension architectural approach was applied to forces at the molecular level, considering atomic interactions as compressive (repulsive) and tensile (attractive) forces. Two particle interactions were considered, followed by a model of the dihydrogen molecule (H₂; two protons and two electrons). Dihydrogen was evaluated as two different types of compression/tension structures: a coaxial spring model and a ring model. Using similar methods, covalent diatomic molecules (made up of C, N, O, or F) were evaluated. Finally, the compression/tension model was extended to the nuclear level, based on the observation that nuclei with certain numbers of protons/neutrons (magic numbers) have extra stability compared to other nucleon ratios. A hollow spherical model was developed that combines elements of the classic nuclear shell model and liquid drop model. Nuclear structure and the trend of the “island of stability” for the current and extended periodic table were studied."],"dc:identifier.uri":["https://hdl.handle.net/10355/45947"],"dc:language.iso":["eng"],"dc:title":["Mathematical Analysis of Compressive/Tensile Molecular and Nuclear Structures"],"dc:type":["Thesis"],"thesis:degree_discipline":["Chemistry (UMKC)","Physics (UMKC)"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Missouri--Kansas City"]},"updated_at":"2026-07-24T05:16:57Z"}