Thermal expansion in small metal clusters and its impact on the electric polarizability

The thermal expansion coefficients of $\mathrm{Na}_{N}$ clusters with $8 \le N \le 40$ and $\mathrm{Al}_{7}$, $\mathrm{Al}_{13}^-$ and $\mathrm{Al}_{14}^-$ are obtained from {\it ab initio} Born-Oppenheimer LDA molecular dynamics. Thermal expansion of small metal clusters is considerably larger than that in the bulk and size-dependent. We demonstrate that the average static electric dipole polarizability of Na clusters depends linearly on the mean interatomic distance and only to a minor extent on the detailed ionic configuration when the overall shape of the electron density is enforced by electronic shell effects. The polarizability is thus a sensitive indicator for thermal expansion. We show that taking this effect into account brings theoretical and experimental polarizabilities into quantitative agreement.