  The stability of atomic intercalated carbon $K_{4}$ crystals, XC$_{2}$ (X=H,
Li, Be, B, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Ca, Ga, Ge, As, Se, Br, Rb
or Sr) is evaluated by geometry optimization and frozen phonon analysis based
on first principles calculations. Although C $K_{4}$ is unstable, NaC$_{2}$ and
MgC$_{2}$ are found to be stable. It is shown that NaC$_{2}$ and MgC$_{2}$ are
metallic and semi conducting, respectively.
