The interaction of acetylene with the surface of ice was investigated using two quantum ab initio methods. The adsorption energies were calculated with the periodic Hartree-Fock method. It was found that the acetylene molecule is hydrogen bonded to the surface and acts as a proton acceptor. The cluster Hartree-Fock method was applied in order to calculate the vibrational frequency shifts induced by this adsorption process. The theoretical values were compared to the experimental results and proved instrumental in explaining the observed spectra, whereas the dimer H2O-C2H2 data (experimental and theoretical) failed in this interpretation. This paper includes a discussion on how to interpret the failure of the dimer model compared to the periodic model.