Wigner-Seitz truncated time-dependent density functional theory approach for the calculation of exciton binding energies in solids

Time-dependent density functional theory (TDDFT) has established itself as a computationally efficient and effective alternative to the many-body perturbation theory for calculating the optical properties of solids. Within the framework of linear response formalism, TDDFT exhibits good agreement between optical absorption spectra and experimental data, as well as the possibility of directly determining exciton binding energies. However, the family of exchange-correlation kernels, known as long-range-corrected kernels, which accurately capture excitonic features, face challenges in simultaneously generating visually appealing spectra and precise exciton binding energies. Recently, progress has been made in addressing this discrepancy through a hybrid-TDDFT approach. Our study reveals that the key lies in the numerical treatment of the long-range Coulomb singular term. We conduct a meticulous investigation of the impact of the term in both pure-TDDFT and hybrid approaches using a Wigner-Seitz truncated kernel. Notably, we show that computing this term presents formidable technical difficulties in both approaches, pointing to the need for an improved description of the electron-hole interaction.