Despite the detection of numerous interstellar complex organic molecules (iCOMs) for decades, it is still a matter of debate whether they are synthesized in the gas phase or on the icy surface of interstellar grains. In the past, molecular deuteration has been used to constrain the formation paths of small and abundant hydrogenated interstellar species. More recently, the deuteration degree of formamide, one of the most interesting iCOMs, has also been explained with the hypothesis that it is formed by the gas-phase reaction NH2 + H2CO. In this paper, we aim at using molecular deuteration to constrain the formation of another iCOM, glycolaldehyde, which is an important prebiotic species. More specifically, we have performed dedicated electronic structure and kinetic calculations to establish the glycolaldehyde deuteration degree in relation to that of ethanol, which is its possible parent species according to the suggestion of Skouteris et al. We found that the abundance ratio of the species containing one D atom over the all-protium counterpart depends on the produced D isotopomer and varies from 0.9 to 0.5. These theoretical predictions compare extremely well with the monodeuterated isotopomers of glycolaldehyde and that of ethanol measured toward the solar-like protostar IRAS 16293-2422, supporting the hypothesis that glycolaldehyde could be produced in the gas phase for this source. In addition, the present work confirms that the deuterium fractionation of iCOMs cannot be simply anticipated based on the deuterium fractionation of the parent species but necessitates a specific study, as already shown for the case of formamide.
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