Numerical methods for the inverse problem of density functional theory

Jensen, Daniel S.; Wasserman, Adam

doi:10.1002/qua.25425

Numerical methods for the inverse problem of density functional theory

Journal Article · Mon Jul 17 00:00:00 EDT 2017 · International Journal of Quantum Chemistry

DOI:https://doi.org/10.1002/qua.25425· OSTI ID:1421863

^[1]; Wasserman, Adam ^[2]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Purdue Univ., West Lafayette, IN (United States)

Here, 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.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: NSF Funded from Graduate School; USDOE

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1421863

Report Number(s):: SAND--2017-7018J; 655000

Journal Information:: International Journal of Quantum Chemistry, Journal Name: International Journal of Quantum Chemistry Journal Issue: 1 Vol. 118; ISSN 0020-7608

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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Self-Consistent Density-Functional Embedding: A Novel Approach for Density-Functional Approximations Mordovina, Uliana; Reinhard, Teresa E.; Theophilou, Iris Journal of Chemical Theory and Computation, Vol. 15, Issue 10 https://doi.org/10.1021/acs.jctc.9b00063	journal	September 2019
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