Normal mode determination in crystals

The group theoretical methods by which the symmetries of normal modes in crystals may be determined are outlined, and a series of tables are presented to facilitate rapid determination of the selection rules for vibrational transitions. Emphasis is placed on the method of nuclear site group analysis in which the number of infrared and Raman active modes of each symmetry may be obtained without detailed analysis of the symmetry elements in the crystallographic unit cell or the construction of tables. By using the tables presented here for most cases identification of the crystallographic space group is sufficient information to allow determination of the vibrational mode selection rules by inspection. Several examples are included in which crystals are analyzed by each of the methods.