A systematic theoretical study of the adsorption of CO on the Pt{100}, Pt{110}, and Pt{111} surfaces is presented. The calculated equilibrium geometries and vibrational frequencies have been found to be rather independent of the cluster model chosen to represent the surface. However, calculated interaction energies are found to be very sensitive to the surface cluster model. The analysis of the chemisorption bond has been carried out by means of the constrained space orbital variation, CSOV, and of projection operator techniques. These analysis reveal that the bonding interactions are dominated by the pi-back-donation although sigma-donation plays a significant role. It is also clearly shown that all bonding mechanisms, other than Pauli repulsion, but specially pi-back-donation, contribute to the observed red shift. However, the pi-back-donation contribution to the red shift is very similar for CO on different sites. Hence, pi-back-donation cannot be the mechanism responsible for the observed difference for the CO vibrational frequency on on-top and bridge sites. The CSOV decomposition reveals that the lending term contributing to this difference in vibrational frequency of chemisorbed CO is the initial Pauli repulsion or "wall effect"; this is a new, important and unexpected conclusion.