Time-dependent density functional theory versus Bethe-Salpeter equation: an all-electron study.

We perform first-principle calculations for the macroscopic dielectric function within an all-electron full-potential framework, i.e., the linearized augmented planewave (LAPW) method. To this extent we pursue two different routes, which are, on the one hand, many-body perturbation theory (MBPT) by solving the Bethe-Salpeter equation (BSE), and time-dependent density functional theory (TDDFT), on the other hand. The implementation into one program package, i.e., the EXC!TiNG code, allows a direct comparison of these approaches, in terms of accuracy as well as efficiency. We briefly review the theory, and describe in detail the quantities specific to the LAPW method. As an example we show the results for GaAs which is well-investigated in the literature, and hence serves as a stringent test case.