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A theory of special points in two‐dimensional solid‐state calculations
Author(s) -
Hall G. G.,
Rees D.
Publication year - 1999
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/(sici)1097-461x(1999)74:6<601::aid-qua1>3.0.co;2-1
Subject(s) - symmetry (geometry) , planar , grid , gaussian , skew , mathematics , space (punctuation) , computer science , physics , geometry , quantum mechanics , telecommunications , computer graphics (images) , operating system
A theory of special points in solid‐state calculations is developed using a finite‐dimensional function space. This generalizes many of the ideas of the present authors about Gaussian‐type cubature since the special points are identified with the grid points of a quadrature. The theory is applied to planar square lattices with C 4 v symmetry. By the systematic use of symmetry, substantial grids of points can be calculated economically. The accuracy of the sets of points is discussed and a redefinition of accuracy offered. Examples are given, some of which agree with those already known, but a new category of skew direct product grids is introduced which enables a large number of suitable grids to be generated. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 601–615, 1999