  We present an approach to calculate the optical absorption spectra that
combines the quasiparticle self-consistent GW method [Phys. Rev. B, 76 165106
(2007)] for the electronic structure with the solution of the ladder
approximation to the Bethe-Salpeter equation for the macroscopic dielectric
function. The solution of the Bethe-Salpeter equation has been implemented
within an all-electron framework, using a linear muffin-tin orbital basis set,
with the contribution from the non-local self-energy to the transition dipole
moments (in the optical limit) evaluated explicitly. This approach addresses
those systems whose electronic structure is poorly described within the
standard perturbative GW approaches with as a starting point density-functional
theory calculations. The merits of this approach have been exemplified by
calculating optical absorption spectra of a strongly correlated transition
metal oxide, NiO, and a narrow gap semiconductor, Ge. In both cases, the
calculated spectrum is in good agreement with the experiment. It is also shown
that for systems whose electronic structure is well-described within the
standard perturbative GW, such as Si, LiF and h-BN, the performance of the
present approach is in general comparable to the standard GW plus
Bethe-Salpeter equation. It is argued that both vertex corrections to the
electronic screening and the electron-phonon interaction are responsible for
the observed systematic overestimation of the fundamental bandgap and spectrum
onset.
