Structure and stability of copper clusters: A tight-binding molecular dynamics study

Abstract

In this paper we propose a tight-binding molecular dynamics with parameters fitted to first-principles calculations on the smaller clusters and with an environment correction, to be a powerful technique for studying large transition-metal/noble-metal clusters. In particular, the structure and stability of ${\text{Cu}}_{n}$ clusters for $n=3--55$ are studied by using this technique. The results for small ${\text{Cu}}_{n}$ clusters $(n=3--9)$ show good agreement with ab initio calculations and available experimental results. In the size range $10\ensuremath{\leqslant}n\ensuremath{\leqslant}55$ most of the clusters adopt icosahedral structure which can be derived from the 13-atom icosahedron, the polyicosahedral 19-, 23-, and 26-atom clusters, and the 55-atom icosahedron, by adding or removing atoms. However, a local geometrical change from icosahedral to decahedral structure is observed for $n=40--44$ and return to the icosahedral growth pattern is found at $n=45$ which continues. Electronic ``magic numbers'' ($n=2$,$8$,$20$,$34$,$40$) in this regime are correctly reproduced. Due to electron pairing in highest occupied molecular orbitals (HOMOs), even-odd alternation is found. A sudden loss of even-odd alternation in second difference of cluster binding energy, HOMO-LUMO (LUMO, lowest unoccupied molecular orbital) gap energy and ionization potential is observed in the region $n\ensuremath{\sim}40$ due to structural change there. Interplay between electronic and geometrical structure is found.