Construction of meta-GGA functionals through restoration of exact constraint adherence to regularized SCAN functionals

TL;DR

This paper develops a series of meta-GGA functionals that balance adherence to exact constraints with numerical stability, showing improved accuracy through smoother interpolation methods.

Contribution

It introduces a progression of functionals (rSCAN, r++SCAN, r2SCAN, r4SCAN) that enhance constraint adherence while maintaining numerical efficiency.

Findings

r2SCAN exhibits better general accuracy than SCAN and r4SCAN.

Smoother interpolation improves numerical stability and overall performance.

Progression of functionals systematically increases adherence to exact conditions.

Abstract

The SCAN meta-GGA exchange-correlation functional [Phys. Rev. Lett. 115, 036402 (2015)] is constructed as a chemical environment-determined interpolation between two separate energy densities: one describes single orbital electron densities accurately, and another describes slowly-varying densities accurately. To conserve constraints known for the exact exchange-correlation functional, the derivatives of this interpolation vanish in the slowly-varying limit. While theoretically convenient, this choice introduces numerical challenges that degrade the functional's efficiency. We have recently reported a modification to the SCAN functional, termed r$^2$SCAN [J. Phys. Chem. Lett. 11, 8208 (2020)] that introduces two regularizations into SCAN which improve its numerical performance at the expense of not recovering the fourth order term of the slowly-varying density gradient expansion for exchange. Here we show the derivation of a progression of functionals (rSCAN, r++SCAN, r$^2$SCAN, and r$^4$SCAN) with increasing adherence to exact conditions while maintaining a smooth interpolation. The greater smoothness of r$^2$SCAN seems to lead to better general accuracy than the additional exact constraint of SCAN or r$^4$SCAN does.