A nearly endless amount of technology relies on the understanding of the properties of matter and materials. Because the properties emerge from the motion of the electrons within matter, deepest and most accurate understanding can only be achieved by measuring or simulating the electronic structure. This thesis considers the computational simulation aspect, and currently the most popular way of conducting these simulations on a computer is density functional theory (DFT). The accuracy of the DFT calculations mostly depends on a small, but very important, component of the total energy — the exchange-correlation (XC) energy. The exact form of the XC energy term is not known and therefore always has to be approximated. When calculating very big systems also the kinetic energy term has to approximated in an orbital-free manner, because computing the electronic orbitals is too expensive for the big systems. 

Firstly, a new gradient-level XC approximation calledQNAis presented, and it is designed for the calculation of metallic bulk alloys. QNA exploits the subsystem functional scheme to address the issue of inconsistent performance that current gradient-level approximations have with many alloys. QNA is shown to produce more accurate binary alloy formation energies, and the good accuracy of formation energies is very important in alloy theory. 

Secondly, a new method of computing the kinetic energy without orbitals is presented and tested in practice. This method allows one, in principle, to perform orbital-free calculations for spherically symmetric systems at the high accuracy level of orbital DFT. A succesful orbital-free solution for the electronic structure of the Be atom is presented. One of the ultimate goals in DFT research is to combine the high accuracy of orbital DFT with the excellent computational speed of orbital-free DFT, and the proofof-concept solution for the Be atom is a step in this direction.