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

Spin signature of nonlocal-correlation binding in metal organic frameworks