  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.
