to with respect to this parameter. The Brillouin zone was sampled using the Monkhorst-Pack scheme [@monkhorst1976special]: the maximum reciprocal volume per sampling point was .

Using this approach, the lattice constant of diamond agrees with experiment ([@riley1944lattice]) to within . All defect structures were modeled using simple-cubic supercells based upon the 8-atom conventional unit cell, with lattice spacing of $4a_0$ containing 512 atoms.

Donor and acceptor levels were found using the formation energy method[@goss2004; @chemp], with the formation energy ($E^f$) for a certain charge state, $q$, obtained using $$\label{eq:form}
E^f(X,q) = E_{\text{tot}}(X,q) - \sum \mu_i + q(E^X_V + \mu_e) + \chi(X,q).$$ Here $E_{\text{tot}}$ is the total energy of a defect structure, $E^X_V$ is taken as the valence-band maximum, $\mu_e$ is the electron chemical potential and $\chi$ is a correction term for periodic charge in the supercell [@shim2005density]. $\chi$ comprised of a background electrostatic correction of order and the Madelung term for the $4a_0$ supercell calculated at $q^2$ . Binding energies were calculated using formation energies [@goss2008dissociation; @goss2004], as the energy released in the formation of the complex from the component parts. Hyperfine tensor principal values and directions were determined as described previously [@Goss2007; @shaw2005importance].

Results
=======

Annealing {#subsec:annealing}
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Initially 