The use of special points in the Brillouin zone allows calculations to be carried out on a small number of k-point within the irreducible part of the Brillouin zone. The charge density obtained from these calculations can then be associated with other points throughout the zone by use of the point group operations, T.
This can be done as follows: let the special set of Chadi-Cohen or Monkhorst-Pack k-points be . Each k-point has a weighting of , as described above. If the wavefunction for each band, i, at the special k-point is then the reciprocal space charge density at that point in the irreducible part of the Brillouin zone is
The symmeterised charge density associated with the point with respect to the full point group T is then
where is the number of operations, , in the point group T. It is then simple to construct the full reciprocal space charge density by
The fully symmeterised real space charge density for a crystal with point group operations, T, is obtained by Fourier transforming .