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,r s (N, ζ), of neutral and singly ionized "generic" N -electron clusters for their various spin polarizations, ζ. Our results reveal thatr s (N, ζ) as a function of ζ behaves differently depending on whether N corresponds to a closed-shell or an openshell cluster. That is, for a closed-shell one,r s (N, ζ) is an increasing function of ζ over the whole range 0 ≤ ζ ≤ 1, and for an open-shell one, it has a decreasing part corresponding to the range 0 < ζ ≤ ζ 0 , where ζ 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,r s (N, ζ), 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 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.

Equilibrium Sizes of Jellium Metal Clusters in the Stabilized Spin-Polarized Jellium Model

“…1 we have compared the equilibrium r s values of "generic clusters", JM1 (see Ref. 10), with the SJM1 results which reproduce correct trends. [12] To clarify the concept of the "generic cluster", suppose that one solves the self-consistent KS-LSDA equations for a spherical simple JM cluster with jellium radius equal to R = N 1/3 r s and total number of electrons N. For a given N, these calculations are performed for different r s values as well as different spin configurations until the equilibrium r s value,r s (N, ζ), corresponding to the absolute minimum-energy configuration is obtained ( See Fig.…”

“…We have recently shown [10] that it is not always necessary for a finite spherical jellium system to increase its size as the polarization, ζ, is increased. This can be explained by considering the fact that for an open-shell cluster if one increases the spin polarization from the possible minimum value consistent with the Pauli exclusion principle, one should make a spin-flip in the last uncomplete shell.…”

Fragmentation of Positively Charged Metal Clusters in Stabilized Jellium Model With Self-Compression

“…This effect is called self-expansion. The self-expansion has been also predicted for highly polarized metal clusters 17,23 . These two effects have different origins.…”

Energy and pressure versus volume: Equations of state motivated by the stabilized jellium model

“…29. It provides a useful zero-order model for bulk 2 and surface properties, 30 cohesive and vacancy-formation energies, 31,32 and size effects in clusters 33,34 and thin films. 35 Its relationship to other simple models such as the ''ideal metal'' 36 has been discussed in Ref.…”