Numerical methods for the inverse problem of density functional theory. Issue 1 (17th July 2017)

• Record Type: Journal Article
• Authors: Jensen, Daniel S.; Wasserman, Adam
• Other Names: Brändas Erkki guestEditor.; Hoffmann Mark R. guestEditor.
• Is Part Of: International journal of quantum chemistry. Volume 118:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2017-07-17
• Subjects: density functional theory -- inverse problems -- PDE‐constrained optimization; Quantum chemistry -- Periodicals; 541.28
• DOI: 10.1002/qua.25425
• Languages: English
• ISSNs: 0020-7608

Abstract

Abstract: The inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange‐correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one‐dimensional finite and periodic model systems. Abstract : The inverse problem of density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange‐correlation potentials. This tutorial describes several numerical inverse‐DFT methods with a special focus on convergence. A thorough description of numerical errors is also provided and shown to be essential in designing accurate and efficient inverse‐DFT methods.