The Quasi-2D Electron Gas and Density Functional Theory: Finding a Finite Limit*

The uniform electron gas in three and two dimensions is treated exactly by popular Kohn-Sham density functional approximations. However, no general-purpose semi-local functional can find the correct behavior of a 3D electron gas undergoing extreme compression in one dimension. In this talk, I will present our recent work [1] applying the SCAN functional to this perennial problem. While the exact exchange-correlation energy per electron tends to a finite 2D limit, the local density and generalized gradient approximations to it diverge to minus infinity. SCAN tends to a finite limit that is however an order of magnitude too negative. These errors at high compression are in one sense harmless, since the noninteracting kinetic energy, treated exactly in Kohn-Sham density functional theory, overwhelms them. Relevant background in Kohn-Sham density functional theory will be presented, and only passing familiarity is assumed.
[1] A.D. Kaplan, K. Wagle, and J.P. Perdew, Phys. Rev. B. 98, 085147 (2018).