Electronic Structure via Potential Functional Approximations

The universal functional of Hohenberg-Kohn is given as a coupling-constant integral over the density as a functional of the potential. Conditions are derived under which potential-functional approximations are variational. Construction via this method and imposition of these conditions are shown to greatly improve the accuracy of the noninteracting kinetic energy needed for orbital-free Kohn-Sham calculations.

Figure 1

Exact (ex) and approximate (app) kinetic energy densities (above) of Eq. (18) (black, red) and of Eq. (19) (blue, green) with the approximation in Ref. 16, and their absolute errors (below) for one particle in $v(x)=-5{sin}^2(\pi x)$, $0<x<1$.

Figure 2

Exact (ex) total energy (black) compared to the direct approximation of Ref. [16] (green) and $T_S^{\mathrm{cc}}$ of Eq. (18) (red) for $N=2$ and trial potentials $\tilde{v}(x)=-5{sin}^2(\pi x)-\Delta D{sin}^2(2\pi x)$ with the external potential at $\Delta D=0$.

Figure 3

Difference of total exact (ex) energy $E$ and $E_0$ (black) compared to the TF approximation (blue), $T_S^A$ of Ref. 16 (green) and $T_S^{\mathrm{cc}}$ of Eq. (18) (red) for $N=1$ and trial potentials $\Delta \tilde{v}(x)=-D{sin}^2(\pi x)$.