Point Group Symmetries and Gaussian Integration

A computationally efficient and exact method of symmetrizing a complete set of angular functions using Gaussian integration is presented. This technique will be useful in situations such as crystal field-type calculations, full potential electronic structure calculations, and wherever symmetrized fu...

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Bibliographic Details
Published in:Journal of computational physics 1994-06, Vol.112 (2), p.282-290
Main Authors: Fernando, G.W., Weinert, M., Watson, R.E., Davenport, J.W.
Format: Article
Language:English
Subjects:
Computational techniques
Exact sciences and technology
Mathematical methods in physics
Numerical approximation and analysis
Numerical differentiation and integration
Physics
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Summary:A computationally efficient and exact method of symmetrizing a complete set of angular functions using Gaussian integration is presented. This technique will be useful in situations such as crystal field-type calculations, full potential electronic structure calculations, and wherever symmetrized functions of a given irreducible representation are needed. As an example, combinations of spherical harmonics transforming as the completely symmetric irreducible representation are given for all the 32 crystallographic point groups in three dimensions.
ISSN:0021-9991
1090-2716
DOI:10.1006/jcph.1994.1100