  GaSb:N displays promise towards realization of optoelectronic devices
accessing the mid-infrared wavelength regime. Theoretical and experimental
results on its electronic and optical properties are however few. To address
this, we present a first principles, density functional theory study using the
hybrid HSE06 exchange-correlation functional of GaSb doped with 1.6$\%$
nitrogen. To study dilute-nitrides with small band gaps, the local density
approximation (LDA) is insufficient and more accurate techniques such as HSE06
are needed. We conduct a comparative study on GaAs:N, also with 1.6$\%$
nitrogen mole fraction, and find that GaSb:N has a smaller band gap and
displays more band gap bowing than GaAs:N. In addition we examine the orbital
character of the bands, finding the lowest conduction band to be
quasi-delocalized, with a large N-$3s$ contribution. At high concentrations,
the N atoms interact via the host matrix, forming a dispersive band of their
own which governs optoelectronic properties and dominates band gap bowing.
While this band drives the optical and electronic properties of GaSb:N, its
physics is not captured by traditional models for dilute-nitrides. We thus
propose that a complete theory of dilute-nitrides should incorporate orbital
character examination, especially at high N concentrations.
