  The defect in diamond formed by a vacancy surrounded by three
nearest-neighbor nitrogen atoms and one carbon atom,
$\mathrm{N}_{3}\mathrm{V}$, is found in $\approx98\%$ of natural diamonds.
Despite $\mathrm{N}_{3}\mathrm{V}^{0}$ being the earliest electron paramagnetic
resonance spectrum observed in diamond, to date no satisfactory simulation of
the spectrum for an arbitrary magnetic field direction has been produced due to
its complexity. In this work, $\mathrm{N}_{3}\mathrm{V}^{0}$ is identified in
$^{15}\mathrm{N}$-doped synthetic diamond following irradiation and annealing.
The $\mathrm{^{15}N}_{3}\mathrm{V}^{0}$ spin Hamiltonian parameters are revised
and used to refine the parameters for $\mathrm{^{14}N}_{3}\mathrm{V}^{0}$,
enabling the latter to be accurately simulated and fitted for an arbitrary
magnetic field direction. Study of $\mathrm{^{15}N}_{3}\mathrm{V}^{0}$ under
excitation with green light indicates charge transfer between
$\mathrm{N}_{3}\mathrm{V}$ and $\mathrm{N_s}$. It is argued that this charge
transfer is facilitated by direct ionization of $\mathrm{N}_{3}\mathrm{V}^{-}$,
an as-yet unobserved charge state of $\mathrm{N}_{3}\mathrm{V}$.
