{"id":{"repo_id":"purdue-thes","oai_identifier":"oai:docs.lib.purdue.edu:open_access_dissertations-2603"},"canonical_url":"https://search.dev.ndltd.org/etd/purdue-thes/oai:docs.lib.purdue.edu:open_access_dissertations-2603","repository":{"repo_id":"purdue-thes","name":"Purdue University","base_url":"https://docs.lib.purdue.edu/do/oai/"},"display":{"title":"Density-to-Potential Inversions in Density Functional Theory","abstract":"Density functional theory and many of its extensions are formally exact quantum many-body theories. In practice, however, implementations of these theories use approximations for all but the most trivial systems. We present a set of inversion methods to numerically compute the exact potentials corresponding to given input densities. The results of these inversions may then be used to evaluate the quality of different density functional approximations and guide the design of new approximations. The inversion methods use classical gradient-based optimization routines that are constrained to satisfy the governing partial differential equations. Numerous examples are given to illustrate the strengths and weaknesses of the different inversion methods.","abstract_html":"Density functional theory and many of its extensions are formally exact quantum many-body theories. In practice, however, implementations of these theories use approximations for all but the most trivial systems. We present a set of inversion methods to numerically compute the exact potentials corresponding to given input densities. The results of these inversions may then be used to evaluate the quality of different density functional approximations and guide the design of new approximations. The inversion methods use classical gradient-based optimization routines that are constrained to satisfy the governing partial differential equations. Numerous examples are given to illustrate the strengths and weaknesses of the different inversion methods.","abstract_has_math":false,"creators":["Jensen, Daniel Spencer"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Physics & Astronomy","degree_department":null,"school":null,"contributors":["Adam Wasserman","Christopher H Greene","Kenneth P Ritchie","Yuli Lyanda-Geller"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-01-01T08:00:00Z","date_published":"2016-01-01T08:00:00Z","updated_at":"2026-07-24T03:54:38Z","subjects":["density functional theory","inverse problems","PDE-constrained optimization","time-dependent density functional theory"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://docs.lib.purdue.edu/open_access_dissertations/1387","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Adam Wasserman","Christopher H Greene","Kenneth P Ritchie","Yuli Lyanda-Geller"]},{"key":"dc:creator","label":"Author","values":["Jensen, Daniel Spencer"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics & Astronomy"]},{"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":["density functional theory","inverse problems","PDE-constrained optimization","time-dependent density functional theory"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://docs.lib.purdue.edu/open_access_dissertations/1387"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Density functional theory and many of its extensions are formally exact quantum many-body theories. In practice, however, implementations of these theories use approximations for all but the most trivial systems. We present a set of inversion methods to numerically compute the exact potentials corresponding to given input densities. The results of these inversions may then be used to evaluate the quality of different density functional approximations and guide the design of new approximations. The inversion methods use classical gradient-based optimization routines that are constrained to satisfy the governing partial differential equations. Numerous examples are given to illustrate the strengths and weaknesses of the different inversion methods."]},{"key":"dc:title","label":"Title","values":["Density-to-Potential Inversions in Density Functional Theory"]}]}],"canonical_facts":{"dc:contributor":["Adam Wasserman","Christopher H Greene","Kenneth P Ritchie","Yuli Lyanda-Geller"],"dc:creator":["Jensen, Daniel Spencer"],"dc:description.abstract":["Density functional theory and many of its extensions are formally exact quantum many-body theories. In practice, however, implementations of these theories use approximations for all but the most trivial systems. We present a set of inversion methods to numerically compute the exact potentials corresponding to given input densities. The results of these inversions may then be used to evaluate the quality of different density functional approximations and guide the design of new approximations. The inversion methods use classical gradient-based optimization routines that are constrained to satisfy the governing partial differential equations. Numerous examples are given to illustrate the strengths and weaknesses of the different inversion methods."],"dc:identifier":["https://docs.lib.purdue.edu/open_access_dissertations/1387"],"dc:subject":["density functional theory","inverse problems","PDE-constrained optimization","time-dependent density functional theory"],"dc:title":["Density-to-Potential Inversions in Density Functional Theory"],"thesis:degree_discipline":["Physics & Astronomy"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:54:38Z"}