Stability of metallic hollow cluster systems: Jellium model approach

It is discussed that the quantum stability of a metallic cluster system with respect to the variation in the cluster shape transforms a spherical volume distribution of ionic charge core of the cluster into a spherical hollow configuration. Calculations are performed within the jellium model approach based on the Hartree-Fock theory and also within the local-density approximation. It is demonstrated that for such spherical cluster systems, there are two stable states characterized by the different distribution of the positive charge of the ionic core. One of the states corresponds to a spherical charge distribution of the ionic core uniform over the entire cluster volume. The second fullerenelike stable state arises when positive charge is uniformly distributed over a spherical shell of a certain width.

Figure 1

Total cluster energy per atom as a function of the (a) radius $R_{\text{min}}$ and the (b) thickness $\Delta R$ of the positively charged shell calculated within the HF approximation for different cluster sizes.

Figure 2

Total cluster energy per atom calculated within the (a) HF and the (b) LDA for different cluster sizes at $r_s=4\text{a}\text{.u}\text{.}$

Figure 3

HF single-electron energies as a function of $R_{\text{min}}$ for clusters (a) $N=40$ and (b) $N=92$.

Figure 4

Total energy per atom for the cluster with two different electronic configurations versus the spherical shell thickness: $N=40$, $r_s=4\text{a}\text{.u}\text{.}$

Figure 5

HF total energy per atom as a function (a) $R_{\text{min}}$ and (b) $\Delta R$ for the different densities of positive core $r_s$.

Figure 6

Total cluster HF energy per atom for (a) $N=1$ and 2 versus the radius $R_{\text{min}}$ and the same for (b) $N=8$ versus the shell thickness parameter $\Delta R$ obtained within the HF and Hartree approximations.