  Excitons are electron-hole pairs appearing below the band gap in insulators
and semiconductors. They are vital to photovoltaics, but are hard to obtain
with time-dependent density-functional theory (TDDFT), since most standard
exchange-correlation (xc) functionals lack the proper long-range behavior.
Furthermore, optical spectra of bulk solids calculated with TDDFT often lack
the required resolution to distinguish discrete, weakly bound excitons from the
continuum. We adapt the Casida equation formalism for molecular excitations to
periodic solids, which allows us to obtain exciton binding energies directly.
We calculate exciton binding energies for both small- and large-gap
semiconductors and insulators, study the recently proposed bootstrap xc kernel
[S. Sharma et al., Phys. Rev. Lett. 107, 186401 (2011)], and extend the
formalism to triplet excitons.
