Systematic B3LYP/6-31G* and B3LYP/6-311+G* calculations have been performed for families of closoborane, alane, and gallane clusters consisting of A(12)H(12)(2-) (A = B, Al, and Ga) cages with endohedral or exohedral Ln+ metal cations (Ln+ = Li+, Na+, Cu+, Be2+, Mg2+, Zn2+, Al+, Al3+, Ga+, and Ga3+). Exohedral structure 1, with tridentate cation coordination at an icosabedron face, is a global minimum for most species; bidentate coordination (structure 2) is the transition state for cation migration around the dianion exterior. Migrational barriers (h(migr)), which range from 3 to 5 kcal/mol for monocations and 10-15 kcal/mol for dications, increase with increased cation charge and increased cationic radius. Ln+@B12H122- (Ln+ = Li+, Be2+, Na+, Mg2+, Al3+), Ln+@Al12H122-(Ln+ = Li+, Na+, Mg2+, Al+), and Ln+@Ga12H122- (Ln+ = Li+, Na+, Mg2+, Ga3+) endohedral clusters, with their cations located at the A(12)H(12)(2-) cage centers, are local I-h minima (3). Endohedral-exohedral isomer relative energies, E-rel(311), which are very high for the boranes, decrease rapidly down the borane-alane-gallane group and decrease along the He-Li+-Be2+-B3+ and Ne-Na+-Mg2+Al3+ isoelectronic series. Endohedral isomers of gallane clusters with heavy multicharged cations are predicted to be most favorable in energy. Two types of transition structures for a 3 --> 1 endohedral-exohedral rearrangement exist: cation exit through an edge and Ln+ exit via a ruptured pentagonal "neck" of the cage. Li+ and Bell borane salts prefer the former pathway, whereas Li+, Na+, and Mg2+ alane and gallane salts favor the latter mechanism. Cation exit barriers, h(rear), range from similar to15-55 kcal/mol and in an isoelectronic series decrease with increasing cation charge and increasing atomic mass. Endohedral Ln+@A(12)H(12)(2-) clusters show significant charge transfer from the anion to the cation; the hydrogen shell [H](12) donates electrons to Ln+ via the internal [A](12) shell, which in many cases serves as an electron "conductor".