  Exchange interactions between isolated pairs of spin centers in diamond have
been calculated, based on an accurate atomistic electronic structure for
diamond and any impurity atoms, for spin-center separations up to 2~nm. The
exchange interactions exceed dipolar interactions for spin center separations
less than 3~nm. NV$^-$ spin centers, which are extended defects, interact very
differently depending on the relative orientations of the symmetry axis of the
spin center and the radius vector connecting the pair. Exchange interactions
between transition-metal dopants behave similarly to those of NV$^-$ centers.
The Mn\---Mn exchange interaction decays with a much longer length scale than
the Cr\---Cr and Ni\---Ni exchange interactions, exceeding dipolar interactions
for Mn\---Mn separations less than 5~nm. Calculations of these highly
anisotropic and spin-center-dependent interactions provide the potential for
design of the spin-spin interactions for novel nanomagnetic structures.
