Smoothing techniques to tame Laplacian-dependent exchange-correlation functionals

Inclusion of dimensionless, density-Laplacian variable dependence has

proven essential for useful orbital-free meta-GGA exchange-correlation

(XC) approximations [Phys. Rev. B 102,121109 (2020); Phys. Rev. A 96, 052512 (2017) ]

That dependence introduces fourth-order spatial derivatives in the Kohn-Sham equation

that have caused numerical difficulties in orbital-free DFT

calculations. In particular, the number of SCF iterations required

can vary widely over a modest density range in the zero-temperature

pressure-density equation of state (EOS). The computed EOS can be

almost unusably rough. We present a few self-consistent smoothing

methods based on gaussian convolution that can reduce the number of

iterations by as much as a factor of 5 and provide a smoother EOS. We

give example results from calculations that combine the LKT kinetic

energy functional and the r²SCAN-L XC functional and show that the

smoothing does not does not remove the contributions of the Laplacian

dependence.