Hartree-Fock and Moller-Plesset second order (MP2) calculations have been carried out in order to study the stability and structure of open-shell group 11 monocarbonyl compounds MCO (M=Cu,Ag,Au). AgCO is calculated to be a very weakly bound molecule with a dissociation energy of less than 1 kJ/mol, and this casts some doubt on the previously reported identification of this species in matrix isolation studies. AuCO is stable only if relativistic effects are included, which explains the recently observed anomaly in the strength of the metal-CO interaction within the group 11 series. The metal-carbonyl interactions in CuCO and AuCO are relatively weak, with dissociation energies of about 30 kJ/mol and may be best described as a combination of dispersion, donor-acceptor (charge-transfer) and repulsive interactions. The MP2 Cu-CO dissociation energy of 32 kJ/mol is in good agreement with the estimated experimental value of 23+/-6 kJ/mol. At the highest level of theory, AuCO possesses a bent geometry with a bond angle of 151 degrees at the MP2 level, but this arrangement lies only 2 kJ/mol below the linear structure. The basis set superposition error and the role of metal f functions are discussed. Dipole polarizabilities are calculated for the group 11 elements at various levels of electron correlation in order to discuss dispersion interactions. These are found to be very sensitive to relativistic and electron correlation effects. For the neutral gold atom, relativistic effects in the dipole polarizability become comparable to electron correlation contributions. The multielectron adjusted group 11 pseudopotentials give reliable results for the atomic and molecular properties discussed.