The equilibrium geometry and infrared spectra for the five isotopomers of the linear weakly bound complex between the C2H2 and CO monomeric units have been calculated at the MP2 (Moller-Plesset second-order perturbation theory) level employing the [5s4p1d/3s1p] basis set. The energy barrier for interconversion between the DCCH...CO and HCCD... CO configurations is evaluated with the HCCD...CO isotopomer predicted to be the more stable form. The dipole moment and nuclear-quadrupole coupling constant are also calculated. There is good agreement with a recent experimental study.