Papers › Construction of meta-GGA functionals through restoration of exact constraint adherence...
Construction of meta-GGA functionals through restoration of exact constraint adherence to regularized SCAN functionals
James W. Furness, Aaron D. Kaplan, Jinliang Ning, John P. Perdew, Jianwei Sun
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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 r²SCAN [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, r²SCAN, and r⁴SCAN) with increasing adherence to exact conditions while maintaining a smooth interpolation. The greater smoothness of r²SCAN seems to lead to better general accuracy than the additional exact constraint of SCAN or r⁴SCAN does.
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