Collapse of the electron gas from three to two dimensions in Kohn-Sham density functional theory

Article

关键词: EXCHANGE-CORRELATION ENERGY;    JELLIUM MODEL;    APPROXIMATIONS;    ACCURACY;    SYSTEMS;   

DOI  :  10.1103/PhysRevB.98.085147

来源: SCIE

【 摘 要 】

Under pressure, a quasi-two-dimensional electron gas can collapse toward the true two-dimensional (2D) limit. In this limit, the exact exchange-correlation energy per electron has a known finite limit, but general-purpose semilocal approximate density functionals, such as the local density approximation (LDA) and the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE GGA), are known to diverge to minus infinity. Here we consider a model density for a non-interacting electron gas confined to a thickness L by infinite-barrier walls, with a fixed 2D density 1/[pi(r(s)(2D))(2)] and r(s)(2D) = 4 Bohr. We estimate that LDA, PBE, and the strongly constrained and appropriately normed (SCAN) meta-GGA are accurate for the exchange-correlation energy over a wide quasi-2D range, 1.5 < L/r(s)(2D) < 3.85, but not for smaller L. Of these functionals, only SCAN tends to a finite limit when L tends to 0. Since the non-interacting kinetic energy, treated exactly in Kohn-Sham theory, dominates in this limit within a deformable jellium model, all of the general-purpose functionals can estimate the pressure required to achieve any thickness (with SCAN and LDA better than PBE). This pressure vanishes around L/r(s)(2D) = 3.85, where the 3D electron density is roughly that of the valence electrons in metallic potassium, and it reaches about 20 GPa at L/r(s)(2D) = 1.5 and 400 GPa at L/r(s)(2D) = 0.6.

【 授权许可】

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