Two-dimensional limit of exchange-correlation energy functional approximations

Two-dimensional limit of exchange-correlation energy functional approximations in density functional theory

We investigate the behavior of three-dimensional (3D) exchange-correlation energy functional approximations of density functional theory in anisotropic systems with two-dimensional (2D) character. Using two simple models, quasi-2D electron gas and two-electron quantum dot, we show a fundamental limitation of the local density approximation (LDA), and its semi-local extensions, generalized gradi...

Density-functional approximations for exchange and correlation

Density-functional theory (DFT) is based on two pivotal theorems due to Hohenberg and Kohn [1]. The first theorem states that the ground-state density ρ(r) of a system of electrons uniquely determines the Hamiltonian and hence all properties that can be derived from it. Using mathematical language we can say that the total electronic energy of the system is a functional of the electron density,

Correlation energy of two electrons in the high-density limit.

We consider the high-density-limit correlation energy E(c) in D > or = 2 dimensions for the (1)S ground states of three two-electron systems: helium (in which the electrons move in a Coulombic field), spherium (in which they move on the surface of a sphere), and hookium (in which they move in a quadratic potential). We find that the E(c) values are strikingly similar, depending strongly on D bu...

Correlation energy in a spin-polarized two-dimensional electron liquid in the high-density limit

Relativistic exchange-correlation energy functional: Gauge dependence of the no-pair correlation energy

We analyze the gauge dependence of the relativistic electron gas correlation energy Ec resulting from the no-pair approximation. In particular, we evaluate the relativistic no-pair Lindhard function as the basic ingredient of the random-phase approximation ~RPA! for Ec . The resulting gauge-dependent no-pair RPA is compared with a gauge-invariant counterpart. The implications for relativistic d...