Endohedral and exohedral polyhedral cage molecules of the form (HAO3/2)8 (A = C, Si, Ge) with double
four-membered ring D4R units complexed with the atomic or ionic species (Li+, Na+, K+, F-, Cl-, Br-, He,
Ne, Ar) have been investigated at the B3LYP/6-31G(d) and B3LYP/6-311++G(d,p) levels. Geometric,
electronic, and energetic properties were obtained. For the endohedral complexes the noble gas atoms (X =
He, Ne, and Ar) inside the cage cause the cages to expand, and the extent of the expansion depends on the
size of the included atom. Endohedral alkali ions, in contrast, exhibit both attractive and repulsive interactions
with the cage atoms. The cage expands when X = K+ and contracts when X = Li+ or Na+ for A = Si, Ge,
and for A = C, the cage expands for all three ions. Encapsulation of the halide ions results in cage expansion
throughout. Furthermore, the symmetry of the endohedral complexes when X is a cation depends critically
on the relative cation and cage sizes. The binding energies of the endohedral and exohedral complexes document
a clear preference for the latter, except for halides, where the endohedral complexes are more stable. The
stability of endohedral complexes containing the isoelectronic species X = Na+, Ne, F- is determined by the
charge transfer to the A−O cage bonding sites. The formation of the endohedral complexes is discussed in
terms of transition states that connect the exohedral and endohedral minima as well as the activation barriers
for insertion of the guest into the cage. Our studies predict that a fluoride anion can penetrate into the (HAO3/2)8
cage without destroying it. For X = Cl-, in contrast, the cage ruptures upon insertion of the impurity.