We present new models of the deuterium chemistry in protoplanetary disks, including, for the first time, multiply deuterated species. We use these models to explore whether observations in combination with models can give us clues as to which desorption processes occur in disks. We find, in common with other authors, that photodesorption can allow strongly bound molecules such as HDO to exist in the gas phase in a layer above the midplane. Models including this process give the best agreement with the observations. In the midplane, cosmic-ray heating can desorb weakly bound molecules such as CO and N_2. We find the observations suggest that N_2 is gaseous in this region, but that CO must be retained on the grains to account for the observed DCO~+/HCO~+. This could be achieved by CO having a higher binding energy than N_2 (as may be the case when these molecules are accreted onto water ice) or by a smaller cosmic-ray desorption rate for CO than assumed here, as suggested by recent theoretical work. For gaseous molecules the calculated deuteration can be greatly changed by chemical processing in the disk from the input molecular cloud values. On the grains singly deuterated species tend to retain the D/H ratio set in the molecular cloud, whereas multiply deuterated species are more affected by the disk chemistry. Consequently, the D/H ratios observed in comets may be partly set in the parent cloud and partly in the disk, depending on the molecule.
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