Tetrahedron method

Calculations were done with a full-potential version of the LMTO method with nonoverlapping spheres. The contributions from the interstitial region were accounted for by expanding the products of Hankel functions in a series of atom-ce- -ered Hankels of three different kinetic energies. The corrected tetrahedron method was used for Brillouin zone integration. Electronic exchange and correlation contributions to the total energy were obtained from the local-density functional calculated by Ceperley and Alder " and parametrized by Vosko, Wilk, and Nusair. ... 

In the tetrahedron method, one divides the irreducible wedge of the Bril-louin zone into tetrahedra, and the integral (9.24) is then evaluated as the sum... 

Whilst the Accident Tetrahedron method might be seen as yet another technique to be added to the tool set of the safety practitioner, it is suggested that the procedure actually gives some order to the wealth of tools already in use. An exercise in contrast-and-compare is useful to demonstrate the positioning of the proposed tool. 

Adolph, B., Bechstedt, F. (1998). Ab initio second-harmonic susceptibilities of semiconductors generalized tetrahedron method and quasiparticle effects. Physical Review B - Condensed Matter andMaterials Physics, 57(11), 6519-6526. 

With the advent of the computationally much faster linearized methods, the computation of reliable densities of states has become much easier. These techniques allow the calculation of energies for a great number of k points in an energy band. The DOS is then obtained by means of the tetrahedron method (67). 

Bldchl, P. E. (1994). Improved tetrahedron method for Brillouin-zone integrations. Physical Review B, 50, 16223-16233. 

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