Symmetry Coordinates and Factorization of Vibrational Problems for Crystals with Symmorphic Space Groups

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Abstract
In this paper a method is presented for construction of symmetry coordinates for crystals with symmorphic space groups. By using projection operators for both the translation group and the rotational part of the space group, formulas for symmetry coordinates are given, which reduce the vibrational problem into irreducible blocks under both the translational group and the little group Ĝ k Further, a short discussion is given for selection rules for infrared and Raman transitions and the importance of the dispersion surface in analyzing empirical spectra is pointed out.