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

Abstract

In the framework of spherical geometry for jellium and local spin density approximation, we have obtained the equilibrium $r_s$ values, $\bar{r}_s(N,ζ)$, of neutral and singly ionized &#34;generic&#34; $N$-electron clusters for their various spin polarizations, $ζ$. Our results reveal that $\bar{r}_s(N,ζ)$ as a function of $ζ$ behaves differently depending on whether $N$ corresponds to a closed-shell or an open-shell cluster. That is, for a closed-shell one, $\bar{r}_s(N,ζ)$ is an increasing function of $ζ$ over the whole range $0\leζ\le 1$, and for an open-shell one, it has a decreasing part corresponding to the range $0<ζ\leζ_0$, where $ζ_0$ is a polarization that the cluster assumes in a configuration consistent with Hund&#39;s first rule. In the context of the stabilized spin-polarized jellium model, our calculations based on these equilibrium $r_s$ values, $\bar{r}_s(N,ζ)$, show that instead of the maximum spin compensation (MSC) rule, Hund&#39;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 $ζ$ 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 $ζ$ 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.