Effects of van der Waals interactions on the structure and stability of Cu_8-xPd_x (x = 0, 4, 8) cluster isomers

Detailed knowledge of the minimum energy and low-lying structures of metal clusters is crucial to understand their physicochemical properties. In this work, the effect of van der Waals (vdW) interactions on the structure and stability of Cu-Pd clusters is investigated. With this aim, a global search algorithm that combines the basin-hopping method and density functional theory is used to explore the potential energy surface of Cu_8-xPd_x (x = 0, 4, 8) clusters. We present the structural motifs adopted by the low-energy isomers obtained with the PBE gereralized gradient exchange-correlation functional, and with PBE supplemented by dispersion energy corrections as given by Grimme's D3 method. The isomeric structures obtained by PBE and PBE-D3 methods are in general quite similar, except for minor changes in some particular isomers. Global structural explorations were also performed with the meta-GGA TPSS and the hybrid PBE0 functionals, showing a reasonable agreement with the results obtained with the PBE and corrected PBE-D3 functionals. The energetics of the clusters is investigated by analyzing the binding energy per atom. Binding ;1;energies become larger when vdW forces are included, and this contribution increases from Cu₈ to Pd₈ and then to Cu₄Pd₄. Mixing between Cu and Pd atoms to form nanoalloys is favorable, a feature consistent with the well-known formation of intermetallic compounds in the bulk Cu-Pd alloys. The HOMO-LUMO gap indicates that some isomers in Cu₈ and Cu₄Pd₄ are more reactive than the lowest energy isomer, a feature that gives a hint into the importance that low-lying isomers may have in catalytic reactions. Binding energies and HOMO-LUMO gaps present a stronger dependence on the exchange-correlation functional than the cluster structures.