  The band structure of $\beta$-LiGaO$_2$ is calculated using the quasiparticle
self-consistent QS$G\hat W$ method where the screened Coulomb interaction $\hat
W$ is evaluated including electron-hole interaction ladder diagrams and $G$ is
the one-electron Green's function. Improved convergence compared to previous
calculations leads to a significantly larger band gap of about 7.0 eV. However,
exciton binding energies are found to be large and lead to an exciton gap of
about 6.0 eV if also a zero-point-motion correction of about $-0.4$ eV is
included. These results are in excellent agreement with recent experimental
results on the onset of absorption. Besides the excitons observed thus far, the
calculations indicate the existence of a Rydberg-like series of exciton excited
states, which is however modified from the classical Wannier exciton model by
the anisotropies of the material and the more complex mixing of Bloch states in
the excitons resulting from the Bethe-Salpeter equation. The exciton fine
structure and the exciton wave functions are visualized and analyzed in various
ways.
