  We have systematically studied the mechanical stability of group V transition
metal carbides TMC$_2$ (TM = Hf, Ta, W, Re, Os, Ir, Pt, and Au) in the pyrite
and fluorite phase, by calculating their elastic constants within the density
functional theory scheme. It was found that all but ReC$_2$ and OsC$_2$ are
stable in pyrite phase. On the other hand, all metal carbides studied were
unstable in the fluorite phase.
