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The use of symmetry in reciprocal space integrations. Asymmetric units and weighting factors for numerical integration procedures in any crystal symmetry
Author(s) -
Ramirez Rafael,
Böhm Michael C.
Publication year - 1988
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560340609
Subject(s) - homogeneous space , weighting , reciprocal lattice , brillouin zone , symmetry (geometry) , reciprocal , space (punctuation) , rotational symmetry , mathematics , theoretical physics , physics , statistical physics , quantum mechanics , geometry , computer science , diffraction , linguistics , philosophy , acoustics , operating system
A systematic collection of spatial domains for reciprocal space integrations is derived for all possible crystal symmetries. This set can be used as a simpler alternative to the conventional Brillouin zones. The analysis is restricted to integrations where the function in the integrand satisfies inversion symmetry in k space. In this case only 24 different spatial domains have to be defined in order to allow for k space integrations in the 230 different crystal symmetries. A graphic representation of the asymmetric unit for each of the 24 integration domains is given. Special positions and the associated weighting factors required for numerical integrations in theoretical solid‐state approaches are tabulated.