International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2013 
International Tables for Crystallography (2013). Vol. D, ch. 2.3, pp. 339341
Section 2.3.3.4. Centrosymmetric crystals^{a}Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ18221 Prague 8, Czech Republic 
In those point groups that contain the inversion operation, i.e. in the eleven centrosymmetric (nonpolar) crystal classes the irreducible representations are divided into two groups, odd and even, according to the parity. Since secondrank polar tensors must transform according to the even parity representations only, whereas polar vectors transform according to odd parity representations, the selection rules for electric dipole absorption (infrared activity) and for Raman scattering are incompatible. This is often expressed as the mutual exclusion rule or complementarity principle: The excitations in a crystal belonging to a centrosymmetric class cannot be simultaneously active in infrared absorption and in Raman scattering. Let us note, however, that evenparity excitations are not necessarily all Raman active, and that oddparity excitations are not necessarily infrared active.
In the remaining noncentrosymmetric crystal classes, the excitations have no defined parity with respect to inversion and can be, in principle, both Raman and infrared active.
Example: Consider a Raman scattering experiment on a crystal of tetragonal symmetry, class . Ramanactive phonons, allowed in conventional symmetric scattering, are of the symmetry species , , and . (the species admits purely antisymmetric scattering only). Straightforward application of Table 2.3.3.1 makes it possible to determine the polarization selection rules, i.e. to determine which symmetry species will contribute to the scattering cross section in various experimental configurations. Choosing the Cartesian axes , , consistent with the standard setting of the point group, i.e. the fourfold rotation axis , let us further introduce the notation , . Then the contributions to the cross section for different symmetry species can be distinguished by their dependence on the polarization vectors and of the incident and scattered light:
Examples of some special scattering geometries that permit the separation of the contributions of different symmetry species are shown in Table 2.3.3.2 (five distinct configurations are sufficient to determine the five independent parameters a, b, d, e, f of the symmetric Raman tensors).

If, for some reason, antisymmetric scattering is allowed, possible contribution of the modes should be considered as well. The contribution to cross section from these modes is proportional to , hence it can be distinguished from the contribution of the symmetry species by a suitable choice of the scattering geometry.