Interstitial carbon, Ci, defects in Si exhibit a number of unexplained features. The Ci defect in the neutral charge state gives rise to two almost degenerate vibrational modes at 920 and 931 cm-1 whose 2:1 absorption intensity ratio naturally suggests a trigonal defect in conflict with uniaxial stress measurements. The dicarbon, Cs-Ci, defect is bistable, and the energy difference between its A and B forms is surprisingly small even though the bonding is very different. In the B form appropriate to the neutral charge state, a silicon interstitial is believed to be located near a bond-centered site between two Cs atoms. This must give rise to vibrational modes which involve the motion of both C atoms in apparent conflict with the results of photoluminescence experiments. We use an ab initio local density functional cluster method, AIMPRO, to calculate the structure and vibrational modes of these defects and find that the ratio of the absorption intensities of the local modes of Ci is in reasonable agreement with experiment even though the structure of the defect is not trigonal. We also show that modes in the vicinity of those detected by photoluminescence for the B form of the dicarbon center involve independent movements of the two C atoms. Finally, the trends in the relative energies of the A and B forms in three charge states are investigated.