Correlations between bonding, size, and second hyperpolarizability (gamma) of small semiconductor clusters: ab initio...

A comprehensive investigation of the correlation between the second hyperpolarizability and the bonding and structural characteristics of stoichiometric aluminum phosphide clusters up to 18 atoms is presented. Several aluminum phosphide species displaying different types of configurations and bonding have been studied. The obtained ab initio and density functional finite field results suggest that the ionic AlP clusters are considerably less hyperpolarizable than the covalent bonded species. Other structural features such as symmetry, atoms' arrangement, and shape also play an important role on the hyperpolarizabilities of those species. However, they are only noticeable among clusters characterized by the same bonding patterns. Furthermore, the results of this study demonstrate that the bonding which is determined by the atoms' arrangement of a cluster has a more profound effect on the second hyperpolarizability than the cluster's composition or size. In addition, the mean second hyperpolarizability increases with the increasing number of atoms, assuming that the bonding characteristics among the clusters of increasing size are similar. On the other hand, the hyperpolarizability per atom rapidly decreases with the increase of atoms' number in the cluster and converges to values of approximately 900e(4)a(0)(4) and approximately 1300e(4)a(0)(4)E(h) (-3) at the HF/cc-pVDZ and MP2/cc-pVDZ levels of theory respectively. Lastly, this work provides the first systematic study on the hyperpolarizabilities of small aluminum phosphide clusters which, in their covalent forms, exhibit larger second order hyperpolarizabilities than the well studied small gallium arsenide clusters.