Accommodation of vapor-phase water molecules into ice crystal surfaces is a fundamental process controlling atmospheric ice crystal growth. Experimental studies investigating the accommodation process with various techniques report widely spread values of the water accommodation coefficient on ice, αice, and the results on its potential temperature dependence are inconclusive. We run molecular dynamics simulations of molecules condensing onto the basal plane of ice Ih using the TIP4P/Ice empirical force field and characterize the accommodated state from this molecular perspective, utilizing the interaction energy, the tetrahedrality order parameter, and the distance below the instantaneous interface as criteria. Changes of the order parameter turn out to be a suitable measure to distinguish between the surface and bulk states of a molecule condensing onto the disordered interface. In light of the findings from the molecular dynamics, we discuss and re-analyze a recent experimental data set on αice obtained with an environmental molecular beam (EMB) setup [Kong, X.; J. Phys. Chem. A 2014, 118 (22), 3973-3979] using kinetic molecular flux modeling, aiming at a more comprehensive picture of the accommodation process from a molecular perspective. These results indicate that the experimental observations indeed cannot be explained by evaporation alone. At the same time, our results raise the issue of rapidly growing relaxation times upon decreasing temperature, challenging future experimental efforts to cover relevant time scales. Finally, we discuss the relevance of the water accommodation coefficient on ice in the context of atmospheric cloud particle growth processes.