The adsorption of CO on the Fe(001) surface has been investigated by ab initio density functional methods. The surface is modeled using both an infinite periodic slab End a finite cluster which allows a detailed comparison of these two approaches. We have studied CO adsorption at three different surface locations and find that the energetically preferred site for CO adsorption corresponds to the 4-fold hollow site (alpha (3)) followed by binding to the on-top (ali and 2-fold (alpha (2)) positions. Our study is in good agreement with experiments, which show that the alpha (3) site is the preferred binding site. The theoretical value for the tilting angle in the alpha (3) position (54 degrees in both slab and cluster calculations) agrees with the experimental value of 45 +/- 10 degrees, while the greatly increased theoretical CO bond length of 1.30 Angstrom (compared to 1.11 Angstrom in the gas phase) demonstrates the activation of the CO bond in the alpha (3) position and correlates well to the observed CO stretch frequency of 1200 cm(-1) as opposed to the gas-phase value of 2143 cm(-1). Both the alpha (2) Site and alpha (1) position are known to exist experimentally, but the precise energetic ordering of these sites has not been established unambiguously. In these sites the theoretical CO bond length increases to about 1.18-1.20 Angstrom in correspondence to the experimentally observed vibrational features that are shifted to lower frequencies of about 2010 cm(-1). In our calculations we find that the eel CO is bound mon strongly than the alpha (2) CO by 7.6 kcal/mol.