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Charge Symmeterisation

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 tex2html_wrap_inline5654 . Each k-point has a weighting of tex2html_wrap_inline5658 , as described above. If the wavefunction for each band, i, at the special k-point tex2html_wrap_inline5664 is tex2html_wrap_inline5666 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 tex2html_wrap_inline5664 with respect to the full point group T is then


where tex2html_wrap_inline5670 is the number of operations, tex2html_wrap_inline5672 , 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 tex2html_wrap_inline5484 for a crystal with point group operations, T, is obtained by Fourier transforming tex2html_wrap_inline5678 .

Stewart Clark
Thu Oct 31 19:32:00 GMT 1996