  We develop a proper nonempirical spin-density formalism for the van der Waals
density functional (vdW-DF) method. We show that this generalization, termed
svdW-DF, is firmly rooted in the single-particle nature of exchange and we test
it on a range of spin systems. We investigate in detail the role of spin in the
nonlocal-correlation driven adsorption of H$_2$ and CO$_2$ in the linear
magnets Mn-MOF74, Fe-MOF74, Co-MOF74, and Ni-MOF74. In all cases, we find that
spin plays a significant role during the adsorption process despite the general
weakness of the molecular-magnetic responses. The case of CO$_2$ adsorption in
Ni-MOF74 is particularly interesting, as the inclusion of spin effects results
in an increased attraction, opposite to what the diamagnetic nature of CO$_2$
would suggest. We explain this counter-intuitive result, tracking the behavior
to a coincidental hybridization of the O $p$ states with the Ni $d$ states in
the down-spin channel. More generally, by providing insight on nonlocal
correlation in concert with spin effects, our nonempirical svdW-DF method opens
the door for a deeper understanding of weak nonlocal magnetic interactions.
