  Spinel ferrites in general show a rich interplay of structural, electronic,
and magnetic properties. Here, we particularly focus on zinc ferrite (ZFO),
which has been observed experimentally to crystallise in the cubic $normal$
spinel structure. However, its magnetic ground state is still under dispute. In
addition, some unusual magnetic properties in ZFO thin films or nanostructures
have been explained by a possible partial cation inversion and a different
magnetic interaction between the two cation sublattices of the spinel structure
compared to the crystalline bulk material. Here, density functional theory has
been applied to investigate the influence of different inversion degrees and
magnetic couplings among the cation sublattices on the structural, electronic,
magnetic, and optical properties. Effects of exchange and correlation have been
modelled using the generalised gradient approximation (GGA) together with the
Hubbard `+$U$' parameter, and the more elaborate hybrid functional PBE0. While
the GGA+$U$ calculations yield an antiferromagnetically coupled $normal$ spinel
structure as the ground state, in the PBE0 calculations the ferromagnetically
coupled $normal$ spinel is energetically slightly favoured, and the hybrid
functional calculations perform much better with respect to structural,
electronic and optical properties.
