The electronic structure, structural stability, and lattice dynamics of cerium mononitride are investigated using ab initio density-functional methods involving an effective potential derived from the generalized gradient approximation and without special treatment for the 4f states. The 4f states are hence allowed to hop from site to site, without an on-site Hubbard U, and contribute to the bonding, in a picture often referred to as itinerant. It is argued that this picture is appropriate for CeN at low temperatures, while the anomalous thermal expansion observed at elevated temperatures indicates entropy-driven localization of the Ce f electrons, similar to the behavior of elemental cerium. The elastic constants are predicted from the total energy variation of strained crystals and are found to be large, typical for nitrides. The phonon dispersions are calculated showing no soft modes, and the Grüneisen parameter behaves smoothly. The electronic structure is also calculated using the quasiparticle self-consistent GW approximation (where G denotes the Green's function and W denotes the screened interaction). The Fermi surface of CeN is dominated by large egg-shaped electron sheets centered on the X points, which stem from the p-f mixing around the X point. In contrast, assuming localized f electrons leads to a semimetallic picture with small band overlaps around X. © 2011 American Physical Society.