Density functionals for nondynamical correlation constructed from an upper bound to the exact exchange energy density

ABSTRACT

Hyper-generalised-gradient approximations (hGGAs) for the exact exchange-correlation functional are increasingly popular in density functional theory. HGGAs model nondynamical correlation using a flexible local combination of exact (Hartree–Fock, HF) exchange and approximate exchange. We present a simplified ‘Rung 3.5’ upper bound to the HF exchange energy density, the essential ingredient of hGGAs. We also present a nonempirical generalised gradient approximation for this upper bound. Both upper bounds go to zero in the high-density and density tail limits, facilitating the construction of hGGAs that recover HF exchange in these limits. The ‘Rung 3.5’ construction enables facile evaluation of analytic derivatives and calculations in periodic boundary conditions. Extensive numerical tests show that the upper bounds capture the critical difference between HF and approximate exchange, showing these ingredients' promise for building simple hGGAs. The tests also indicate a need for more sophisticated semi-local upper bounds.

GRAPHICAL ABSTRACT

KEYWORDS:

• Density functional theory
• hyper-generalised-gradient
• rung 3.5

Acknowledgments

The authors thank the TCU High Performance Computing Center for providing HPC resources, and acknowledge Prof. Dieter Cremer for his pioneering theoretical work.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Benjamin G. Janesko  http://orcid.org/0000-0002-2572-5273

Additional information

Funding

This work was supported by the Division of Materials Research (NSF) [grant DMR-1505343].