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We assess the performance of nonempirical, truly nonlocal and semi-localfunctionals with regard to structural and thermal properties of $3d$, $4d$, and$5d$ non-magnetic transition metals. We focus on constraint-based functionalsand consider the new consistent-exchange van der Waals density functionalversion vdW-DF-cx [Phys. Rev. B 89, 035412 (2014)], the semi-local PBE [Phys.Rev. Lett. 77, 3865 (1996)] and PBEsol functionals [Phys. Rev. Lett. 100,136406 (2008)] as well as the AM05 meta-functional [Phys. Rev. B 72, 085108(2005)]. Using the quasi-harmonic approximation structural parameters, elasticresponse, and thermal expansion at finite temperatures are computed andcompared to experimental data. We also compute cohesive energies explicitlyincluding zero-point vibrations. It is shown that overall vdW-DF-cx provides anaccurate description of thermal properties and retains a level oftransferability and accuracy that is comparable to or better than some of thebest constraint-based semi-local functionals. Especially, with regard to thecohesive energies the consistent inclusion of spin polarization effects in theatoms turns out to be crucial and it is important to use the rigorousspin-vdW-DF-cx formulation [Phys. Rev. Lett. 115, 136402 (2015)]. Thisdemonstrates that vdW-DF-cx has general-purpose character and can be used tostudy systems that have both sparse and dense electron distributions.

Finite-temperature properties of non-magnetic transition metals: Comparison of the performance of constraint-based semi and nonlocal functionals