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.Comment: 8 pages, 3 figure