We examine the mystery of the disputed high-magnetization alpha-Fe16N2 phase, employing the Heyd-Scuseria-Ernzerhof screened hybrid functional method, perturbative many-body corrections through the GW approximation, and onsite Coulomb correlations through the GGA+U method. We present a first-principles computation of the effective on-site Coulomb interaction (Hubbard U) between localized 3d electrons employing the constrained random-phase approximation (cRPA), finding only somewhat stronger on-site correlations than in bcc Fe. We find that the hybrid functional method, the GW approximation, and the GGA+U method (using parameters computed from cRPA) yield an average spin moment of 2.9, 2.6 - 2.7, and 2.7 mu_B per Fe, respectively.
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