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Two extensions of the widely used tetrahedron method for the evaluation of spectral properties of solids are presented. The first provides explicit formulae for including matrix element variation inside tetrahedral microzones in the same spirit in which the energy variation is included in the original method. The second is a scheme for using local quadratic interpolation inside some tetrahedra to provide the matrix element and energy values required to apply the tetrahedron method to a large number of tetrahedra into which the original tetrahedra have been divided. This scheme is similar to the hybrid method of extension of the Gilat-Raubenheimer method. Application to the calculation of the density of states of a single tight-binding band in a FCC crystal shows that its efficiency is comparable with that of the method recently proposed by Chen (1977).
MacDonald et al. (Tue,) studied this question.