  We have investigated the electronic structure of fluorite Cu$_{2}$Se using
density functional theory calculations within the LDA, PBE and AM05
approximations as well as with the non-local hybrid PBE0 and HSE
approximations. Our results show that Cu$_{2}$Se is a zero gap semiconductor
when using either a local or semi-local density functional approximation while
there exists a gap when using the PBE0 functional. For the HSE approximation,
we find that the presence of a gap depends on the range separation for the
non-local exchange within the HSE approximation. For the occupied states we
find that the LDA, PBE, AM05, PBE0 and HSE agrees when regarding the overall
structure, however, the hybrid functionals are shifted towards lower energy
values compared to the LDA, PBE and AM05. The valence bands obtained using the
hybrid functionals are in good agreement with experimental valence band
spectra. We also find that the PBE, PBE0 and HSE approximations give similar
results regarding bulk properties, such as lattice constants and bulk modulus.
In addition, we have investigated the localization of the Cu d-states and its
effect on the band gap in the material using the LDA+U approach. We find that a
gap is opened up by increasing the $U$, however, the $U$ values required for a
gap opening is unrealistically high.

Materials Science