First-principles melting of gallium clusters down to nine atoms: structural and electronic contributions to melting.

First-principles Born-Oppenheimer molecular dynamics simulations of small gallium clusters, including parallel tempering, probe the distinction between cluster and molecule in the size range of 7-12 atoms. In contrast to the larger sizes, dynamic measures of structural change at finite temperature demonstrate that Ga7 and Ga8 do not melt, suggesting a size limit to melting in gallium exists at 9 atoms. Analysis of electronic structure further supports this size limit, additionally demonstrating that a covalent nature cannot be identified for clusters larger than the gallium dimer. Ga9, Ga10 and Ga11 melt at greater-than-bulk temperatures, with no evident covalent character. As Ga12 represents the first small gallium cluster to melt at a lower-than-bulk temperature, we examine the structural properties of each cluster at finite temperature in order to probe both the origins of greater-than-bulk melting, as well as the significant differences in melting temperatures induced by a single atom addition. Size-sensitive melting temperatures can be explained by both energetic and entropic differences between the solid and liquid phases for each cluster. We show that the lower-than-bulk melting temperature of the 12-atom cluster can be attributed to persistent pair bonding, reminiscent of the pairing observed in α-gallium. This result supports the attribution of greater-than-bulk melting in gallium clusters to the anomalously low melting temperature of the bulk, due to its dimeric structure.