Parameter-free density functional for the correlation energy in two dimensions

Accurate treatment of the electronic correlation in inhomogeneous electronic systems, combined with the ability to capture the correlation energy of the homogeneous electron gas, allows to reach high predictive power in the application of density-functional theory. For two-dimensional systems we can achieve this goal by generalizing our previous approximation [Phys. Rev. B 79, 085316 (2009)] to a parameter-free form, which reproduces the correlation energy of the homogeneous gas while preserving the ability to deal with inhomogeneous systems. The resulting functional is shown to be very accurate for finite systems with an arbitrary number of electrons with respect to numerically exact reference data.

Figure 1

Upper panel: optimal coefficients $c_{\sigma \sigma }$ for locally reproducing the correlation energy densities of the homogeneous two-dimensional electron gas. The inset show the detailed behavior in the high-density limit $r_s\to 0$. Lower panel: same for $c_{\sigma \overline{\sigma }}$. Solid and dashed lines correspond to two difference approximations for the polarized component of the correlation energy in the unpolarized electron gas (see text). The inset corresponds to the high-density result in the first approximation (APP1).

Figure 2

(Color online). Relative errors produced by the present functional (circles) and the local spin-density approximation (squares) in correlation energies of spin-polarized quantum dots with respect to numerically accurate results in Ref. 2 (see text).