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Deuterium fractionation, i.e. the enhancement of deuterated species withrespect to the non-deuterated ones, is considered to be a reliable chemicalclock of star-forming regions. This process is strongly affected by theortho-to-para (o-p) H$_2$ ratio. In this letter we explore the effect of theo-p H$_2$ conversion on grains on the deuteration timescale in fully depleteddense cores, including the most relevant uncertainties that affect this complexprocess. We show that (i) the o-p H$_2$ conversion on grains is not stronglyinfluenced by the uncertainties on the conversion time and the stickingcoefficient and (ii) that the process is controlled by the temperature and theresidence time of ortho-H$_2$ on the surface, i.e. by the binding energy. Wefind that for binding energies in between 330-550 K, depending on thetemperature, the o-p H$_2$ conversion on grains can shorten the deuteriumfractionation timescale by orders of magnitude, opening a new route to explainthe large observed deuteration fraction $D_\mathrm{frac}$ in dense molecularcloud cores. Our results suggest that the star formation timescale, whenestimated through the timescale to reach the observed deuteration fractions,might be shorter than previously proposed. However, more accurate measurementsof the binding energy are needed to better assess the overall role of thisprocess.

H$_2$ ortho-to-para conversion on grains: A route to fast deuterium fractionation in dense cloud cores?