We have performed density functional theory calculations on the adsorption of ethene onto the {111} surface of platinum. We find that the adsorption energy is sensitive to the k-point sampling used, with low k-point sampling giving rise to overestimated adsorption energies, close to the values predicted from small cluster calculations. Six adsorption modes (bridge, fee hollow, hcp hollow, atop bridge, atop hollow, and cross bridge) were investigated on a rigid Pt {111} surface. The most stable site was the bridge site (di-sigma type adsorption) with an adsorption energy of 108.7 kJ mol(-1) and C-C bond length of to 1.483 Angstrom, which is significantly longer than the calculated gas-phase ethene bond length of 1.334 Angstrom. The recently proposed fee hollow site adsorption was found to be significantly less stable (63.6 kJ mol(-1)) although slightly more favorable than the atop (pi adsorbed) modes. The effect of surface relaxation on the adsorption energy and structure was investigated by allowing the entire Pt {111) slab to relax, giving rise to large changes in the positions of the coordinating Pt atoms. The bridge site shows displacements of 0.235 Angstrom out of the surface for the two Pt atoms directly coordinated to the ethene C atoms with an increase in the adsorption energy of 18.6 kJ mol(-1) compared to the rigid surface case from 108.7 to 127.3 kJ mol(-1). The effect of Pt relaxation was greatest on the atop sites with the single Pt atoms coordinated to the ethene moving 0.356 Angstrom out of the surface for both adsorption modes. This was accompanied by an increase of the adsorption energy of 26 kJ mol(-1) with the atop bridge (85.8 kJ mol(-1)) slightly more stable than the atop hollow (84.8 kJ mol(-1)). The hollow sites were affected by surface relaxation so much so that the energetic order of the atop and hollow sites is reversed when surface relaxation is included, indicating that the latter are unlikely to be observed. We conclude that the large effect of both the k-point sampling and surface relaxation on the adsorption energy is based on a compromise between the extended electronic states and localized bonding. The effect of periodic calculations with converged k-point sampling is to accurately treat the repulsion between the extended electronic states and the molecule. The effect of surface relaxation is to allow the atoms involved in localized bonding to move out of the surface, reducing the repulsion due to the extended electronic states and so increasing the adsorption energy. As such, the use of cluster calculations, especially for molecules with weak interactions with the surface, would be expected to result in significant overestimation of the adsorption energies.