Semilocal density functional approximations occupy the second rung of the Jacob’s ladder model and are thus expected to have certain limits to their applicability. A recent study [Y. Zhang, G. Kresse, and C. Wolverton, Phys. Rev. Lett. 112, 075502 (2014)] hypothesizes that the formation energy, being one of the key quantities in alloy theory, would be beyond the grasp of semilocal density functional theory (DFT). Here, we explore the physics of semilocal DFT formation energies and shed light on the connection between the accuracy of the formation energy and the ability of a semilocal approximation to produce accurate lattice constants. We demonstrate that semilocal functionals designed to perform well for alloy constituents can concomitantly solve the problem of alloy formation energies.

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• Electronic structure
• First-principles calculations
• Alloys
• Density functional theory