Numerical methods for the inverse problem of density functional theory
Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchangecorrelation 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 onedimensional finite and periodic model systems.
 Authors:

^{[1]}
;
^{[2]}
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Purdue Univ., West Lafayette, IN (United States)
 Publication Date:
 Report Number(s):
 SAND20177018J
Journal ID: ISSN 00207608; 655000
 Grant/Contract Number:
 AC0494AL85000
 Type:
 Accepted Manuscript
 Journal Name:
 International Journal of Quantum Chemistry
 Additional Journal Information:
 Journal Volume: 118; Journal Issue: 1; Journal ID: ISSN 00207608
 Publisher:
 Wiley
 Research Org:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org:
 NSF Funded from Graduate School; USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; density functional theory; inverse problems; PDEconstrained optimization
 OSTI Identifier:
 1421863
Jensen, Daniel S., and Wasserman, Adam. Numerical methods for the inverse problem of density functional theory. United States: N. p.,
Web. doi:10.1002/qua.25425.
Jensen, Daniel S., & Wasserman, Adam. Numerical methods for the inverse problem of density functional theory. United States. doi:10.1002/qua.25425.
Jensen, Daniel S., and Wasserman, Adam. 2017.
"Numerical methods for the inverse problem of density functional theory". United States.
doi:10.1002/qua.25425. https://www.osti.gov/servlets/purl/1421863.
@article{osti_1421863,
title = {Numerical methods for the inverse problem of density functional theory},
author = {Jensen, Daniel S. and Wasserman, Adam},
abstractNote = {Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchangecorrelation 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 onedimensional finite and periodic model systems.},
doi = {10.1002/qua.25425},
journal = {International Journal of Quantum Chemistry},
number = 1,
volume = 118,
place = {United States},
year = {2017},
month = {7}
}