Reverse-Engineering the Exchange-Correlation hole for the SCAN and r²SCAN Functional

The success of density functional theory (DFT) of electronic structure is dependent on the development of accurate and efficient density functional approximations (DFAs). These DFAs are limited by the approximation of its exchange-correlation (XC) energy which can be defined by the XC hole. Understanding this XC hole has played a vital role developing DFAs and explaining their success and limitations. We present a construction of the XC hole model for SCAN [1] and the recent r²SCAN [2] by reverse engineering from known exact hole constraints. The hole models are tested for atoms and simple molecules.

[1] J. Sun, A. Ruzsinszky, and J. Perdew, Phys. Rev. Lett. 115, 1 (2015).
[2] J. W. Furness, A. D. Kaplan, J. Ning, J. P. Perdew, and J. Sun, J. Phys. Chem. Lett. 11, 8208 (2020).