Projected Unrestricted Hartree−Fock Calculations and the Magnetism of Large Nickel Clusters

The study of the multiplicity (M) of transition metal clusters of different sizes has been motivated by its importance in relation to the reactivity of the structures. For this reason, the accuracy and utility of restricted and unrestricted HF methodologies have been extensively analyzed. We compare rather time-consuming restricted open-shell Hartree−Fock calculations followed by multireference CI (ROHF/MRCI) with fully projected unrestricted Hartree−Fock (PUHF) methodologies for the evaluation of the M of small Ni<INF>n</INF><INF></INF> clusters (n = 4, 6, 8, 13) using the intermediate neglect of differential overlap model Hamiltonian (INDO). Different geometry and lattice parameters are considered, searching for the best way of dealing with the open-shell electronic distributions that are strongly related to reactivity. We examine both the optimized, most stable structures, and those associated with the observed interatomic bulk distance. Our results are compared with those obtained from density functional and ab initio calculations, as well as with experimental data, when available. On the basis of the results of this comparison, the PUHF model is applied to the study of trilayer and bilayer surface-slab Ni clusters of 20 and 51 atoms, respectively.