We investigated the behavior of H$_2$, main constituent of the gas phase in dense clouds, after collision with amorphous solid water (ASW) surfaces, one of the most abundant chemical species of interstellar ices. We developed a general framework to study the adsorption dynamics of light species on interstellar ices. We provide binding energies and their distribution, sticking probabilities for incident energies between 1 meV and 60 meV, and thermal sticking coefficients between 10 and 300 K for surface temperatures from 10 to 110 K. We found that the sticking probability depends strongly on the adsorbate kinetic energy and the surface temperature, but hardly on the angle of incidence. We observed finite sticking probabilities above the thermal desorption temperature. Adsorption and thermal desorption should be considered as separate events with separate time scales. Laboratory results for these species have shown a gap in the trends attributed to the differently employed experimental techniques. Our results complement observations and extend them, increasing the range of gas temperatures under consideration. We plan to employ our method to study a variety of adsorbates, including radical and charged species.
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