Volume change of bulk metals and metal clusters due to spin-polarization

Abstract

The stabilized jellium model (SJM) provides us a method to calculate the volume changes of different simple metals as a function of the spin polarization, $ζ$, of the delocalized valence electrons. Our calculations show that for bulk metals, the equilibrium Wigner-Seitz (WS) radius, $\bar r_s(ζ)$, is always a n increasing function of the polarization i.e., the volume of a bulk metal always increases as $ζ$ increases, and the rate of increasing is higher for higher electron density metals. Using the SJM along with the local spin density approximation, we have also calculated the equilibrium WS radius, $\bar r_s(N,ζ)$, of spherical jellium clusters, at which the pressure on the cluster with given numbers of total electrons, $N$, and their spin configuration $ζ$ vanishes. Our calculations f or Cs, Na, and Al clusters show 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. For a closed-shell cluster, it is an increasing function of $ζ$ over the whole range $0\leζ\le 1$, whereas in open-shell clusters it has a decreasing behavior over the range $0\leζ\leζ_0$, where $ζ_0$ is a polarization that the cluster has a configuration consistent with Hund's first rule. The resu lts show that for all neutral clusters with ground state spin configuration, $ζ_0$, the inequality $\bar r_s(N,ζ_0)\le\bar r_s(0)$ always holds (self-compression) but, at some polarization $ζ_1>ζ_0$, the inequality changes the direction (self-expansion). However, the inequality $\bar r_s(N,ζ)\le\bar r_s(ζ)$ always holds and the equality is achieved in the limit $N\to\infty$.