Treating different bonding situations: Revisiting Au-Cu alloys using the random phase approximation

Abstract

The ground-state equilibrium properties of copper-gold alloys have been explored with the state-of-the-art random phase approximation (RPA). Our estimated lattice constants agree with the experiment within a mean absolute percentage error of 1.4 percent. Semilocal functionals, such as the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) and the strongly constrained and appropriately normed (SCAN) functional, fail to provide accurate bulk moduli, which indicates their inability to describe the system in a stretched or compressed state with respect to the equilibrium geometry. The PBE, PBE revised for solids, and revised Tao-Perdew-Staroverov-Scuseria functionals by Perdew et al. predict too-low formation energies, while the SCAN slightly overestimates it. The inclusion of thermal correction or the long-range dispersion provides a negligible contribution to the formation energies estimated with semilocal density functional theory. The spin-orbit coupling improves the formation energies of PBE only by 7--8 meV, while it intensifies the overestimation of SCAN. We found that the nonlocality present in RPA is able to describe the transition between two delocalized electron densities (bulk elemental constituents to crystallized alloys), as required to provide accurate formation energies without any further corrections. Based on our results, we conclude that it is difficult to find a universal density functional which can give accurate results for a wide range of properties of intermetallic alloys. However, RPA can capture different bonding situations, often better than other density functionals. It gives accurate results for a wide range of ground-state properties for the alloys, generated from metals with completely filled $d$ shells.