DFT-1/2 and shell DFT-1/2 methods: electronic structure calculation for semiconductors at LDA complexity.

Area of Science:

• Computational Materials Science
• Condensed Matter Physics
• Quantum Chemistry

Background:

• Kohn-Sham eigenvalues in DFT do not directly yield experimental excitation energies.
• Local Density Approximation (LDA) in DFT typically underestimates semiconductor band gaps.
• Accurate band gap calculations often require computationally expensive methods like hybrid functionals or GW, especially for non-strongly correlated semiconductors.

Purpose of the Study:

• To provide a detailed derivation and review of the DFT-1/2 method for semiconductor band structure calculations.
• To explore the assumptions, principles, and various developments of DFT-1/2.
• To clarify the relationship between DFT-1/2 and other advanced computational techniques.

Main Methods:

• Detailed mathematical derivation of the Slater half occupation technique.
• Verification of the self-energy potential approach within DFT-1/2.
• Review of DFT-1/2 developments including shell DFT-1/2, conduction band correction, and DFT+A-1/2.

Main Results:

• Mathematical derivations confirm the validity of the self-energy potential approach in DFT-1/2.
• The review comprehensively covers the aims, features, and principles of DFT-1/2 for covalent semiconductors.
• Relationships and comparisons are drawn between DFT-1/2 and methods like hybrid functionals, GW, and DFT+U.

Conclusions:

• DFT-1/2 presents a feasible and increasingly utilized approach for rectifying semiconductor band gaps with LDA-level complexity.
• The method addresses the demand for computationally efficient yet accurate band gap calculations.
• A thorough understanding of DFT-1/2's applications, issues, and limitations is provided.