Foundations of the Ionization Potential Condition for Localized Electron Removal in Density Functional Theory

Area of Science:

• Computational physics
• Quantum chemistry
• Materials science

Background:

• Density functional theory (DFT) approximations are optimized using the ionization potential theorem for finite systems.
• This method was extended to periodic systems via an ansatz generalizing the ionization potential theorem to Wannier orbitals.
• The Wannier-localization-based optimal tuning method accurately predicts properties of periodic systems, but lacks theoretical justification.

Purpose of the Study:

• To provide a rigorous theoretical justification for the ansatz used in extending the ionization potential theorem to periodic systems.
• To establish an ionization potential condition for electron removal from Wannier-localized orbitals.
• To support the theoretical findings with numerical evidence.

Main Methods:

• Extending piecewise linearity and Janak's theorems in DFT.
• Developing a theoretical framework for Wannier-localized electron removal.
• Conducting numerical calculations to validate the theory.

Main Results:

• An ionization potential condition for electron removal from Wannier orbitals is established.
• The theoretical framework is supported by numerical evidence.
• The justification strengthens the application of DFT optimal tuning to periodic systems.

Conclusions:

• The theoretical justification for the Wannier-localization-based optimal tuning method is now established.
• This work validates and enhances the predictive power of DFT for periodic materials.
• The findings pave the way for more accurate nonempirical electronic structure calculations.