The focus of this work is to develop theoretical methods that will accurately describe electron-electron and electron-hole correlation in nanoparticles using many-body diagrammatic techniques. Diagrammatic representation is a more complex representation of quantum mechanics, however, it becomes a more advantageous representation in its application to this work due to its ease of use. Diagrammatic techniques are essential to the ve methods presented here as they prove to be pivotal in theoretical development as well as providing useful information in extracting and visualizing fundamental physics to make useful approximations to the methods. In the projected congruent transformed Hamiltonian method with partial innite order summation of diagrams (PCTH-PIOS), diagrammatic summation approach was used. In the geminal projected conguration interaction (GPCI) method, diagrammatic factorization techniques were used. In the geminal screened electron-hole interaction kernel (GSIK) method, we conclude that only linked diagrams contribute to the exciton binding energy. The approximation is made to only include rst order diagrams which captures the essential physics of the electron-hole interaction. In the composite control-variate stratied sampling (CCSS) method the calculation of the vertices of the diagrams using stratied sampling. Lastly we investigate the eect of electromagnetic (EM) eld on the generation of 2e-2h states from 1e-1h states. In this work, time independent diagrams are calculated once and used for the rest of the calculation. Diagrammatic techniques are essential to the theoretical development of the methods in this work for understanding the optical and electronic properties of nanoparticles.
","abstract_html":"<p>The focus of this work is to develop theoretical methods that will accurately describe electron-electron and electron-hole correlation in nanoparticles using many-body diagrammatic techniques. Diagrammatic representation is a more complex representation of quantum mechanics, however, it becomes a more advantageous representation in its application to this work due to its ease of use. Diagrammatic techniques are essential to the ve methods presented here as they prove to be pivotal in theoretical development as well as providing useful information in extracting and visualizing fundamental physics to make useful approximations to the methods. In the projected congruent transformed Hamiltonian method with partial innite order summation of diagrams (PCTH-PIOS), diagrammatic summation approach was used. In the geminal projected conguration interaction (GPCI) method, diagrammatic factorization techniques were used. In the geminal screened electron-hole interaction kernel (GSIK) method, we conclude that only linked diagrams contribute to the exciton binding energy. The approximation is made to only include rst order diagrams which captures the essential physics of the electron-hole interaction. In the composite control-variate stratied sampling (CCSS) method the calculation of the vertices of the diagrams using stratied sampling. Lastly we investigate the eect of electromagnetic (EM) eld on the generation of 2e-2h states from 1e-1h states. In this work, time independent diagrams are calculated once and used for the rest of the calculation. Diagrammatic techniques are essential to the theoretical development of the methods in this work for understanding the optical and electronic properties of nanoparticles.</p>","abstract_has_math":false,"creators":["Bayne, Michael Gray"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Chemistry","degree_department":null,"school":null,"contributors":["Arindam Chakraborty"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-12-21T08:00:00Z","date_published":"2018-12-21T08:00:00Z","updated_at":"2026-07-24T04:55:37Z","subjects":["Physical Sciences and Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://surface.syr.edu/etd/959","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Arindam Chakraborty"]},{"key":"dc:creator","label":"Author","values":["Bayne, Michael Gray"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Chemistry"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Physical Sciences and Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://surface.syr.edu/etd/959"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The focus of this work is to develop theoretical methods that will accurately describe electron-electron and electron-hole correlation in nanoparticles using many-body diagrammatic techniques. Diagrammatic representation is a more complex representation of quantum mechanics, however, it becomes a more advantageous representation in its application to this work due to its ease of use. Diagrammatic techniques are essential to the ve methods presented here as they prove to be pivotal in theoretical development as well as providing useful information in extracting and visualizing fundamental physics to make useful approximations to the methods. In the projected congruent transformed Hamiltonian method with partial innite order summation of diagrams (PCTH-PIOS), diagrammatic summation approach was used. In the geminal projected conguration interaction (GPCI) method, diagrammatic factorization techniques were used. In the geminal screened electron-hole interaction kernel (GSIK) method, we conclude that only linked diagrams contribute to the exciton binding energy. The approximation is made to only include rst order diagrams which captures the essential physics of the electron-hole interaction. In the composite control-variate stratied sampling (CCSS) method the calculation of the vertices of the diagrams using stratied sampling. Lastly we investigate the eect of electromagnetic (EM) eld on the generation of 2e-2h states from 1e-1h states. In this work, time independent diagrams are calculated once and used for the rest of the calculation. Diagrammatic techniques are essential to the theoretical development of the methods in this work for understanding the optical and electronic properties of nanoparticles.
"]},{"key":"dc:title","label":"Title","values":["Development of explicitly correlated and many-body diagrammatic techniques for the investigation of electron-hole correlation in nanomaterials"]}]}],"canonical_facts":{"dc:contributor":["Arindam Chakraborty"],"dc:creator":["Bayne, Michael Gray"],"dc:description.abstract":["The focus of this work is to develop theoretical methods that will accurately describe electron-electron and electron-hole correlation in nanoparticles using many-body diagrammatic techniques. Diagrammatic representation is a more complex representation of quantum mechanics, however, it becomes a more advantageous representation in its application to this work due to its ease of use. Diagrammatic techniques are essential to the ve methods presented here as they prove to be pivotal in theoretical development as well as providing useful information in extracting and visualizing fundamental physics to make useful approximations to the methods. In the projected congruent transformed Hamiltonian method with partial innite order summation of diagrams (PCTH-PIOS), diagrammatic summation approach was used. In the geminal projected conguration interaction (GPCI) method, diagrammatic factorization techniques were used. In the geminal screened electron-hole interaction kernel (GSIK) method, we conclude that only linked diagrams contribute to the exciton binding energy. The approximation is made to only include rst order diagrams which captures the essential physics of the electron-hole interaction. In the composite control-variate stratied sampling (CCSS) method the calculation of the vertices of the diagrams using stratied sampling. Lastly we investigate the eect of electromagnetic (EM) eld on the generation of 2e-2h states from 1e-1h states. In this work, time independent diagrams are calculated once and used for the rest of the calculation. Diagrammatic techniques are essential to the theoretical development of the methods in this work for understanding the optical and electronic properties of nanoparticles.
"],"dc:identifier":["https://surface.syr.edu/etd/959"],"dc:subject":["Physical Sciences and Mathematics"],"dc:title":["Development of explicitly correlated and many-body diagrammatic techniques for the investigation of electron-hole correlation in nanomaterials"],"thesis:degree_discipline":["Chemistry"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T04:55:37Z"}