  This paper presents first principles calculations of paramagnetic cubic
CrN$_x$ with the aim to provide deeper insight into recently published
transmission electron microscopy-based study on this material. Among several
types of point defects which may result in N-deficient material, N vacancy is
found to be energetically preferred to Cr interstitial and anti-sites. Electron
Energy Loss Near Edge Structure of N K-edge transition is calculated for
various concentrations of N vacancies in CrN$_x$, yielding the same trends as
experimentally observed. Analysis of the electronic structure reveals decreased
charge transfer from Cr sites with increased N vacancy content, hence
increasing the metallic character of the defected material. Finally, the
electronic structure is found to be strongly dependent on the local environment
(i.e. presence of the N vacancies).
