Systematic evaluation of the accuracy of exchange-correlation functionals is essential to guide scientists in their choice of an optimal method for a given problem when using density functional theory. In this work, accuracy of one Generalized Gradient Approximation (GGA) functional, three meta-GGA functionals, one Nonseparable Gradient Approximation (NGA) functional, one meta-NGA, and three hybrid GGA functionals was evaluated for calculations of the closest interatomic distances, cohesive energies, and bulk moduli of all 3d, 4d, and 5d bulk transition metals that have face centered cubic (fcc), hexagonal closed packed (hcp), or body centered cubic (bcc) structures (a total of 27 cases). Our results show that including the extra elements of kinetic energy density and Hartree-Fock exchange energy density into gradient approximation density functionals does not usually improve them. Nevertheless, the accuracies of the Tao-Perdew-Staroverov-Scuseria (TPSS) and M06-L meta-GGAs and the MN12-L meta-NGA approach the accuracy of the Perdew-Burke-Ernzerhof (PBE) GGA, so usage of these functionals may be advisable for systems containing both solid-state transition metals and molecular species. The N12 NGA functional is also shown to be almost as accurate as PBE for bulk transition metals, and thus it could be a good choice for studies of catalysis given its proven good performance for molecular species.

The performance of various commonly used density functionals is established by comparing calculated values of atomic structure data, cohesive energies, and bulk moduli of all transition metals to available experimental data. The functionals explored are the Ceperley-Alder (CA), Vosko-Wilk-Nussair (VWN) implementation of the Local Density Approximation (LDA); the Perdew-Wang (PW91) and Perdew-Burke-Ernzerhof (PBE) forms of the Generalized Gradient Approximation (GGA), and the RPBE and PBEsol modifications of PBE, aimed at better describing adsorption energies and bulk solid lattice properties, respectively. The present systematic study shows that PW91 and PBE consistently provide the smallest differences between the calculated and experimental values. Additional calculations of the (111) surface energy of several face centered cubic (fcc) transition metals reveal that LDA produces the most accurate results, while all other functionals significantly underestimate the experimental values. RPBE severely underestimates surface energy, which may be the origin for the reduced surface chemical activity and the better performance of RPBE describing adsorption energies.