IV. Symmetry and its Implications

Abstract

Abstract Significance of symmetry in representing real‐ and reciprocal‐space properties of a crystal and of its constituents is discussed in terms of symmetry eigenfunctions. The formation of the site‐symmetrized multipole expansion for the 32 crystal point symmetries is shown, and the mutual relations between the real‐ and reciprocal‐space expansions are discussed. The origin of the symmetry‐based phase relations, equivalences and extinction rules of structure amplitudes is pointed out. Distinction is made between the accurate and approximate ones arising from the true space‐group symmetry and from the approximate free‐particle symmetry of the constituents, respectively. Finally, the symmetry imposed by reality of charge density and its violation through anomalous dispersion are discussed in terms of symmetric and antisymmetric contributions of atomic charge densities.