First-principles calculations within the density-functional theory (DFT) have been carried out to study the geometric and electronic structures of Pb${}_n$ clusters with dimensions of up to 3 nm. As distinguished from prolate silicon, germanium, and tin clusters, amorphouslike lead clusters containing more independent pentagonal bipyramid Pb${}_7$ units are more favorable than octahedral ($O_h$) fragments as $n$ up to 147. On the other hand, covalently bonded Pb${}_7$ units obstruct the electronic delocalization process, i.e., the transition from clusters to metallic bulk characters. The average bond length (charge density) within the Pb${}_7$ unit is usually shorter (higher) than that among the Pb${}_7$ units. By tracing two kinds of bond forms in the Pb${}_7$ unit and between Pb${}_7$ units, we find that the melting process begins from the weaker bond between the Pb${}_7$ units. The existence of significant covalent bonding in metal clusters may also generally hold for explaining why some Sn and Pb clusters also remain solid above the bulk melting temperature as previously reported.

• Received 4 October 2010

DOI:https://doi.org/10.1103/PhysRevB.83.075429