The construction of nonempirical density functional approximations is typically guided by the satisfaction of exact constraints. More recent constructions of semilocal correlation, which tend to satisfy the maximum number of constraints, drop the gradient of the spin polarization ($\nabla \zeta$) as a semilocal ingredient. In this work we prescribe a theoretically sound method for reintroducing explicit $\nabla \zeta$ dependence in the correlation energy of such DFAs. The proposed scheme, when applied to the Strongly Constrained and Appropriately Normed (SCAN) functional, preserves nearly all of its exact constraints. Additionally, one recovers potentially important $\nabla \zeta$-dependent terms in the gradient expansion of the correlation that SCAN drops. The inclusion of $\nabla \zeta$-dependent terms in SCAN correlation is shown to improve the functional description of transition-metal atoms and molecules without significantly affecting SCAN's accurate description of $sp$ systems. For the binding energy curve of the chromium dimer ${\mathrm{Cr}}_2$, the SCAN underbinding is fully corrected at large bond lengths and reduced at short bond lengths.

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• Electronic structure
• First-principles calculations