Recent experiments suggest that divalent hexaborides like SrB6 and CaB
6, traditionally considered small-gap semiconductors, can actually be
semimetals. We calculate the structural and electronic properties of S
rB6, CaB6 and of ferromagnetic EuB6, using the full-potential lineariz
ed augmented plane wave (FLAPW) method, within the local (spin) densit
y approximation. The lattice constants and internal parameters are in
very good agreement with the measured ones. Because of a small band ov
erlap at the X point, all the materials are semimetals. The calculated
Hall coefficient for SrB6 changes sign around zero doping, and has th
e free-electron value for doping beyond approximate to 1.5%. The plasm
a frequency has a minimum at zero doping. We interpret the high-temper
ature transport properties of SrB6 and CaB6 in terms of a thermal gap
deduced from the shape of the density of states around the Fermi energ
y. We also calculate the imaginary part of the dielectric function for
SrB6, which can be compared to recent experiments.