Several improvements of the tetrahedron method for Brillouin-zone integrations are presented. (1) A translational grid of k points and tetrahedra is suggested that renders the results for insulators identical to those obtained with special-point methods with the same number of k points. (2) A simple correction formula goes beyond the linear approximation of matrix elements within the tetrahedra and also improves the results for metals significantly. For a required accuracy this reduces the number of k points by orders of magnitude. (3) Irreducible k points and tetrahedra are selected by a fully automated procedure, requiring as input only the space-group operations. (4) The integration is formulated as a weighted sum over irreducible k points with integration weights calculated using the tetrahedron method once for a given band structure. This allows an efficient use of the tetrahedron method also in plane-wave-based electronic-structure methods.
Abstract This book gives the complete theory of the irreducible representations of the crystallographic point groups and space groups. This is important in the quantum-mechanica...
The phonon spectrum of reactor grade graphite is computed by means of the essentially exact root sampling technique for a sampling 47 788 points in an irreducible segment of the...
We show that the widely used tetrahedron scheme for integrating functions over the Brillouin zone misweights the contributions from the $\stackrel{\ensuremath{\rightarrow}}{\mat...
Abstract A method is given for the numerical calculation of energy surface integrals within the Brillouin zone like density of states, conductivity, susceptibility, dielectric f...
We present sets of special points in the Brillouin zone from which the average over the Brillouin zone of a periodic function of wave vector (e.g., energy, charge density, dipol...
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