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.
Partitioning is problematic.
Only few basis functions non-zero at any given grid point.