WHY DFT UNDERESTIMATE BAND GAP

DFT (Density Functional Theory) is a powerful tool to calculate electronic structure efficiently, which has been widely used in various fields of physics and chemistry. However, it is well-known that DFT band gaps are usually underestimated compared with experimental values, especially for semiconductors and insulators. Why DFT underestimate band gap? This article aims to explore the reasons behind this discrepancy and provide some strategies to improve the accuracy of DFT band gap calculations.

1. The Nature of DFT

DFT is a first-principles method that relies on the Hohenberg-Kohn theorem, which states that the ground state properties of a many-electron system can be fully determined by the electron density. The exchange-correlation functional (XC) is a key component of DFT, which accounts for the interactions between electrons. The accuracy of DFT calculations depends on the choice of XC functional.

2. The Self-Interaction Error (SIE)

One of the main reasons for the underestimation of DFT band gaps is the self-interaction error (SIE). SIE arises from the fact that the XC functional includes the interaction of an electron with itself. This self-interaction leads to an overestimation of the Coulomb repulsion between electrons, resulting in a smaller band gap.

3. The Band Gap Problem

The band gap is the energy difference between the valence band and the conduction band. In a semiconductor or insulator, the band gap determines the material's electrical properties such as conductivity and optical absorption. DFT calculations often underestimate the band gap because the XC functional fails to properly account for the long-range interactions between electrons.

4. Strategies to Improve DFT Band Gap Calculations

To improve the accuracy of DFT band gap calculations, several strategies can be employed:

• Using hybrid functionals: Hybrid functionals combine a portion of Hartree-Fock exchange with DFT exchange and correlation. This approach can reduce the SIE and improve the band gap accuracy.

• Using range-separated functionals: Range-separated functionals separate the short-range and long-range interactions between electrons, which can help to correct the SIE and improve the band gap accuracy.

• Using many-body perturbation theory (MBPT) methods: MBPT methods are a class of post-DFT methods that can be used to improve the accuracy of DFT band gap calculations. MBPT methods include GW approximation and Bethe-Salpeter equation (BSE).

5. Conclusion

DFT is a powerful tool for electronic structure calculations, but it is important to be aware of the limitations of DFT, especially the underestimation of band gaps. By employing strategies such as using hybrid functionals, range-separated functionals, and MBPT methods, the accuracy of DFT band gap calculations can be improved.

FAQs

1. Why does DFT underestimate band gaps?
DFT underestimates band gaps due to the self-interaction error (SIE), which arises from the overestimation of Coulomb repulsion between electrons.

2. What strategies can be used to improve the accuracy of DFT band gap calculations?
Strategies to improve the accuracy of DFT band gap calculations include using hybrid functionals, range-separated functionals, and many-body perturbation theory (MBPT) methods.

3. What is the self-interaction error (SIE)?
SIE is the error that arises from the fact that the XC functional includes the interaction of an electron with itself, leading to an overestimation of the Coulomb repulsion between electrons.

4. What is the band gap problem?
The band gap problem refers to the underestimation of band gaps in DFT calculations due to the limitations of the XC functional.

5. What is the importance of band gap calculations?
Band gap calculations are important for understanding the electronic properties of materials, such as their conductivity, optical absorption, and chemical reactivity.