Failure of Hund's J in Contemporary DFT+U+J: Insights from Spin-Crossover Fe(II) Complexes

The effect of the Hund's J terms in the DFT+U+J family of corrective functionals for (semi)local spin-density functional theory is assessed for a series of four octahedrally coordinated Fe(II) spin-crossover molecules spanning the covalent end of the ligand field spectrum. We report values and analyze trends for the Hubbard U and Hund's J parameters determined via minimum-tracking linear response for all valence atomic subspaces and relevant spin states. These parameters are then systematically applied by using simplified rotationally invariant Hubbard functionals to identify the simplest technique capable of yielding reliable adiabatic energy differences with respect to CASPT2/CC benchmarks. Consistent with previous findings, DFT+U improves the underlying DFT electronic density toward the CASPT2 reference, whereas the inclusion of an unlike-spin Hund's J energy term exerts only a marginal additional effect. Notably, the inclusion of this canonical, positively signed Hund's J term fails to remedy, and in fact, exacerbates the deficiencies of DFT+U in describing adiabatic energy differences in strongly covalent molecular systems. It further reveals intrinsic limitations of the contemporary DFT+U+J framework in simultaneously reproducing the charge distribution and energetics of these systems and hints at directions for its improvement.