Localization and delocalization errors in density functional theory and implications for band-gap prediction.

By P. Mori-Sánchez, A. Cohen, Weitao Yang. Physical Review Letters, 2007

948 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/6cb41bee6d6e08e412937743eeca9d4a9f26ea8f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Ivo Souza
2. Nicola Marzari
3. D. Vanderbilt
4. Arash A. Mostofi
5. Jonathan R. Yates
6. Neil Qiang Su
7. Xin Xu
8. Xiao Zheng

In Materials Chemistry

1. Neil Qiang Su
2. Jinlong Yang
3. Xin Xu
4. J. Dai
5. Weitao Yang
6. Nicola Marzari
7. X. Zeng
8. D. Vanderbilt

Citations in the corpus

• Localized Orbital Scaling Correction for Systematic Elimination of Delocalization Error in Density Functional Approximations (2017, background): “Therefore, the positive error bar in the orbital energy for M = 1 exactly agrees in absolute value with the negative error bar in the total energy for M = ∞, demonstrating that the delocalization error for finite (small) and bulk systems are similar but are manifested in two different ways [3].”
• Two-dimensional boron monolayer sheets. (2012, methodology): “This has been attributed to their inherent lack of derivative discontinuity(41) and to the delocalization error.(42)Mucheffort hasbeendevoted to resolve this band gap problem, such as using the GW approximation,(43) time-dependent DFT,(44) exact exchange,(45) hybrid and screened hybrid functionals,(”