The Point Groups as Semi-direct Products

Abstract

In this appendix the semi-direct product structure of the point groups is described, and it is shown how the general procedures summarized in Appendix 3 lead to a systematic determination of point group irreducible representations. McIntosh [146] has emphasized that the resulting nomenclature for the IRs is perhaps more rational than the familiar notation established by Placzek (cf. [6,85]); the point symmetry groups have also been treated from this viewpoint by Altmann [125,174], Bradley and Cracknell [175], and Fritzer [176,177] (see also [186,187]). The semi-direct decomposition of the point groups is helpful in the construction of rigid/nonrigid correlation diagrams, as discussed in Chapter 4.