Integration of DFT exchange and correlation

Integration of exchange and correlation interaction has to be done numerically since the various functionals - and their derivatives - describing the interaction are too complex to evaluate analytically. There are a number of items that has to be implemented efficiently to quickly compute the interaction in question:

• The grid for the numerical integration (point positions and weights) has to be generated in a linearly-scaling fashion.
• Since the number of grid point will increase linearly with the system size, subsequent evaluation of density and other properties at each grid point must have a constant cost.