Improving the exchange and correlation potential in density-functional approximations through constraints

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Density-functional approximations (DFAs) are crucial for electronic structure calculations.
• Accurate prediction of electronic band-gaps in solids is a significant challenge for semi-local DFAs.
• The exact Kohn-Sham (KS) potential exhibits properties like derivative discontinuity that are difficult to capture.

Purpose of the Study:

• To review and expand on imposing constraints on the effective KS potential.
• To demonstrate the numerical robustness of the optimized effective potential (OEP) equations.
• To show that constrained OEP can improve the accuracy of DFAs for solid-state properties.

Main Methods:

• Constraining the minimization of approximate total energy density-functionals.
• Solving the resulting optimized effective potential (OEP) equations.
• Applying constraints to the 'screening charge' corresponding to the Hartree, exchange, and correlation potential.

Main Results:

• The OEP equations are numerically robust despite known mathematical issues with finite basis sets.
• Constraining the screening charge corrects the asymptotic behavior of the KS potential.
• The constrained KS potential exhibits a non-zero derivative discontinuity.

Conclusions:

• Constrained OEP provides a viable route to improve DFAs.
• This method accurately captures essential features of the exact KS potential.
• The approach is promising for accurate band-gap prediction in solids.