The geometries of MgC2, (MgC2)(2), and (MgC2)(4) in their ground and low-lying excited electronic states have been determined via ab initio electronic structure methods with flexible basis sets and using various approaches for treating electron correlation. We find these species to involve primarily ionic bonding and to be very thermodynamically stable. We find the C-2(2-) moiety to exhibit both 1- and 2-fold coordination to the Mg2+ sites in the two larger clusters, which is reminiscent of what is seen in transition metal met-car compounds.