Gauge effects in local hybrid functionals evaluated for weak interactions and the GMTKN30 test set

ABSTRACT

The so-called ‘gauge problem’, due to the non-uniqueness of exchange-energy densities, is a fundamental challenge for density functionals depending on these energy densities, such as local hybrid functionals. We have recently demonstrated how gauge effects influence the potential-energy curves of the argon dimer, and other quantities depending on ‘non-physical’ Pauli repulsions introduced by incompatible gauges of (semi-)local and exact-exchange energy densities . Introduction of suitable calibration functions depending only on semi-local quantities allowed to correct for these deficiencies and suggested ways to obtain more accurate local hybrid functionals beyond the local spin density approximation (LSDA) exchange-energy density. Here we extend the study of the gauge problem by comparing a number of uncalibrated and calibrated local hybrids for (1) the potential-energy curves of further noble-gas dimers and (2) for the entire GMTKN30 test set and its individual subsets. We find that DFT-D3 dispersion corrections fitted to be compatible with uncalibrated local hybrids have to correct not only for missing London dispersion but also for gauge artefacts that make weak interactions too repulsive. This burden is taken away when using properly calibrated local hybrids, which perform much better for dispersion-sensitive quantities already without D3 corrections, and which require only the physically relevant dispersion to be corrected for. The present results suggest directions for further improvement of calibration functions for local hybrids.

GRAPHICAL ABSTRACT

KEYWORDS:

• Local hybrid functional
• local mixing function
• exchange-energy density
• calibration function
• DFT-D3 corrections
• GMTKN30 test set
• S22 test set
• weak interactions

Acknowledgments

We are grateful to the TURBOMOLE developers’ consortium for access to the source code. Part of this work has been funded by DFG project KA1187/13-1.

Supplemental data for this article can be accessed at http://dx.doi.org/10.1080/00268976.2016.1139209.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

DFG [project number KA1187/13-1].