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 .

Thu Oct 31 19:32:00 GMT 1996