Electronic structures and binding energies of ${\mathrm{Al}}_{13}$, ${\mathrm{Al}}_{43}$, and ${\mathrm{Al}}_{55}$ clusters with ${\mathit{I}}_{\mathit{h}}$ and fcc (${\mathit{O}}_{\mathit{h}}$) symmetries are calculated by density-functional theory (DFT) with a spin-unrestricted local-density-approximation discrete-variational-method Xα scheme. The ${\mathit{I}}_{\mathit{h}}$ structure is found to be much more stable than fcc for ${\mathrm{Al}}_{13}$. For ${\mathrm{Al}}_{55}$, the total binding energy of the fcc cuboctrahedron is about 0.5 eV lower than the ${\mathit{I}}_{\mathit{h}}$, which implies a transition from a polyhedral to a lattice-based structure with cluster size. The ionization energies, electron affinities, and energy spectra and densities of states are also calculated for selected sizes and geometries. The ionization potentials and electron affinities agree with experimental data very well. The crystal-field splitting is estimated by correlating energy levels with those from jellium-model calculations of Chou and Cohen and explains the anomalies of the experimental ionization-potential curve successfully.

• Received 27 August 1990

DOI:https://doi.org/10.1103/PhysRevB.43.10647