Minimization of Laplacian-level orbital-free exchange-correlation functionals*

Several Laplacian-level orbital-free kinetic energy density functionals (KEDFs) such as PerdewConstantin (PC) [1] and Cancio-Red (CR) [2, 3] have been used to de-orbitalize meta-GGA exchange-correlation XC functionals to yield SCAN-L [4] and R2SCANL-L [5]. Those XC functionals yield rather accurate results in the context of the conventional Kohn-Sham equation. Here we investigate the use of such XC functionals together with modern KEDFs for self-consistent solution of the orbital-free Kohn-Sham equation. We find that direct minimization of these Laplacian-level kinetic functionals induces huge fluctuations in the potential and discuss ways to mitigate the problem.

[1] J. P. Perdew and L. A. Constantin, Phys. Rev. B 75, 155109 (2007).

[2] A. C. Cancio, D. Stewart, and A. Kuna, The Journal of Chemical Physics 144, 084107 (2016).

[3] A. C. Cancio and J. J. Redd, Molecular Physics 115, 618 (2017).

[4] D. Mejia-Rodriguez and S. B. Trickey, Phys. Rev. A 96, 052512 (2017).

[5] D. Mejia-Rodriguez and S. B. Trickey, Phys. Rev. B 102, 121109 (2020).