{"id":{"repo_id":"baylor","oai_identifier":"oai:baylor-ir.tdl.org:2104/14838"},"canonical_url":"https://search.dev.ndltd.org/etd/baylor/oai:baylor-ir.tdl.org:2104/14838","repository":{"repo_id":"baylor","name":"Baylor University","base_url":"https://baylor-ir.tdl.org/server/oai/request"},"display":{"title":"Hubbard-corrected density functional theory : sensitivity to projection-space and renormalization of Coulomb interaction.","abstract":"Density functional theory augmented with a Hubbard correction (DFT+U ) has become a widely used framework for modeling materials in which localized d or f electrons give rise to strong electronic correlations. By introducing an explicit on-site Coulomb interaction, DFT+U can substantially improve the description of electronic structure, lattice properties, and phase stability in transition-metal oxides and related correlated materials. However, despite its conceptual simplicity and broad applicability, the predictive reliability of DFT+U calculations is known to depend sensitively on methodological choices, particularly the definition of the correlated subspace and the associated Hubbard interaction parameters. In practical implementations, the correlated subspace is defined through projection onto localized orbitals, whose spatial extent is controlled by choices such as the muffin-tin radius in all-electron methods or the projector construction in pseudopotential approaches. As a result, the projected orbital occupancies n(RMT) entering the Hubbard correction depend explicitly on the projection size. When a fixed Hubbard interaction is employed, this dependence introduces an artificial sensitivity into DFT+U results, leading to significant and sometimes qualitative variations in predicted lattice parameters, electronic band structures, and relative phase stabilities. In this dissertation, we first systematically investigate the consequences of this projection-size dependence using rutile and anatase TiO2 as representative model systems. By varying the muffin-tin radius over a physically relevant range, we demonstrate that conventional DFT+U calculations with a fixed Hubbard parameter yield inconsistent structural, electronic, and energetic trends. The inconsistency in the calculated results becomes worse with an increasing U value. These discrepancies are traced directly to changes in the projected d-orbital occupancies induced by the expanding projection region, which in turn control the strength of the Hubbard potential acting on the correlated subspace. Building on these insights, we further investigate the dependence of U on the projection size of space. Using constrained density functional theory within an all-electron formalism, the effective Coulomb interaction Ueff is computed ab initio for each choice of projection size. The resulting Ueff (RMT) values exhibit a systematic decrease with increasing projection radius. We propose that the dependence of Ueff results from the change in the relaxation & screening effects of the localized electrons as the projection size values. This implies that the Hubbard interaction is not an external parameter independent of the projection choice, but rather a quantity intrinsically linked to the spatial definition of the correlated subspace. When these projection-dependent Ueff values are employed in DFT+U calculations, the previously observed inconsistencies are resolved. The structural parameters, electronic band structures, and relative phase stabilities become robust and internally consistent across a wide range of projection sizes. Overall, this work establishes a unified framework that connects the definition of localized orbitals with the determination of the effective Coulomb interaction, providing a physically transparent route to mitigating projection-size sensitivity in DFT+U methodologies. The renormalized Ueff scheme proposed here improve the quantitative accuracy, reproducibility, and interpretability of first-principles simulations and have broader implications for computational studies of strongly correlated materials, where the interplay between orbital localization and electronic screening plays a central role.","abstract_html":"Density functional theory augmented with a Hubbard correction (DFT+U ) has become a widely used framework for modeling materials in which localized d or f electrons give rise to strong electronic correlations. By introducing an explicit on-site Coulomb interaction, DFT+U can substantially improve the description of electronic structure, lattice properties, and phase stability in transition-metal oxides and related correlated materials. However, despite its conceptual simplicity and broad applicability, the predictive reliability of DFT+U calculations is known to depend sensitively on methodological choices, particularly the definition of the correlated subspace and the associated Hubbard interaction parameters. In practical implementations, the correlated subspace is defined through projection onto localized orbitals, whose spatial extent is controlled by choices such as the muffin-tin radius in all-electron methods or the projector construction in pseudopotential approaches. As a result, the projected orbital occupancies n(RMT) entering the Hubbard correction depend explicitly on the projection size. When a fixed Hubbard interaction is employed, this dependence introduces an artificial sensitivity into DFT+U results, leading to significant and sometimes qualitative variations in predicted lattice parameters, electronic band structures, and relative phase stabilities. In this dissertation, we first systematically investigate the consequences of this projection-size dependence using rutile and anatase TiO2 as representative model systems. By varying the muffin-tin radius over a physically relevant range, we demonstrate that conventional DFT+U calculations with a fixed Hubbard parameter yield inconsistent structural, electronic, and energetic trends. The inconsistency in the calculated results becomes worse with an increasing U value. These discrepancies are traced directly to changes in the projected d-orbital occupancies induced by the expanding projection region, which in turn control the strength of the Hubbard potential acting on the correlated subspace. Building on these insights, we further investigate the dependence of U on the projection size of space. Using constrained density functional theory within an all-electron formalism, the effective Coulomb interaction Ueff is computed ab initio for each choice of projection size. The resulting Ueff (RMT) values exhibit a systematic decrease with increasing projection radius. We propose that the dependence of Ueff results from the change in the relaxation & screening effects of the localized electrons as the projection size values. This implies that the Hubbard interaction is not an external parameter independent of the projection choice, but rather a quantity intrinsically linked to the spatial definition of the correlated subspace. When these projection-dependent Ueff values are employed in DFT+U calculations, the previously observed inconsistencies are resolved. The structural parameters, electronic band structures, and relative phase stabilities become robust and internally consistent across a wide range of projection sizes. Overall, this work establishes a unified framework that connects the definition of localized orbitals with the determination of the effective Coulomb interaction, providing a physically transparent route to mitigating projection-size sensitivity in DFT+U methodologies. The renormalized Ueff scheme proposed here improve the quantitative accuracy, reproducibility, and interpretability of first-principles simulations and have broader implications for computational studies of strongly correlated materials, where the interplay between orbital localization and electronic screening plays a central role.","abstract_has_math":false,"creators":["Raman, Manjula, 1997-"],"institution":"Baylor University.","degree_name":"Ph.D.","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Park, Kenneth Taesung, 1965-"],"committee_chairs":[],"committee_members":[],"year":2026,"date_issued":"2026-05","date_published":"2026-05","updated_at":"2026-07-24T01:08:13Z","subjects":["Projection-space sensitivity.","Density functional theory (DFT)","Renormalized Hubbard Ueff values."],"languages":["en"],"rights":["Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2104/14838","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Park, Kenneth Taesung, 1965-"]},{"key":"dc:creator","label":"Author","values":["Raman, Manjula, 1997-"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2026-05-13T03:01:03Z"]},{"key":"dc:date.issued","label":"Date","values":["2026-05"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Baylor University."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Projection-space sensitivity.","Density functional theory (DFT)","Renormalized Hubbard Ueff values."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/2104/14838"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Density functional theory augmented with a Hubbard correction (DFT+U ) has become a widely used framework for modeling materials in which localized d or f electrons give rise to strong electronic correlations. By introducing an explicit on-site Coulomb interaction, DFT+U can substantially improve the description of electronic structure, lattice properties, and phase stability in transition-metal oxides and related correlated materials. However, despite its conceptual simplicity and broad applicability, the predictive reliability of DFT+U calculations is known to depend sensitively on methodological choices, particularly the definition of the correlated subspace and the associated Hubbard interaction parameters. In practical implementations, the correlated subspace is defined through projection onto localized orbitals, whose spatial extent is controlled by choices such as the muffin-tin radius in all-electron methods or the projector construction in pseudopotential approaches. As a result, the projected orbital occupancies n(RMT) entering the Hubbard correction depend explicitly on the projection size. When a fixed Hubbard interaction is employed, this dependence introduces an artificial sensitivity into DFT+U results, leading to significant and sometimes qualitative variations in predicted lattice parameters, electronic band structures, and relative phase stabilities. In this dissertation, we first systematically investigate the consequences of this projection-size dependence using rutile and anatase TiO2 as representative model systems. By varying the muffin-tin radius over a physically relevant range, we demonstrate that conventional DFT+U calculations with a fixed Hubbard parameter yield inconsistent structural, electronic, and energetic trends. The inconsistency in the calculated results becomes worse with an increasing U value. These discrepancies are traced directly to changes in the projected d-orbital occupancies induced by the expanding projection region, which in turn control the strength of the Hubbard potential acting on the correlated subspace. Building on these insights, we further investigate the dependence of U on the projection size of space. Using constrained density functional theory within an all-electron formalism, the effective Coulomb interaction Ueff is computed ab initio for each choice of projection size. The resulting Ueff (RMT) values exhibit a systematic decrease with increasing projection radius. We propose that the dependence of Ueff results from the change in the relaxation & screening effects of the localized electrons as the projection size values. This implies that the Hubbard interaction is not an external parameter independent of the projection choice, but rather a quantity intrinsically linked to the spatial definition of the correlated subspace. When these projection-dependent Ueff values are employed in DFT+U calculations, the previously observed inconsistencies are resolved. The structural parameters, electronic band structures, and relative phase stabilities become robust and internally consistent across a wide range of projection sizes. Overall, this work establishes a unified framework that connects the definition of localized orbitals with the determination of the effective Coulomb interaction, providing a physically transparent route to mitigating projection-size sensitivity in DFT+U methodologies. The renormalized Ueff scheme proposed here improve the quantitative accuracy, reproducibility, and interpretability of first-principles simulations and have broader implications for computational studies of strongly correlated materials, where the interplay between orbital localization and electronic screening plays a central role."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Hubbard-corrected density functional theory : sensitivity to projection-space and renormalization of Coulomb interaction."]}]}],"canonical_facts":{"dc:contributor.advisor":["Park, Kenneth Taesung, 1965-"],"dc:creator":["Raman, Manjula, 1997-"],"dc:date.accessioned":["2026-05-13T03:01:03Z"],"dc:date.issued":["2026-05"],"dc:description.abstract":["Density functional theory augmented with a Hubbard correction (DFT+U ) has become a widely used framework for modeling materials in which localized d or f electrons give rise to strong electronic correlations. By introducing an explicit on-site Coulomb interaction, DFT+U can substantially improve the description of electronic structure, lattice properties, and phase stability in transition-metal oxides and related correlated materials. However, despite its conceptual simplicity and broad applicability, the predictive reliability of DFT+U calculations is known to depend sensitively on methodological choices, particularly the definition of the correlated subspace and the associated Hubbard interaction parameters. In practical implementations, the correlated subspace is defined through projection onto localized orbitals, whose spatial extent is controlled by choices such as the muffin-tin radius in all-electron methods or the projector construction in pseudopotential approaches. As a result, the projected orbital occupancies n(RMT) entering the Hubbard correction depend explicitly on the projection size. When a fixed Hubbard interaction is employed, this dependence introduces an artificial sensitivity into DFT+U results, leading to significant and sometimes qualitative variations in predicted lattice parameters, electronic band structures, and relative phase stabilities. In this dissertation, we first systematically investigate the consequences of this projection-size dependence using rutile and anatase TiO2 as representative model systems. By varying the muffin-tin radius over a physically relevant range, we demonstrate that conventional DFT+U calculations with a fixed Hubbard parameter yield inconsistent structural, electronic, and energetic trends. The inconsistency in the calculated results becomes worse with an increasing U value. These discrepancies are traced directly to changes in the projected d-orbital occupancies induced by the expanding projection region, which in turn control the strength of the Hubbard potential acting on the correlated subspace. Building on these insights, we further investigate the dependence of U on the projection size of space. Using constrained density functional theory within an all-electron formalism, the effective Coulomb interaction Ueff is computed ab initio for each choice of projection size. The resulting Ueff (RMT) values exhibit a systematic decrease with increasing projection radius. We propose that the dependence of Ueff results from the change in the relaxation & screening effects of the localized electrons as the projection size values. This implies that the Hubbard interaction is not an external parameter independent of the projection choice, but rather a quantity intrinsically linked to the spatial definition of the correlated subspace. When these projection-dependent Ueff values are employed in DFT+U calculations, the previously observed inconsistencies are resolved. The structural parameters, electronic band structures, and relative phase stabilities become robust and internally consistent across a wide range of projection sizes. Overall, this work establishes a unified framework that connects the definition of localized orbitals with the determination of the effective Coulomb interaction, providing a physically transparent route to mitigating projection-size sensitivity in DFT+U methodologies. The renormalized Ueff scheme proposed here improve the quantitative accuracy, reproducibility, and interpretability of first-principles simulations and have broader implications for computational studies of strongly correlated materials, where the interplay between orbital localization and electronic screening plays a central role."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/2104/14838"],"dc:language.iso":["en"],"dc:rights":["Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission."],"dc:subject":["Projection-space sensitivity.","Density functional theory (DFT)","Renormalized Hubbard Ueff values."],"dc:title":["Hubbard-corrected density functional theory : sensitivity to projection-space and renormalization of Coulomb interaction."],"dc:type":["Thesis"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["Baylor University."]},"updated_at":"2026-07-24T01:08:13Z"}