Spin-polarized density functional theory has been used to investigate the C-2v, C-infinity v and D-infinity h isomers of the molecules MC2, M = Sc, Y, Tc, and selected states of the diatomic molecule TcC. According to the theory, the ground state of the diatomic is the (4)Sigma(+) TcC isomer. Bond length comparisons between the doublet and quartet isomers reveal the ground state has a double bond, and the first excited state ((2)Delta TcC) is triple bonded. For MC2, M = Sc, Y, Tc, numerous minima were located, including spin states of the same symmetry. Cyclic isomers were identified as the ground states for each of the three metals. The minimized C-C bond length for (X) over tilde (2)A(1) TcC2 is 1.58 Angstrom, and is close to typical values for carbon-carbon single bonds, whereas the corresponding bond distances in (X) over tilde (2)A(1) MC2, M = Sc, Y, are closer to typical values for carbon-carbon double bonds. Examination of the isomer structures and energies for TcC2 suggests a preference for double bond formation with the carbon atoms of the C-2 unit. This is in contrast to scandium and yttrium dicarbides which prefer to form single bonds with the C-2 unit.