Binding energy and electronic structure of small copper particles

The equilibrium geometry, binding energy, and electronic structure of small metal particles are investigated using self-consistent one-electron local-density theory. Results for ${\mathrm{Cu}}_2$, ${\mathrm{Cu}}_4$, and fcc ${\mathrm{Cu}}_{13}$ and ${\mathrm{Cu}}_{79}$ clusters show an increasing equilibrium bond length with cluster size, and a stiffening of the $a_1$ vibrational force constants. The calculated binding energies of 1.05 (${\mathrm{Cu}}_2$), 1.26 (${\mathrm{Cu}}_4$), 2.19 (${\mathrm{Cu}}_{13}$), and 3.03 (${\mathrm{Cu}}_{79}$) eV/atom compare well with the experimental values of 1.00 (${\mathrm{Cu}}_2$) and 3.50 (bulk) eV/atom. For ${\mathrm{Cu}}_2$ the theoretical bond length and vibrational frequency are found to be in good agreement with experiment. Densities of states and core-level shifts are analyzed to display cluster-size effects. Charge-density maps are used to display the buildup of metallic bonding charge with increasing particle size.