centrosymmetric

Centrosymmetric describes an object that possesses a center of symmetry, also known as an inversion center. An inversion center is a point within the object such that for every element at position r relative to the center, there is an equivalent element at position −r. In other words, the structure is invariant under inversion through that central point.

In chemistry and crystallography, centrosymmetry is used to characterize molecules and crystal structures. A centrosymmetric molecule has an inversion center, which implies that it is achiral and cannot be superimposed on its mirror image. In crystals, a structure is centrosymmetric if its space group contains an inversion operation. Such crystals often exhibit particular spectroscopic and optical properties as a consequence of the symmetry.

One notable implication concerns vibrational spectroscopy. For centrosymmetric molecules, there is frequently a mutual exclusion between infrared and Raman activity: a normal mode that is IR active tends to be Raman inactive, and vice versa. In crystals, centrosymmetry influences selection rules governing phonons and electronic transitions. In nonlinear optics, centrosymmetric materials do not exhibit second-order nonlinear effects, such as second-harmonic generation, due to the symmetry constraints, though they can show higher-order responses.

Common centrosymmetric crystals include common salts like sodium chloride and some ionic crystals, while many non-centrosymmetric materials, such as quartz, lack an inversion center. The concept helps in predicting physical properties and interpreting spectroscopic data.

See also: inversion center, point group, symmetry operations.