The Importance of Smoothness with Exact Constraints in Functional Design*

There are two core goals in exchange-correlation functional design: accuracy and efficiency. Whilst modern semi-local functionals have greatly improved accuracy, this has often been at the cost of efficiency. Our previous work [1], and that of others [2], has shown the iso-orbital indicator α as a key component in this sensitivity, compounded by sharply varying interpolation functions. In a recent publication [2] Bartók and Yates propose a regularised SCAN (rSCAN) that resolves these numerical problems for the SCAN functional [3] at the expense of breaking some exact constraints. The uniform electron gas and slowly varying density limits are broken, along with incorrect coordinate scaling of the regularised iso-orbital indicator α_r.

We restore these constraints while preserving regularisation to give a new functional, r²SCAN. We explore how constraint restoration affects accuracy and efficiency in simple systems for which exact constraints are important.

[1] J. W. Furness, J. Sun, Phys. Rev. B 99, 041119 (2019).
[2] A. P. Bartók, J. R. Yates, J. Chem. Phys. 150, 161101 (2019).
[3] J. Sun, A. Ruzsinszky, J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015).