Variational QMC study of a hydrogen atom in jellium with comparison to LSDA and self-interaction corrected LSDA solutions

A hydrogen atom immersed in a finite jellium sphere is solved using variational quantum Monte Carlo (VQMC). The same system is also solved using density functional theory (DFT), in both the local spin density (LSDA) and self-interaction correction (SIC) approximations. The immersion energies calculated using these methods, as functions of the background density of the jellium, are found to lie within $1\mathrm{eV}$ of each other with minima in approximately the same positions. The DFT results show overbinding relative to the VQMC result. The immersion energies also suggest an improved performance of the SIC over the LSDA relative to the VQMC results. The atom-induced density is also calculated and shows a difference between the methods, with a more extended Friedel oscillation in the case of the VQMC result.

Figure 1

The immersion energy versus jellium sphere radius for jellium spheres of background density $0.007a_B^{-3}$. The straight line is the value of the immersion energy for hydrogen in infinite jellium of the same background density and the sinusoidal line is a guide for the eye. The highlighted points correspond to $N=10$ and $N=50$.

Figure 2

Plots of immersion energy versus background density for a hydrogen atom immersed in jellium spheres of size 10 (solid curve) and 50 (dashed curve) electrons. Also plotted is the immersion energy curve for a hydrogen atom in infinite jellium (dot-dash curve).

Figure 3

Plots of LSDA atom-induced densities for hydrogen in finite jellium spheres of background density $0.01a_B^{-3}$, with (a) 10, (b) 50, and (c) 338 electrons (solid lines). Also plotted is the atom-induced density for a hydrogen atom in infinite jellium at the same background density (dashed lines). The jellium sphere radius is shown by a vertical straight line.

Figure 4

Total energy of a hydrogen atom immersed in a 10-electron jellium sphere for different background densities.

Figure 5

Total energy of a 10-electron jellium sphere for different background densities.

Figure 6

Immersion energies for a hydrogen atom immersed in a 10-electron jellium sphere for different background densities.

Figure 7

Atom-induced density as calculated using the different methods, for $n_0=0.004a_B^{-3}$. The solid line is the LSDA density, the dashed line is the SIC density, and the noisy line is the VQMC density.