  The electronic structure of bulk GaAs$_{1-x}$Bi$_x$ systems for different
atomic configurations and Bi concentrations is calculated using density
functional theory. The results show a Bi-induced splitting between the
light-hole and heavy-hole bands at the $\Gamma$-point. We find a good agreement
between our calculated splittings and experimental data. The magnitude of the
splitting strongly depends on the local arrangement of the Bi atoms but not on
the uni-directional lattice constant of the supercell. The additional influence
of external strain due to epitaxial growth on GaAs substrates is studied by
fixing the in-plane lattice constants.
