13-atom metallic clusters studied by density functional theory: Dependence on exchange-correlation approximations and pseudopotentials

Abstract

In this study, the 13-atom cluster structures of alkaline metals, alkaline-earth metals, boron group metals, carbon group metals, and 3d ,4 d, and 5d transition metals in the periodic table are investigated by density functional theory with three kinds of exchange-correlation XC functionals: i local-density approximation LDA; ii generalized gradient approximation GGA with Perdew-Wang 91; and iii generalized gradient approximation with Perdew-Burke-Ernzerhof. The dependence on pseudopotentials PPs with and without semicore electrons is also examined. The relative energies of five selected high-symmetry three-dimensional and four low-symmetry layer-type isomers for each element of interest are calculated and studied. Among the 44 metallic 13-atom clusters, our results show that the two GGA XC functionals have a great consistency; LDA and GGA results also reveal a great consistency, apart from the Cr, Mn, Fe, Co, Ni, and Rh 13-atom clusters, for which the results show a significant difference. Meanwhile, for most of the elements, the calculations with and without semicore PPs also produce consistent results, except for Cr, Mo, and V, which require a careful treatment of semicore states in the PPs.