  Carbon monoxide (CO) is the second most abundant molecule in the gas-phase of
the interstellar medium. In dense molecular clouds, it is also present in the
solid-phase as a constituent of the mixed water-dominated ices covering dust
grains. Its presence in the solid-phase is inferred from its infrared (IR)
signals. In experimental observations of solid CO/water mixed samples, its IR
frequency splits into two components, giving rise to a blue- and a redshifted
band. However, in astronomical observations, the former has never been
observed. Several attempts have been carried out to explain this peculiar
behaviour, but the question still remains open. In this work, we resorted to
pure quantum mechanical simulations in order to shed some light on this
problem. We adopted different periodic models simulating the CO/H$_2$O ice
system, such as single and multiple CO adsorption on water ice surfaces, CO
entrapped into water cages and proper CO:H$_2$O mixed ices. We also simulated
pure solid CO. The detailed analysis of our data revealed how the quadrupolar
character of CO and the dispersive forces with water ice determine the
energetic of the CO/H$_2$O ice interaction, as well as the CO spectroscopic
behaviour. Our data suggest that the blueshifted peak can be assigned to CO
interacting {\it via} the C atom with dangling H atoms of the water ice, while
the redshifted one can actually be the result of CO involved in different
reciprocal interactions with the water matrix. We also provide a possible
explanation for the lack of the blueshifted peak in astronomical spectra. Our
aim is not to provide a full account of the various interstellar ices, but
rather to elucidate the sensitivity of the CO spectral features to different
water ice environments.
