{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/kohn-sham-inversion-with-mathematical","title":"Kohn-Sham inversion with mathematical guarantees","arxiv_id":"2409.04372","date":"2024-09-06","proceeding":null,"authors":["Michael F. Herbst","Vebjørn H. Bakkestuen","Andre Laestadius"],"abstract":"We use an exact Moreau-Yosida regularized formulation to obtain the exchange-correlation potential for periodic systems. We reveal a profound connection between rigorous mathematical principles and efficient numerical implementation, which marks the first computation of a Moreau-Yosida-based inversion for physical systems. We develop a mathematically rigorous inversion algorithm which is demonstrated for representative bulk materials, specifically bulk silicon, gallium arsenide, and potassium chloride. Our inversion algorithm allows the construction of rigorous error bounds that we are able to verify numerically. This unlocks a new pathway to analyze Kohn-Sham inversion methods, which we expect in turn to foster mathematical approaches for developing approximate functionals.","url_abs":"https://arxiv.org/abs/2409.04372v3","url_pdf":"https://arxiv.org/pdf/2409.04372v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"kohn-sham-inversion-with-mathematical","repo_url":"https://github.com/mfherbst/supporting-my-inversion","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}