FORMULAS FOR THE CHADI-COHEN PROCESS

For the square and cubic lattices, formulas are designed which yield, for k-space summations over the Brillouin zone, the special points in the irreducible Brillouin zone and the corresponding weighting factors prescribed by the Chadi-Cohen method. For the simple-cubic and fcc lattices these formulas at stage correspond to those of Monkhorst and Pack at stage 2. These formulas allow one to compute the summations to any order of approximation, not necessarily successively. It is demonstrated how extrapolation in the inverse of the number of special points may be used to speed up the calculations. Furthermore, the formulas are shown to be useful for numerically evaluating the integrals of singular functions in two dimensions. © 1990 The American Physical Society.