  We assess the performance of nonempirical, truly nonlocal and semi-local
functionals with regard to structural and thermal properties of $3d$, $4d$, and
$5d$ non-magnetic transition metals. We focus on constraint-based functionals
and consider the new consistent-exchange van der Waals density functional
version 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, elastic
response, and thermal expansion at finite temperatures are computed and
compared to experimental data. We also compute cohesive energies explicitly
including zero-point vibrations. It is shown that overall vdW-DF-cx provides an
accurate description of thermal properties and retains a level of
transferability and accuracy that is comparable to or better than some of the
best constraint-based semi-local functionals. Especially, with regard to the
cohesive energies the consistent inclusion of spin polarization effects in the
atoms turns out to be crucial and it is important to use the rigorous
spin-vdW-DF-cx formulation [Phys. Rev. Lett. 115, 136402 (2015)]. This
demonstrates that vdW-DF-cx has general-purpose character and can be used to
study systems that have both sparse and dense electron distributions.

Materials Science