Molecular-orbital study of aluminum clusters containing up to 43 atoms

The self-consistent-field $X\alpha$ scattered-wave molecular-orbital method has been used to perform electronic-structure calculations for two series of aluminum clusters containing up to 43 atoms, the largest metal cluster so far treated by this method. The first series consisted of clusters of 13, 19, and 43 atoms having the $O_h$ symmetry characteristic of bulk fcc aluminum while the second consisted of 5, 9, and 25 atom clusters having the $C_{4v}$ symmetry appropriate to the (100) surface. The convergence of the calculated results as a function of cluster size has been examined. The largest cluster of each series yields an occupied bandwidth of over 90% [$92\% \left(C_{4v}\right),99\% \left(O_h\right)$] of the bulk band width derived from x-ray emission spectra. These larger clusters also show reasonable agreement with the main features of density-of-states curves derived from band-structure calculations and those inferred from recent photoemission measurements. The differences and similarities between various cluster- and band-theory results are discussed. Examination of projected densities of states for the various atoms provides a possible explanation of the smaller occupied bandwidth observed in the photoemission spectrum, compared with the x-ray or band-structure results. It is also suggested that similar projected density-of-states plots for the case of transition-metal clusters might prove useful for the study of structure sensitivity in heterogeneous catalysis.