The 12(12) closomers form a rapidly expanding class of compounds where a 12-vertex cage is surrounded by 12 identical substituents. Density functional theory (B3LYP/6-31G(d)) is used to study a number of these closomers in different states of oxidation (dianion, radical anion, and neutral cages). The cage stability increases as the group electronegativity of the substituent increases. Also, the 12(12) closomer becomes easier to oxidize as the Hammett sigma(p) parameter becomes more negative (electron-donating). As the closomer is oxidized, the size of the cage increases and the B-B distances become more asymmetric. The Raman-active breathing mode in the 404-434 cm(-1) range moves to lower frequency as the cage is oxidized, which is caused by removing one or two electrons from a cage-bonding molecular orbital.