Global and local curvature in density functional theory
Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within density...
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| Format: | Article |
| Language: | en_US |
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American Institute of Physics (AIP)
2017
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| Online Access: | http://hdl.handle.net/1721.1/107972 https://orcid.org/0000-0002-5535-0513 https://orcid.org/0000-0001-9342-0191 |
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| author | Zhao, Qing Ioannidis, Efthymios Ioannis Kulik, Heather Janine |
| author2 | Massachusetts Institute of Technology. Department of Chemical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Chemical Engineering Zhao, Qing Ioannidis, Efthymios Ioannis Kulik, Heather Janine |
| author_sort | Zhao, Qing |
| collection | MIT |
| description | Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within density functional theory (DFT) fail to reproduce this behavior, giving rise to deviations from linearity with a convex global curvature that is evidence of many-electron, self-interaction error and electron delocalization. Popular functional tuning strategies focus on reproducing piecewise linearity, especially to improve predictions of optical properties. In a divergent approach, Hubbard U-augmented DFT (i.e., DFT+U) treats self-interaction errors by reducing the local curvature of the energy with respect to electron removal or addition from one localized subshell to the surrounding system. Although it has been suggested that DFT+U should simultaneously alleviate global and local curvature in the atomic limit, no detailed study on real systems has been carried out to probe the validity of this statement. In this work, we show when DFT+U should minimize deviations from linearity and demonstrate that a “+U” correction will never worsen the deviation from linearity of the underlying xc approximation. However, we explain varying degrees of efficiency of the approach over 27 octahedral transition metal complexes with respect to transition metal (Sc–Cu) and ligand strength (CO, NH3, and H2O) and investigate select pathological cases where the delocalization error is invisible to DFT+U within an atomic projection framework. Finally, we demonstrate that the global and local curvatures represent different quantities that show opposing behavior with increasing ligand field strength, and we identify where these two may still coincide. |
| first_indexed | 2024-09-23T16:16:54Z |
| format | Article |
| id | mit-1721.1/107972 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:16:54Z |
| publishDate | 2017 |
| publisher | American Institute of Physics (AIP) |
| record_format | dspace |
| spelling | mit-1721.1/1079722022-09-29T19:21:40Z Global and local curvature in density functional theory Zhao, Qing Ioannidis, Efthymios Ioannis Kulik, Heather Janine Massachusetts Institute of Technology. Department of Chemical Engineering Massachusetts Institute of Technology. Department of Mechanical Engineering Sloan School of Management Kulik, Heather J Zhao, Qing Ioannidis, Efthymios Ioannis Kulik, Heather Janine Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within density functional theory (DFT) fail to reproduce this behavior, giving rise to deviations from linearity with a convex global curvature that is evidence of many-electron, self-interaction error and electron delocalization. Popular functional tuning strategies focus on reproducing piecewise linearity, especially to improve predictions of optical properties. In a divergent approach, Hubbard U-augmented DFT (i.e., DFT+U) treats self-interaction errors by reducing the local curvature of the energy with respect to electron removal or addition from one localized subshell to the surrounding system. Although it has been suggested that DFT+U should simultaneously alleviate global and local curvature in the atomic limit, no detailed study on real systems has been carried out to probe the validity of this statement. In this work, we show when DFT+U should minimize deviations from linearity and demonstrate that a “+U” correction will never worsen the deviation from linearity of the underlying xc approximation. However, we explain varying degrees of efficiency of the approach over 27 octahedral transition metal complexes with respect to transition metal (Sc–Cu) and ligand strength (CO, NH3, and H2O) and investigate select pathological cases where the delocalization error is invisible to DFT+U within an atomic projection framework. Finally, we demonstrate that the global and local curvatures represent different quantities that show opposing behavior with increasing ligand field strength, and we identify where these two may still coincide. National Science Foundation (U.S.) (Grant ECCS-1449291) MIT Energy Initiative (Seed Grant) Massachusetts Institute of Technology 2017-04-07T19:41:33Z 2017-04-07T19:41:33Z 2016-08 2016-07 Article http://purl.org/eprint/type/JournalArticle 0021-9606 1089-7690 http://hdl.handle.net/1721.1/107972 Zhao, Qing, Efthymios I. Ioannidis, and Heather J. Kulik. “Global and Local Curvature in Density Functional Theory.” The Journal of Chemical Physics 145.5 (2016): 054109. https://orcid.org/0000-0002-5535-0513 https://orcid.org/0000-0001-9342-0191 en_US http://dx.doi.org/10.1063/1.4959882 The Journal of Chemical Physics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf American Institute of Physics (AIP) Prof. Kulik |
| spellingShingle | Zhao, Qing Ioannidis, Efthymios Ioannis Kulik, Heather Janine Global and local curvature in density functional theory |
| title | Global and local curvature in density functional theory |
| title_full | Global and local curvature in density functional theory |
| title_fullStr | Global and local curvature in density functional theory |
| title_full_unstemmed | Global and local curvature in density functional theory |
| title_short | Global and local curvature in density functional theory |
| title_sort | global and local curvature in density functional theory |
| url | http://hdl.handle.net/1721.1/107972 https://orcid.org/0000-0002-5535-0513 https://orcid.org/0000-0001-9342-0191 |
| work_keys_str_mv | AT zhaoqing globalandlocalcurvatureindensityfunctionaltheory AT ioannidisefthymiosioannis globalandlocalcurvatureindensityfunctionaltheory AT kulikheatherjanine globalandlocalcurvatureindensityfunctionaltheory |