Density-functional study of electronic structure and related properties of aluminum-doped sodium clusters

Abstract

Equilibrium geometric structures, stability, ionization potentials, electron affinities, hardness, and static dipole polarizabilities of aluminum-doped sodium clusters $({\mathrm{Na}}_{n}\mathrm{Al},$ $nl~10)$ are studied with the linear combination of atomic-orbitals scheme within density-functional theory, using both the local and nonlocal approximations for exchange-correlation effects. GGA is found to extend bond lengths, and to widen the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), compared to LSDA. The evolution of the HOMO-LUMO gap, ionization potential, electron affinity, hardness, and polarizability with size of cluster shows ${\mathrm{Na}}_{5}\mathrm{Al}$ and ${\mathrm{Na}}_{7}\mathrm{Al}$ to be the most stable of those studied. The enhanced stability of these two clusters is due to shell closure. Aluminum exhibits a trivalent nature in these systems in contrast to its monovalent nature in small, pure aluminum clusters.