First-principles determination of the structure of NaN and ${\rm Na}_N^-$NaN− clusters with up to 80 atoms

We have performed an extensive computational search for the global minimum (GM) structures of both neutral and anionic sodium clusters with up to 80 atoms. The theoretical framework combines basin hopping unbiased optimizations based on a Gupta empirical potential (EP) and subsequent reoptimization of many candidate structures at the density functional theory level. An important technical point is that the candidates are selected based on cluster shape descriptors rather than the relative stabilities of the EP model. An explicit comparison of the electronic density of states of cluster anions to experimental photoemission spectra suggests that the correct GM structures have been identified for all but two sizes (N = 47 and 70). This comparison validates the accuracy of the proposed methodology. Furthermore, our GM structures either match or improve over the results of previous works for all sizes. Sodium clusters are seen to accommodate strain very efficiently because: (a) many structures are based on polyicosahedral packing; (b) others are based on Kasper polyhedra and show polytetrahedral order; (c) finally, some (N + 1)-atom structures are obtained by incorporating one adatom into the outermost atomic shell of a compact N-atom cluster, at the cost of increasing the bond strain. GM structures of neutrals and anions differ for most sizes. Cluster stabilities are analyzed and shown to be dominated by electron shell closing effects for the smaller clusters and by geometrical packing effects for the larger clusters. The critical size separating both regimes is around 55 atoms. Some implications for the melting behavior of sodium clusters are discussed.