A minimal TDDFT model for excitons

Optical processes in insulators and semiconductors, including excitonic effects, can be accurately described with linear-response TDDFT, provided one uses suitable exchange-correlation kernels. We have developed a conceptually and computationally simple formalism for calculating exciton binding energies with TDDFT, based on a two-band approximation. This formalism is implemented in a one-dimensional Kronig-Penney model, and we discuss the requirements for excitonic binding in this model. The performance of different types of exchange-correlation kernels (long- versus short-ranged, adiabatic versus nonadiabatic) is analyzed, with a particular emphasis on the excitonic Rydberg series.