Some developments in (TD)DFT: From exact constraints to dynamics

Here we present an overview of our three recent works on the development and application of DFT and TDDFT. First, we consider the lower bound on the indirect Coulomb interaction, commonly known as the Lieb-Oxford bound, which acts as a key constraint in several density functionals for the exchange-correlation energy. Using physical arguments we propose a tighter form of the bound. Moreover, we generalize the bound for systems of lower dimensionality (2D and 1D). Secondly, we present a simple density functional for the exchange potential, which can be regarded as a universal extension to the commonly applied Becke-Johnson approximation. Promising results for different systems, e.g., atomic chains exposed to external fields are presented. Finally, we present the current status of our transport calculations within TDDFT and the Octopus code. In particular, we show how the interactions and system characteristics affect the Aharonov-Bohm effect in a semiconductor quantum ring.