  Rare-earth based scintillators in general and lanthanum bromide (LaBr_3) in
particular represent a challenging class of materials due to pronounced
spin-orbit coupling and subtle interactions between d and f states that cannot
be reproduced by standard density functional theory (DFT). Here a detailed
investigation of the electronic band structure of LaBr_3 using the
quasi-particle self-consistent GW (QPscGW) method is presented. This
parameter-free approach is shown to yield an excellent description of the
electronic structure of LaBr_3. Specifically it is able to reproduce the band
gap, the correct level ordering and spacing of the 4f and 5d states, as well as
the spin-orbit splitting of La-derived states. The QPscGW results are
subsequently used to benchmark several computationally less demanding
techniques including DFT+U, hybrid exchange-correlation functionals, and the
G_0W_0 method. Spin-orbit coupling is included self-consistently at each QPscGW
iteration and maximally localized Wannier functions are used to interpolate
quasi-particle energies. The QPscGW results provide an excellent starting point
for investigating the electronic structure of excited states, charge
self-trapping, and activator ions in LaBr_3 and related materials.
