  We present an orbital-resolved extension of the Hubbard $U$ correction to
density-functional theory (DFT). Compared to the conventional shell-averaged
approach, the prediction of energetic, electronic and structural properties is
strongly improved, particularly for compounds characterized by both localized
and hybridized states in the Hubbard manifold. The numerical values of all
Hubbard parameters are readily obtained from linear-response calculations. The
relevance of this more refined approach is showcased by its application to bulk
solids pyrite (FeS$_2$) and pyrolusite ($\beta$-MnO$_2$), as well as to six
Fe(II) molecular complexes. Our findings indicate that a careful definition of
Hubbard manifolds is indispensable for extending the applicability of DFT+$U$
beyond its current boundaries. The present orbital-resolved scheme aims to
provide a computationally undemanding yet accurate tool for electronic
structure calculations of charge-transfer insulators, transition-metal (TM)
complexes and other compounds displaying significant orbital hybridization.
