Potential energy curves for the low-lying electronic states of the Pt2CO complex are studied using the Moller-Plesset second-order perturbation theory (MP(2)) and the complete active space multiconfiguration self-consistent field method (CASSCF). Multireference singles and doubles configuration interaction (MRSDCI) computations that included up to two million configurations were also made. The results for Pt2CO are compared with experimental results for chemisorption of CO on a Pt surface. The atop and bridged bondings of CO on the Pt-surface are modeled using potential energy curves for the ground state linear and bridged Pt2CO structures. It is shown that the atop interaction proceeds without a barrier while the bridge interaction has to surmount a barrier, even though the bridge bonding leads to a more stable equilibrium complex. The calculated vibrational frequencies at the MP2 level for Pt2CO and Pt3CO are compared with the experimentally determined values for different chemisorptive sites. The differences between the atop and bridged chemical bonds are discussed using the Mulliken population analysis, The spin-orbit effect is studied utilizing a relativistic configuration interaction (RCI) approach.