Effects of nonlocal ion pseudopotential on the electronic shell structure of metal clusters

Abstract

Electronic shell and supershell structures in lithium and gallium clusters taking into account ion pseudopotentials, within both local and nonlocal approaches, are investigated. The results differ noticeably from those of the jellium background model (JBM). Some low magic numbers, underestimated in the JBM, are corrected. However, in particular, with regard to the supershell pattern, non-negligible discrepancies with experiment remain. For lithium the location of the first node in the supershell structure is found at higher sizes relative to the experimental results. For gallium the supershell node is located around ${\mathit{N}}_{\mathit{e}}$=2500 valence electrons in experiment, in striking disagreement with the JBM prediction ${\mathit{N}}_{\mathit{e}}$=1150. The pseudopotential effects shift the supershell node in the correct direction but the magnitude of the shift is insufficient to recover complete agreement with experiment. These discrepancies prove that, in addition to the pseudopotential effects, the supershell pattern observed in mass spectra depends probably on the ionic structure at the surface. Inhomogeneous ionic density at the cluster surface is then introduced in order to achieve better agreement with the experimental results. In contrast with gallium clusters for which the surface density has to be softened, the surface ionic density in lithium clusters has to be increased, suggesting a partial ion layering. Sensitivity of the supershell pattern on the pseudopotential parametrization and surface ionic density is also emphasized. In particular, the importance of the nonlocality of the pseudopotential for lithium is pointed out, in accordance with previous studies related to the optical response of small lithium clusters.