Multiply deuterated molecules and constraints on interstellar chemistry

We consider the formation of molecules containing two or more deuterium atoms, and show how the abundances of such molecules may be used as interstellar isotopic labelling experiments to elucidate the principal chemical processes occurring in molecular clouds. Although the overall D/H ratios in deuterated isotopomers will depend on the source of the D, we show that in many cases the relative D/H ratios in singly:doubly deuterated isotopomers depends only on the chemical mechanism forming the molecule. We derive analytic expressions for the steady-state fractionation ratios in a number of molecules, including water, formaldehyde, methanol, ammonia, methane, and acetylene, and show how observations of isotopomers of these species may be used to discriminate between a gas-phase or grain-surface origin. We also briefly consider deuteration of polycyclic aromatic hydrocarbons.