Numerical Integration of Exchange Energy in the Two-Dimensional Brillouin Zone

Frank E. Harris, J. G. Fripiat, and J. Delhalle

Department of Physics, University of Utah
Quantum Theory Project, University of Florida
Facultes Universitaires, Notre-Dame de la Paix, Namur (Belgium)

(Submitted to Phys. Rev. B, February 2002).


  A method is described for performing accurate numerical integration of the electronic exchange energy over polygonal regions in the two-dimensional Brillouin zone. It is illustrated by application to Bloch states constructed from Gaussian type orbitals.