  Using ab-initio computational techniques on crystal determined clusters, we
report on the similarities and differences of Al$_{50}$(C$_5$(CH$_3)_5)_{12}$,
Ga$_{23}$(N(Si(CH$_3)_{3}$)$_{2}$)$_{11}$, and
Au$_{102}$(SC$_7$O$_2$H$_5$)$_{44}$ ligand-protected clusters. Each of the
ligand-protected clusters in this study show the similar stable character which
can be described via a electronic shell model. We show here that the same type
of analysis leads consistently to derive a superatomic electronic counting
rule, independently of the metal and ligand compositions. One can define the
cluster core as the set of atoms where delocalized
single-angular-momentum-character orbitals have hight weight using a
combination of Bader analysis and the evaluation of Khon-Sham orbitals.
Subsequently one can derive the nature of the ligand-core interaction. These
results yield further insight into the superatom analogy for the class of
ligand-protected metal clusters.
