Fitting a round peg into a round hole: Asymptotically correcting the generalized gradient approximation for...

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• The local density approximation (LDA) in density functional theory (DFT) becomes highly accurate in the Lieb-Simon limit, particularly for large atomic numbers.
• Recent work has identified the leading correction to the LDA for correlation in neutral atoms.
• The Perdew-Burke-Ernzerhof (PBE) correlation functional is a widely used generalized gradient approximation (GGA).

Purpose of the Study:

• To design an asymptotically corrected generalized gradient approximation (acGGA) for correlation in DFT.
• To improve the accuracy of DFT correlation energy calculations, especially for atoms with increasing atomic number.
• To investigate the performance of the developed acGGA when combined with exchange corrections and applied to atoms and molecules.

Main Methods:

• Utilized the leading correction to the LDA and real-space cutoff properties of the exchange-correlation hole.
• Developed an acGGA correlation functional based on PBE correlation.
• Paired the acGGA correlation with a similar exchange correction and tested it against known exact conditions and experimental data.

Main Results:

• The designed acGGA correlation shows increased accuracy per electron for atoms as atomic number increases.
• When combined with exchange corrections, the acGGA satisfies more exact conditions than the PBE functional.
• The acGGA accurately reproduces correlation energies for closed-shell atoms down to Beryllium and shows consistent improvement over PBE for atoms and molecules.

Conclusions:

• The developed acGGA provides a significant improvement over PBE correlation, particularly for heavier atoms.
• Optimal global hybrids of the acGGA do not surpass PBE0 or meta-GGA functionals.
• The findings contribute to the ongoing development of non-empirical density functional construction, relevant to Jacob's ladder.