During the evolution of diffuse clouds to molecular clouds, gas-phase molecules freeze out on surfaces of small dust particles to form ices. On dust surfaces, water is the main constituent of the icy mantle in which a complex chemistry is taking place. We aim to study the formation pathways and the composition of the ices throughout the evolution of diffuse clouds. For this purpose, we use time-dependent rate equations to calculate the molecular abundances in both gas phase and on solid surfaces (onto dust grains). We fully consider the gas-dust interplay by including the details of freeze-out, chemical and thermal desorption, as well as the most important photo-processes on grain surfaces. The difference in binding energies of chemical species on bare and icy surfaces is also incorporated into our equations. Using the numerical code FLASH, we perform a hydrodynamical simulation of a gravitationally bound diffuse cloud and follow its contraction. We find that while the dust grains are still bare, water formation is enhanced by grain surface chemistry which is subsequently released into the gas phase, enriching the molecular medium. The CO molecules, on the other hand, tend to freeze out gradually on bare grains. This causes CO to be well mixed and strongly present within the first ice layer. Once one monolayer of water ice has formed, the binding energy of the grain surface changes significantly and an immediate and strong depletion of gas-phase water and CO molecules occur. While hydrogenation converts solid CO into formaldehyde (H$_2$CO) and methanol (CH$_3$OH), water ice becomes the main constituent of the icy grains. Inside molecular clumps formaldehyde is more abundant than water and methanol in the gas phase owing its presence in part to chemical desorption.
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