Abstract: We propose a "state of art"tetrahedron sampling scheme based on a nonlocal pseudopotential bandstructure calculation and linear energy interpolation in each tetrahedron cell.In this approach,a relatively small amount of tetrahedrons are produced automatically and the Brillouin integration is calculated with higher precision and efficiency.In an application to diamond materials of Si and Ge,optimized nonuniform meshes are obtained automatically in the 1/48 irreducible wedge of the brillouin zone.A complement is given for the integrality of the present tetrahedron DOS expression and the DOS's for the first and second conductance band of Si and Ge are obtained with this grid and the supplemented expression.

Key words: tetrahedron grid, irreducible wedge of Brillouin zone, nonlocal pseudopotential, Brillouin zone integration