The structures and energies of the binary dititanium dicarbide, Ti2C2, in the lowest singlet, tripler, and quintet states have been investigated by density functional theory using the hybrid B3LYP functionals. Geometries and frequencies for a number of isomeric structures are presented at the B3LYP level. A rhombic structure with a transannular C-C bond (VI) is found to be the global Ti2C2 minimum. The other four-membered planar ring structures (VII and VIII) derived from the two-fold addition of carbon to the Ti-Ti or the TI-C bond of the cyclic (C-2v) Ti2C are characterized as higher energy local minima. A linear structure (I) with terminal titanium atoms is found to be a higher energy minimum in its singlet, tripler, and quintet potential energy surfaces (PES) and has a bonding characteristic of a cumulene-like valence structure. Besides, a unique nonplanar C-2v structure, which has not been obtained in the isovalence electronic Si2C2 and SiC3 systems, has been identified as a minimum. Cyclic structures are energetically favored over the linear structures. A comparison with the tetra-atomic group IVA silicon-carbon clusters is given, where appropriate.