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Excitonic effects in solids can be calculated using the Bethe-Salpeterequation (BSE) or the Casida equation of time-dependent density-functionaltheory (TDDFT). In both methods, the Tamm-Dancoff approximation (TDA), whichdecouples excitations and de-excitations, is widely used to reducecomputational cost. Here, we study the effect of the TDA on exciton bindingenergies of solids obtained from the Casida equation using long-range corrected(LRC) exchange-correlation kernels. We find that the TDA underestimatesTDDFT-LRC exciton binding energies of semiconductors slightly, but those ofinsulators significantly (i.e., by more than 100%), and thus it is essential tosolve the full Casida equation to describe strongly bound excitons. Thesefindings are relevant in the ongoing search for accurate and efficient TDDFTapproaches for excitons.

Excitons in solids from time-dependent density-functional theory: Assessing the Tamm-Dancoff approximation