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

Time-Dependent Density Functional Theory (TDDFT) has been currently established as a computationally cheaper, yet effective, alternative to the Many-Body Perturbation Theory (MBPT) for calculating the optical properties of solids. Within the Linear Response formalism, the optical absorption spectra are in good agreement with experiments, as well as the direct determination of the exciton binding energies. However, the family of exchange-correlation kernels known as long-range corrected (LRC) kernels that correctly capture excitonic features have difficulties simultaneously producing good-looking spectra and accurate exciton binding energies. More recently, this discrepancy has been partially overcome by a hybrid-TDDFT approach. We show that the key resides in the numerical treatment of the long-range Coulomb singular term. We carefully study the effect of this term, both in the pure-TDDFT and hybrid approach using a Wigner-Seitz truncated kernel. We find that computing this term presents technical difficulties that are hard to overcome in both approaches, and that points to the need for a better description of the electron-hole interaction.