  The electronic structure and magnetic properties of pure and doped
{Fe$_{16}$N$_2$} systems have been studied in the local-density (LDA) and
quasiparticle self-consistent {\emph{GW}} approximations. The {\emph{GW}}
magnetic moment of pure {Fe$_{16}$N$_2$} is somewhat larger compared to LDA but
not anomalously large. The effects of doping on magnetic moment and exchange
coupling were analyzed using the coherent potential approximation. The
theoretical Curie temperature in pure {Fe$_{16}$N$_2$} is significantly higher
than the measured value, which is attributed to the quality of available
samples and the interpretation of experimental results. We found that different
Fe sites contribute very differently to the magnetocrystalline anisotropy
energy (MAE), which offers a way to increase MAE by small additions of Co or
Ti. MAE also increases under tetragonal strain.
