Unit Cell Group and the Factor Group in the Theory of the Electronic and Vibrational Spectra of Crystals

Abstract

The unit cell group and the factor group are basic to the theoreticalanalysis of the vibrations, or electronic transitions, in crystals in the k = 0 approximation. Yet some confusion exists in the literature concerning the definitions of these groups. This paper examines the literature definitions, draws attention to inconsistencies in the literature, and describes the unit cell group and the factor group for the specific cases of the symmorphic space group, P2 / m , and the nonsymmorphic space groups P2 1 / m and P2 1 / c .