  We investigate deuterium chemistry coupled with the nuclear spin-state
chemistry of H$_2$ and H$_3^+$ in protoplanetary disks. Multiple paths of
deuterium fractionation are found; exchange reactions with D atoms, such as
HCO$^+$ + D, are effective in addition to those with HD. In a disk model with
grain sizes appropriate for dark clouds, the freeze-out of molecules is severe
in the outer midplane, while the disk surface is shielded from UV radiation.
Gaseous molecules, including DCO$^+$, thus become abundant at the disk surface,
which tends to make their column density distribution relatively flat. If the
dust grains have grown to millimeter size, the freeze-out rate of neutral
species is reduced, and the abundances of gaseous molecules, including DCO$^+$
and N$_2$D$^+$, are enhanced in the cold midplane. Turbulent diffusion
transports D atoms and radicals at the disk surface to the midplane, and stable
ice species in the midplane to the disk surface. The effects of turbulence on
chemistry are thus multifold; while DCO$^+$ and N$_2$D$^+$ abundances increase
or decrease depending on the regions, HCN and DCN in the gas and ice are much
reduced at the innermost radii, compared with the model without turbulence.
When cosmic rays penetrate the disk, the ortho-to-para ratio (OPR) of H$_2$ is
found to be thermal in the disk, except in the cold ($\lesssim 10$ K) midplane.
We also analyze the OPR of H$_3^+$ and H$_2$D$^+$, as well as the main
reactions of H$_2$D$^+$, DCO$^+$, and N$_2$D$^+$ to analytically derive their
abundances in the cold midplane.
