Size effects on the vacancy-formation energy of small sodium clusters in the jellium model

The vacancy-formation energy Δ$E_f$ in small sodium clusters (${\mathrm{Na}}_{\mathrm{N}}$, N<94) is calculated using the density-functional formalism. The clusters are simulated by a jellium background model. According to this model, strong oscillations are predicted for Δ$E_f$ in the size range studied, which makes it difficult to advance any conclusions about the evolution of Δ$E_f$ for larger values of N. The oscillations in Δ$E_f$ can be explained by looking at the binding energy of perfect and defect clusters and in simple terms by looking at the shift of one-electron levels induced by the formation of the vacancy. Δ$E_f$ has large values for the experimental ‘‘magic clusters.’’ On the other hand, low values of Δ$E_f$ correlate with clusters which become ellipsoidally deformed in Clemenger’s ellipsoidal model.