LCAO-TDDFT-k-ω: spectroscopy in the optical limit

Understanding, optimizing, and controlling the optical absorption process, exciton gemination, and electron-hole separation and conduction in low dimensional systems is a fundamental problem in materials science. However, robust and efficient methods capable of modelling the optical absorbance of low dimensional macromolecular systems and providing physical insight into the processes involved have remained elusive. We employ a highly efficient linear combination of atomic orbitals (LCAOs) representation of the Kohn-Sham (KS) orbitals within time dependent density functional theory (TDDFT) in the reciprocal space (k) and frequency (ω) domains, as implemented within our LCAO-TDDFT-k-ωcode, applying eithera prioriora posteriorithe derivative discontinuity correction of the exchange functional Δ_xto the KS eigenenergies as a scissors operator. In so doing we are able to provide a semi-quantitative description of the photoabsorption cross section, conductivity, and dielectric function for prototypical 0D, 1D, 2D, and 3D systems within the optical limit (‖q‖ → 0⁺) as compared to both available measurements and from solving the Bethe-Salpeter equation with quasiparticleG₀W₀eigenvalues (G₀W₀-BSE). Specifically, we consider 0D fullerene (C₆₀), 1D metallic (10, 0) and semiconducting (10, 10) single-walled carbon nanotubes, 2D graphene (Gr) and phosphorene (Pn), and 3D rutile (R-TiO₂) and anatase (A-TiO₂). For each system, we also employ the spatially and energetically resolved electron-hole spectral density to provide direct physical insight into the nature of their optical excitations. These results demonstrate the reliability, applicability, efficiency, and robustness of our LCAO-TDDFT-k-ωcode, and open the pathway to the computational design of macromolecular systems for optoelectronic, photovoltaic, and photocatalytic applicationsin silico.