Origin of the size-dependence of the polarizability per atom in heterogeneous clusters: The case of AlP clusters

An analysis of the atomic polarizabilities α in stoichiometric aluminum phosphide clusters, computed at the MP2 and density functional theory (DFT) levels, the latter using the B3LYP functional, and partitioned using the classic and iterative versions of the Hirshfeld method, is presented. Two sets of clusters are examined: the ground-state Al_n P_n clusters (n=2-9) and the prolate clusters (Al₂ P₂)_N and (Al₃ P₃)_N (N6). In the ground-state clusters, the mean polarizability per atom, i.e., α/2n, decreases with the cluster size but shows peaks at n=5 and at n=7. We demonstrate that these peaks can be explained by a large polarizability of the Al atoms and by a low polarizability of the P atoms in Al₅ P₅ and Al₇ P₇ due to the presence of homopolar bonds in these clusters. We show indeed that the polarizability of an atom within an Al_n P_n cluster depends on the cluster size and the heteropolarity of the bonds it forms within the cluster, i.e., on the charges of the atoms. The polarizabilities of the fragments Al₂ P₂ and Al₃ P₃ in the prolate clusters were found to depend mainly on their location within the cluster. Finally, we show that the iterative Hirshfeld method is more suitable than the classic Hirshfeld method for describing the atomic polarizabilities and the atomic charges in clusters with heteropolar bonds, although both versions of the Hirshfeld method lead to similar conclusions.