  The valence electronic structure of magnetic centers is one of the factors
that determines the characteristics of a magnet. It may refer to orbital
degeneracy, as for $j_\text{eff}=1/2$ Kitaev magnets, or near-degeneracy, e.g.
involving the third and fourth shells in cuprate superconductors. Here we
explore the inner structure of magnetic moments in group-5 lacunar spinels,
fascinating materials featuring multisite magnetic units in the form of
tetrahedral tetramers. Our quantum chemical analysis reveals a very colorful
landscape, much richer than the single-electron, single-configuration
description applied so far to all group-5 Ga$M_4X_8$ chalcogenides, and
clarifies the basic multiorbital correlations on $M_4$ tetrahedral clusters:
while for V strong correlations yield a wave-function that can be well
described in terms of four V$^{4+}$V$^{3+}$V$^{3+}$V$^{3+}$ resonant valence
structures, for Nb and Ta a picture of dressed molecular-orbital-like
$j_\text{eff}=3/2$ entities is more appropriate. These internal degrees of
freedom likely shape vibronic couplings, phase transitions, and
magneto-electric properties in each of these systems.
