Deuterated forms of H${_3^+}$ and their importance in astrochemistry
  At the low temperatures ($\sim$10 K) and high densities ($\sim$100,000 H$_2$
molecules per cc) of molecular cloud cores and protostellar envelopes, a large
amount of molecular species (in particular those containing C and O) freeze-out
onto dust grain surfaces. It is in these regions that the deuteration of
H$_3^+$ becomes very efficient, with a sharp abundance increase of H$_2$D$^+$
and D$_2$H$^+$. The multi-deuterated forms of H$_3^+$ participate in an active
chemistry: (i) their collision with neutral species produces deuterated
molecules such as the commonly observed N$_2$D$^+$, DCO$^+$ and
multi-deuterated NH$_3$; (ii) their dissociative electronic recombination
increases the D/H atomic ratio by several orders of magnitude above the D
cosmic abundance, thus allowing deuteration of molecules (e.g. CH$_3$OH and
H$_2$O) on the surface of dust grains. Deuterated molecules are the main
diagnostic tools of dense and cold interstellar clouds, where the first steps
toward star and protoplanetary disk formation take place. Recent observations
of deuterated molecules are reviewed and discussed in view of astrochemical
models inclusive of spin-state chemistry. We present a new comparison between
models based on complete scrambling (to calculate branching ratio tables for
reactions between chemical species that include protons and/or deuterons) and
models based on non-scrambling (proton hop) methods, showing that the latter
best agree with observations of NH$_3$ deuterated isotopologues and their
different nuclear spin symmetry states.
