The work for my Ph.D. was mainly concerned with different aspects of density-functional theory (DFT), which presently is the dominating method for quantitative calculations of the electronic properties of solids and large molecules. Within this context, the closest competitor to DFT is many-body perturbation theory (MBPT).
In this proposal we suggest i) A new method for improving existing density-functional calculations. The method is based on an accurate modeling of the exchange-correlation hole in real space. ii) A new method for improving on the dynamically-screened exchange approximation which presently is the dominating scheme within MBPT. Our new method is based on dividing the Coulomb interaction in a long-ranged but weak part and strong but short-ranged part. The method accounts for eletron-hole and hole-hole interactions. iii) We have derived a relation connecting time-dependent DFT to time-dependent MBPT. The relation can and will be used to obtain successively better approximations within DFT.