Fundamental gaps with approximate density functionals: the derivative discontinuity revealed from ensemble...

Area of Science:

• Quantum Chemistry
• Condensed Matter Physics
• Computational Materials Science

Background:

• The fundamental gap is key to understanding electronic structure.
• The Kohn-Sham gap from density functional theory (DFT) often differs from the fundamental gap.
• This difference is attributed to the derivative discontinuity of the exchange-correlation energy.

Purpose of the Study:

• To demonstrate that all exchange-correlation functionals inherently possess a derivative discontinuity.
• To provide a method for calculating this discontinuity without empiricism.
• To improve the prediction of fundamental gaps in electronic structure calculations.

Main Methods:

• Utilizing ensemble considerations within DFT to derive the derivative discontinuity.
• Expressing the derivative discontinuity in closed form using standard DFT calculation outputs.
• Applying the corrected gap calculation to small, finite systems and extended solids.

Main Results:

• All exchange-correlation functionals inherently possess a derivative discontinuity.
• The derived discontinuity can be calculated from standard DFT results.
• Correction significantly improves fundamental gap predictions for small systems, even with the Local Density Approximation (LDA).

Conclusions:

• The derivative discontinuity is a fundamental property of exchange-correlation functionals.
• Ensemble DFT provides a non-empirical route to this discontinuity.
• The scheme shows promise for accurate fundamental gap prediction, though LDA limitations persist for solids.