  Excitonic effects in solids can be calculated using the Bethe-Salpeter
equation (BSE) or the Casida equation of time-dependent density-functional
theory (TDDFT). In both methods, the Tamm-Dancoff approximation (TDA), which
decouples excitations and de-excitations, is widely used to reduce
computational cost. Here, we study the effect of the TDA on exciton binding
energies of solids obtained from the Casida equation using long-range corrected
(LRC) exchange-correlation kernels. We find that the TDA underestimates
TDDFT-LRC exciton binding energies of semiconductors slightly, but those of
insulators significantly (i.e., by more than 100%), and thus it is essential to
solve the full Casida equation to describe strongly bound excitons. These
findings are relevant in the ongoing search for accurate and efficient TDDFT
approaches for excitons.
