An extended tetrahedron method for determining Fourier components of Green functions in solids

The linear tetrahedron method (LTM) is extended in order to deal with a rapidly oscillating term in the integrand. This extension, ELTM, is inspired by the need for accurate values of the Fourier components of Green functions in solids. It is shown that LTM and ELTM have a basic equation in common and that the several versions differ only in the expressions for the weighting factors. The presentation of five versions of (E)LTM is given. The symmetry aspects are dealt with extensively, merely implying the introduction of modified weighting factors. After some examples with test purposes ELTM is applied to Cu. The results demonstrate that ELTM is an efficient way of evaluating the Brillouin zone integrals required.