Colle-Salvetti-type local density functional for the exchange-correlation energy in two dimensions

We derive an approximate local density functional for the exchange-correlation energy to be used in density-functional calculations of two-dimensional systems. In the derivation we employ the Colle-Salvetti wave function within the scheme of Salvetti and Montagnani [Phys. Rev. A 63, 052109 (2001)] to satisfy the sum rule for the exchange-correlation hole. We apply the functional to the two-dimensional homogeneous electron gas as well as to a set of quantum dots and find a very good agreement with exact reference data.

Figure 1

Absolute relative error for parabolic quantum dots, (a) $N=2$, $\omega =1$ and (b) $N=12$, $\omega =1/1.{89}^2$, with respect to parameters $\gamma$ and $\alpha$. The crosses mark the values chosen from the fit to the $N=6$ case.

Figure 2

(a) Exchange-correlation energy per particle for the two-dimensional homogeneous electron gas obtained using our functional with the chosen parameters $\gamma =1.12$ and $\alpha =0.45$ (dashed line) in comparison with the exact result (solid line). The inset shows the relative error. (b) Result for the function $q(\rho )$ obtained using our functional (dashed line) in comparison with the optimal values required to reproduce the exact exchange-correlation energy of the two-dimensional homogeneous electron gas.