A Comparison of Exact and Model Exchange-Correlation Potentials for Molecules

Bikash Kanungo; Paul M Zimmerman; Vikram Gavini

doi:10.1021/acs.jpclett.1c03670

A Comparison of Exact and Model Exchange-Correlation Potentials for Molecules

J Phys Chem Lett. 2021 Dec 23;12(50):12012-12019. doi: 10.1021/acs.jpclett.1c03670. Epub 2021 Dec 13.

Authors

Bikash Kanungo¹, Paul M Zimmerman², Vikram Gavini^{1

3}

Affiliations

¹ Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States.
² Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States.
³ Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States.

PMID: 34898217
DOI: 10.1021/acs.jpclett.1c03670

Abstract

Accurate exchange-correlation (XC) potentials for three-dimensional systems─via solution of the inverse density functional theory (DFT) problem─are now available to test the quality of DFT approximations. Herein, the exact XC potential for seven molecules─dihydrogen at four different bond-lengths, lithium hydride, water, and ortho-benzyne─are computed from full configuration interaction reference densities. These are compared to model XC potentials from nonlocal (B3LYP, HSE06, SCAN0, and M08-HX) and semilocal/local (SCAN, PBE, and PW92) XC functionals. Whereas for most systems, relative errors in the ground-state densities are $O (10^{- 3} - 10^{- 2})$ , the model XC potentials have much higher errors of $O (10^{- 1} - 10^{0})$ . Among the model XC functionals, SCAN0 offers the best agreement with the exact XC potential, underlining the significance of satisfying exact conditions as well as including nonlocal effects in XC functionals. This work indicates that tests against the exact XC potential will provide a promising new direction for building more accurate XC functionals for DFT.