Assessing Exchange-Correlation Functionals for Accurate Densities of Solids.

Area of Science:

• Condensed Matter Physics
• Quantum Chemistry
• Computational Materials Science

Background:

• Kohn-Sham density functional theory (KS-DFT) is crucial for predicting electronic properties from first principles.
• The accuracy of KS-DFT hinges on the approximate exchange-correlation functional, which is guided by exact constraints.
• A debate exists whether current approximations prioritize energy accuracy over accurate density representation.

Purpose of the Study:

• To investigate the performance of various exchange-correlation functionals across different rungs of Jacob's ladder.
• To assess functional performance for both energy and density predictions in solid materials.
• To evaluate the impact of incorporating exact constraints in functional design.

Main Methods:

• Utilized near-exact densities and energies for three representative solids: silicon (semiconductor), sodium chloride (insulator), and copper (metal).
• Compared the performance of multiple exchange-correlation functionals, spanning semilocal, hybrid, and meta-hybrid categories.
• Analyzed errors in both energy and density predictions for each functional.

Main Results:

• Several hybrid and semilocal functionals demonstrated consistent performance in predicting both energy and density.
• Functionals designed to satisfy exact constraints generally ranked among the top performers across all material types.
• Functionals developed before the early 2000s showed a better tendency to improve both energy and density predictions simultaneously compared to some newer ones.

Conclusions:

• The study supports the use of exact constraints in constructing more reliable exchange-correlation functionals.
• There is a correlated evolution of errors in energy and density predictions, even in recent functional developments.
• The findings provide valuable insights for selecting and developing accurate KS-DFT functionals for solid-state materials.