  We performed density functional calculations to estimate the formation
energies of intermetallic alloys. We used two semilocal approximations, the
generalized gradient approximation (GGA) by Perdew-Burke-Ernzerhof (PBE) and
the strongly constrained and appropriately normed (SCAN) meta-GGA. In addition,
we utilized two nonlocal DFT functionals, the hybrid HSE06, and the
state-of-the-art random phase approximation (RPA). The nonlocal functionals
such as HSE06 and RPA yield accurate formation energies of binary alloys with
completely-filled d-band metals, where semilocal functionals underperform. The
accuracy at the nonlocal functionals is greatly reduced when a partially-filled
d-band metal is present in an alloy, while PBE-GGA outperforms in these cases.
We show that the accurate prediction of formation energies by any DFT method
depends on its ability to predict the accurate electronic properties, e.g.,
valence d-band contribution to the density of states (DOS). The SCAN meta-GGA
often corrects the PBE-DOS, however, it does not provide accurate formation
energies compared to PBE. This is assumed to be due to the lack of proper error
cancellation that should be expected due to the similar bulk nature of both
alloys and their constituents, which may improve with the modification of
meta-GGA ingredients. RPA yields too negative formation energies of alloys with
partially-filled d-band metals. RPA results can be corrected by restoring the
exchange-correlation kernel, thereby improving the short-range
electron-electron correlation in metallic densities.
