Self-consistent iterative solution of the exchange-only OEP equations for simple metal clusters in jellium model

In this work, employing the exchange-only orbital-dependent functional, we have obtained the optimized effective potential using the simple iterative method proposed by K\"ummel and Perdew [S. K\"ummel and J. P. Perdew, Phys. Rev. Lett. {\bf 90}, 43004-1 (2003)]. Using this method, we have solved the self-consistent Kohn-Sham equations for closed-shell simple metal clusters of Al, Li, Na, K, and Cs in the context of jellium model. The results are in good agreement with those obtained by the different method of Engel and Vosko [E. Engel and S. H. Vosko, Phys. Rev. B {\bf 50}, 10498 (1994)].Comment: RevTex, 6 pages, 5 eps figures. To appear in Journal of Physics:Condensed Matter (2005

Finite-size effects and the stabilized spin-polarized jellium model for metal clusters

In the framework of spherical geometry for jellium and local spin density approximation, we have obtained the equilibrium $r_s$ values, $\bar{r}_s(N,\zeta)$, of neutral and singly ionized "generic" $N$-electron clusters for their various spin polarizations, $\zeta$. Our results reveal that $\bar{r}_s(N,\zeta)$ as a function of $\zeta$ behaves differently depending on whether $N$ corresponds to a closed-shell or an open-shell cluster. That is, for a closed-shell one, $\bar{r}_s(N,\zeta)$ is an increasing function of $\zeta$ over the whole range $0\le\zeta\le 1$, and for an open-shell one, it has a decreasing part corresponding to the range $0<\zeta\le\zeta_0$, where $\zeta_0$ is a polarization that the cluster assumes in a configuration consistent with Hund's first rule. In the context of the stabilized spin-polarized jellium model, our calculations based on these equilibrium $r_s$ values, $\bar{r}_s(N,\zeta)$, show that instead of the maximum spin compensation (MSC) rule, Hund's first rule governs the minimum-energy configuration. We therefore conclude that the increasing behavior of the equilibrium $r_s$ values over the whole range of $\zeta$ is a necessary condition for obtaining the MSC rule for the minimum-energy configuration; and the only way to end up with an increasing behavior over the whole range of $\zeta$ is to break the spherical geometry of the jellium background. This is the reason why the results based on simple jellium with spheroidal or ellipsoidal geometries show up MSC rule.Comment: 10 pages, RevTex, 8 PostScript figures. to appear in J. Chem. Phys., 111 (1999

Self-compressed inhomogeneous stabilized jellium model and surface relaxation of simple metal thin films

The interlayer spacings near the surface of a crystal are different from that of the bulk. As a result, the value of the ionic density in the normal direction and near to the surface shows some oscillations around the bulk value. To describe this behavior in a simple way, we have formulated the self-compressed inhomogeneous stabilized jellium model and have applied it to simple metal thin films. In this model, for a $\nu$-layered slab, each ionic layer is replaced by a jellium slice of constant density. The equilibrium densities of the slices can be determined by minimizing the total energy per electron of the slab with respect to the slice densities. To avoid the complications that arise due to the number of independent slice-density parameters for large-$\nu$ slabs, we consider a simplified version of the model with three jellium slices: one inner bulk slice with density $\bar n_1$ and two similar surface slices of densities $\bar n_2$. In this simplified model, each slice may contain more than one ionic layer. Application of this model to the $\nu$-layered slabs ($3\le\nu\le 10$) of Al, Na, and Cs shows that, in the equilibrium state, $\bar n_1$ and $\bar n_2$ assume different values, which is significant in the Al case, and the state is more stable than that predicted in the homogeneous model in which only one global jellium density is used for the whole system. In addition, we have calculated the overall relaxations, the work functions, and the surface energies, and compared with the results of the earlier works.Comment: 19 pages, 9 figures, in pdf forma

Quantum size correction to the work function and the centroid of excess charge in positively ionized simple metal clusters

In this work, we have shown the important role of the finite-size correction to the work function in predicting the correct positions of the centroid of excess charge in positively charged simple metal clusters with different $r_s$ values ($2\le r_s\le7$). For this purpose, firstly we have calculated the self-consistent Kohn-Sham energies of neutral and singly-ionized clusters with sizes $2\le N\le 100$ in the framework of local spin-density approximation and stabilized jellium model (SJM) as well as simple jellium model (JM) with rigid jellium. Secondly, we have fitted our results to the asymptotic ionization formulas both with and without the size correction to the work function. The results of fittings show that the formula containing the size correction predict a correct position of the centroid inside the jellium while the other predicts a false position outside the jellium sphere.Comment: RevTex, 11 pages with 10 Postscript figure