On the Brillouin zone integration

Abstract A brief and simple description is given of three new methods of integration in the Brillouin zone: direct, ray, and hybrid tetrahedron, proposed by Chen, McDonald et al. These methods are analyzed in detail in application to the calculation of the density and number of states of s.c., b.c.c., and f.c.c. crystals using tight‐binding and empty lattice models. It is shown that all the methods considered exhibit a high accuracy: several hundred initial k points in the irreducible part of the Brillouin zone with not very complicated dispersion relations make it possible to calculate such a quantity, as the density of states, with an average error of less than 1%. The hybrid tetrahedron method is proved to be simpler and many times more effective than the other two methods. Only with dispersion relations close to isotropic is the ray method preferable.