Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction
The band-gap problem and other systematic failures of approximate exchange-correlation functionals are explained from an analysis of total energy for fractional charges. The deviation from the correct intrinsic linear behavior in finite systems leads to delocalization and localization errors in larg...
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| Vydané v: | Physical review letters Ročník 100; číslo 14; s. 146401 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
United States
11.04.2008
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| ISSN: | 0031-9007, 1079-7114 |
| On-line prístup: | Získať plný text |
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| Abstract | The band-gap problem and other systematic failures of approximate exchange-correlation functionals are explained from an analysis of total energy for fractional charges. The deviation from the correct intrinsic linear behavior in finite systems leads to delocalization and localization errors in large and bulk systems. Functionals whose energy is convex for fractional charges such as the local density approximation display an incorrect apparent linearity in the bulk limit, due to the delocalization error. Concave functionals also have an incorrect apparent linearity in the bulk calculation, due to the localization error and imposed symmetry. This resolves an apparent paradox and identifies the physical nature of the error to be addressed to obtain accurate band gaps from density functional theory. |
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| AbstractList | The band-gap problem and other systematic failures of approximate exchange-correlation functionals are explained from an analysis of total energy for fractional charges. The deviation from the correct intrinsic linear behavior in finite systems leads to delocalization and localization errors in large and bulk systems. Functionals whose energy is convex for fractional charges such as the local density approximation display an incorrect apparent linearity in the bulk limit, due to the delocalization error. Concave functionals also have an incorrect apparent linearity in the bulk calculation, due to the localization error and imposed symmetry. This resolves an apparent paradox and identifies the physical nature of the error to be addressed to obtain accurate band gaps from density functional theory. The band-gap problem and other systematic failures of approximate exchange-correlation functionals are explained from an analysis of total energy for fractional charges. The deviation from the correct intrinsic linear behavior in finite systems leads to delocalization and localization errors in large and bulk systems. Functionals whose energy is convex for fractional charges such as the local density approximation display an incorrect apparent linearity in the bulk limit, due to the delocalization error. Concave functionals also have an incorrect apparent linearity in the bulk calculation, due to the localization error and imposed symmetry. This resolves an apparent paradox and identifies the physical nature of the error to be addressed to obtain accurate band gaps from density functional theory.The band-gap problem and other systematic failures of approximate exchange-correlation functionals are explained from an analysis of total energy for fractional charges. The deviation from the correct intrinsic linear behavior in finite systems leads to delocalization and localization errors in large and bulk systems. Functionals whose energy is convex for fractional charges such as the local density approximation display an incorrect apparent linearity in the bulk limit, due to the delocalization error. Concave functionals also have an incorrect apparent linearity in the bulk calculation, due to the localization error and imposed symmetry. This resolves an apparent paradox and identifies the physical nature of the error to be addressed to obtain accurate band gaps from density functional theory. |
| ArticleNumber | 146401 |
| Author | Mori-Sánchez, Paula Yang, Weitao Cohen, Aron J. |
| Author_xml | – sequence: 1 givenname: Paula surname: Mori-Sánchez fullname: Mori-Sánchez, Paula – sequence: 2 givenname: Aron J. surname: Cohen fullname: Cohen, Aron J. – sequence: 3 givenname: Weitao surname: Yang fullname: Yang, Weitao |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/18518055$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1103/PhysRevLett.51.1884 10.1063/1.2741248 10.1103/PhysRevLett.49.1691 10.1103/RevModPhys.74.601 10.1103/PhysRevLett.96.246401 10.1103/PhysRevA.38.3098 10.1063/1.1630011 10.1103/PhysRevLett.51.1888 10.1103/PhysRev.133.A171 10.1103/PhysRevB.37.785 10.1103/PhysRevA.14.36 10.1103/PhysRevLett.84.5172 10.1063/1.2403848 10.1103/PhysRevLett.82.370 10.1063/1.2566637 10.1103/PhysRevLett.77.3865 10.1063/1.464913 |
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