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Rungs 1 to 4 of DFT Jacob's ladder: extensive test on the lattice constant, bulk modulus, and cohesive energy of solids

A large panel of old and recently proposed exchange-correlation functionals belonging to rungs 1 to 4 of Jacob's ladder of density functional theory are tested (with and without a dispersion correction term) for the calculation of the lattice constant, bulk modulus, and cohesive energy of solids. Particular attention will be paid to the functionals MGGA_MS2 [J. Sun et al., J. Chem. Phys. 138, 044113 (2013)], mBEEF [J. Wellendorff et al., J. Chem. Phys. 140, 144107 (2014)], and SCAN [J. Sun et al., Phys. Rev. Lett. 115, 036402 (2015)] that are approximations of the meta-generalized gradient type and were developed with the goal to be universally good. Another goal is also to determine for which semilocal functionals and groups of solids it is beneficial (or not necessary) to use the Hartree-Fock exchange or a dispersion correction term.