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

In this study, the 13-atom cluster structures of alkaline metals, alkaline-earth metals, boron group metals, carbon group metals, and $3d$, $4d$, 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.