Onset of metallic behavior in magnesium clusters.

A collection of metal atoms does not necessarily exhibit metallic behavior. In this paper, we explore the nonmetallic-to-metallic transition in the finite size regime for the case of magnesium. Magnesium is a particularly instructive case because its electronic structure varies dramatically with the number of interacting atoms. For example, when two magnesium atoms interact, only weak, van der Waals bonding results. Yet, when large numbers of magnesium atoms interact in bulk, they form a structural material. Clearly, major changes occur as more and more magnesium atoms interact and metallic properties emerge. The schematic in Fig. 1 provides a simplified, yet useful framework (ignoring the presence of hydridization) for visualizing the evolving electronic structure of magnesium. There, the energies of the most relevant orbitals are plotted versus increasing numbers of interacting magnesium atoms, n. The doubly occupied 3s energy level of the ground state atom along with the empty 3p level above it are shown on the left side of the figure. When two magnesium atoms interact to form a dimer, two molecular orbitals are formed and both are filled. As more magnesium atoms interact, new molecular orbitals are formed in like fashion, with n magnesium atoms giving n molecular orbitals, and with these too being filled to capacity. Above these, molecular orbitals based on the 3p atomic orbitals of magnesium are also formed, but these are empty. As still more atoms interact, both the filled 3s 2 -derived molecular orbitals and the empty 3p-derived molecular orbitals broaden in energy, producing ‘‘fans’’ of molecular orbitals. The energy difference between the highest energy, 3s 2 -derived molecular orbital (the HOMO) and the lowest energy, 3p-derived molecular orbital (the LUMO) is the HOMO-LUMO gap, � , and it becomes smaller with increasing numbers of interacting magnesium atoms. Once � ! 0, however, the filled and empty fans overlap, and electrons from the 3s 2 -derived fan of molecular orbitals spill into the fan of previously unoccupied, 3p-derived molecular orbitals, creating a partially filled band and meeting the usual criterion for the onset of metallic behavior. Figure 1 can also be viewed as representing the evolving electronic structure of individual, neutral magnesium clusters as a function of size, n. If one next imagines adding an extra electron to each of these clusters to form their corresponding ground state cluster anions, then, for clusters smaller than that at the gap closure, that extra electron must reside at the bottom of the previously empty, 3p-derived fan of MO’s. While the energies of the MO’s shown in Fig. 1 as well as the gap between them are quantitatively modified by the addition of one more electron to each cluster size, the figure itself remains a qualitatively viable picture for magnesium cluster anions. Determining the minimum number of interacting magnesium atoms at which the onset of metallicity occurs was the main objective of this work. We approached this problem, as had Busani et al. [1] in the case of mercury cluster anions, by photodetaching electrons from magnesium cluster anions as a function of cluster size in order to track the closure of the energy gap in the anionic system. The electron binding energy (EBE) for an electron photodetached from the bottom of the anion’s singly