Structure of Mg_n and Mg_n⁺ clusters up to n = 30

We present structure calculations of neutral and singly ionized Mg clusters of up to 30 atoms, as well as Na clusters of up to 10 atoms. The calculations have been performed using density functional theory (DFT) within the local (spin-)density approximation, ion cores are described by pseudopotentials. We have utilized a new algorithm for solving the Kohn-Sham equations that is formulated entirely in coordinate space and, thus, permits straightforward control of the spatial resolution. Our numerical method is particularly suitable for modern parallel computer architectures; we have thus been able to combine an unrestricted simulated annealing procedure with electronic structure calculations of high spatial resolution, corresponding to a plane-wave cutoff of 954 eV for Mg. We report the geometric structures of the resulting ground-state configurations and a few low-lying isomers. The energetics and HOMO-LUMO gaps of the ground-state configurations are carefully examined and related to their stability properties. No evidence for a non-metal to metal transition in neutral and positively charged Mg clusters is found in the regime of ion numbers examined here.