GENERAL FORMULAS FOR THE SPECIAL POINTS AND THEIR WEIGHTING FACTORS IN K-SPACE INTEGRATION

General formulae are given for providing sets of the special points and their weighting factors for kappa-space integration without the use of a recurrence process for cubic, hexagonal and tetragonal lattices. The formulae are allowed to be used for intermediate numbers of kappa-points not considered in the method of Chadi and Cohen. It is shown that the special-point method is an open-type Lagrange quadrature of lowest order and that it gives accurate values for moderately varying functions but less accurate values for those with discontinuous derivatives at the Brillouin zone boundaries. In the present method it is possible to incorporate the second-order Lagrange quadrature and the Gaussian method. The efficiencies of these methods are discussed in comparison with the correctly weighted tetrahedron method.