Calculation of the Electronic Structure of Lithium Clusters with the Self-Consistent Linear-Combination - of - Orbitals Method.

The linear-combination-of-orbitals method in the local density approximation (LDA) was used to calculate self-consistently the electronic structure of three lithium clusters, containing 15, 27, and 59 atoms. Subsequently, the 15-atom cluster was corrected for self-interaction self-consistently and on an orbital-by-orbital basis. In the other two clusters the valence electrons were corrected for self-interaction in an average way, and only the 27 -atom cluster was taken to self-consistency. The LDA calculation implies the clusters behave very much like spheres of jellium in both the one-electron energy levels and in the electron density. Jellium electronic shells are easily identifiable in all three clusters, although they are modified somewhat by the aspherical crystal-field splitting of the ionic cores. In the largest cluster the jellium energy levels are clearly seen well above the Fermi level, indicating that a lithium cluster of at least 92 electrons will still have jellium-like electronic properties. Near spherical symmetry in the valence electron densities of the three clusters implies the nuclei are well screened and the effective potential for these electrons is very much like that experienced by the electrons in the spherical jellium model. Further, Friedel oscillations appearing in the density are quite reminiscent of those seen in self -consistent quantum-mechanical calculations of jellium spheres. Mulliken population analysis of the LDA results are consistent with a convergence to bulk with increasing cluster size, the interior of the largest cluster appearing bulk-like in both electron populations and density, even though the Friedel oscillations seem to penetrate to the center of the largest cluster. The self-interaction-correction (SIC) results for the clusters confirm that the eigenvalues of this procedure are much more like electron removal energies than those of the LDA. In addition the orbital-by-orbital SIC calculation of the 15-atom cluster broadened the energy range of the valence electrons to a value close that of a compatible bulk calculation. A simple technique for estimating the amount of SIC implies that clusters with thousands of atoms would still exhibit significant errors in their LDA eigenvalues.