Many-body tight-binding model for aluminum nanoparticles

A new, parametrized many-body tight-binding model is proposed for calculating the potential energy surface for aluminum nanoparticles. The parameters have been fitted to reproduce the energies for a variety of aluminum clusters (${\mathrm{Al}}_{2}$, ${\mathrm{Al}}_{3}$, ${\mathrm{Al}}_{4}$, ${\mathrm{Al}}_{7}$, ${\mathrm{Al}}_{13}$) calculated recently by the PBE0/MG3 method as well as the experimental face-centered-cubic cohesive energy, lattice constant, and a small set of $\mathrm{Al}$ cluster ionization potentials. Several types of parametrization are presented and compared. The mean unsigned error per atom for the best model is less than $0.03\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$.