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

The Stabilized Jellium Model 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 radius, γs(ζ), is always an 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 Stabilized Jellium Model along with the local spin density approximation, we have also calculated the equilibrium Wigner-Seitz radius, γ 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 for Cs, Na and Al clusters show that γs(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 ≤ ζ ≤ 1, whereas in open-shell clusters has a decreasing behavior over the range 0 ≤ ζ ≤ ζ0, where ζ0 is a polarization that the cluster has a configuration consistent with Hund's first rule. The results show that for all neutral clusters with ground state spin configuration, ζ0, the inequality, γs (N, ζ0) ≤ γs (0) always holds (self-compression) but, at some polarization ζ1 > ζ0, the inequality changes the direction (self-expansion). However, the inequality γs (N, ζ) ≤ γs (ζ) always holds and the equality is achieved in the limit N → ∞