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Time-Dependent Density Functional Theory (TDDFT) has been currentlyestablished as a computationally cheaper, yet effective, alternative to theMany-Body Perturbation Theory (MBPT) for calculating the optical properties ofsolids. Within the Linear Response formalism, the optical absorption spectraare in good agreement with experiments, as well as the direct determination ofthe exciton binding energies. However, the family of exchange-correlationkernels known as long-range corrected (LRC) kernels that correctly captureexcitonic features have difficulties simultaneously producing good-lookingspectra and accurate exciton binding energies. More recently, this discrepancyhas been partially overcome by a hybrid-TDDFT approach. We show that the keyresides in the numerical treatment of the long-range Coulomb singular term. Wecarefully study the effect of this term, both in the pure-TDDFT and hybridapproach using a Wigner-Seitz truncated kernel. We find that computing thisterm presents technical difficulties that are hard to overcome in bothapproaches, and that points to the need for a better description of theelectron-hole interaction.

Wigner-Seitz truncated TDDFT approach for the calculation of exciton binding energies in solids