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Many chiral molecules have point chirality, namely a single chiral stereogenic center that coincides with an atom. This stereogenic center usually has four or more bonds to different groups, and may be carbon (as in many biological molecules), phosphorus (as in many organophosphates), silicon, or a metal (as in many chiral coordination compounds).
In three dimensions, every figure that possesses a plane of symmetry or a center of symmetry is achiral. There are, however, achiral figures lacking both plane and center of symmetry. In terms of point groups, all chiral figures lack an improper axis of rotation (S n). This means that they cannot contain a center of inversion (i) or a mirror ...
Center of symmetry or inversion center, abbreviated i. A molecule has a center of symmetry when, for any atom in the molecule, an identical atom exists diametrically opposite this center an equal distance from it. In other words, a molecule has a center of symmetry when the points (x,y,z) and (−x,−y,−z) of the molecule always look identical.
Point groups lacking an inversion center (non-centrosymmetric) can be polar, chiral, both, or neither. A polar point group is one whose symmetry operations leave more than one common point unmoved. A polar point group has no unique origin because each of those unmoved points can be chosen as one.
A center of symmetry of a figure is a point , such that is invariant under the mapping (,,) (,,), when is chosen to be the origin of the coordinate system.) Note, however, that there are achiral figures lacking both plane and center of symmetry.
A chirality center (chiral center) is a type of stereocenter. A chirality center is defined as an atom holding a set of four different ligands (atoms or groups of atoms) in a spatial arrangement which is non-superposable on its mirror image. Chirality centers must be sp 3 hybridized, meaning that a chirality center can only have single bonds. [5]
Spontaneous chiral symmetry breaking may also occur in some theories, as it most notably does in quantum chromodynamics. The chiral symmetry transformation can be divided into a component that treats the left-handed and the right-handed parts equally, known as vector symmetry, and a component that actually treats them differently, known as ...
Chiral and full (or achiral tetrahedral symmetry and pyritohedral symmetry) are discrete point symmetries (or equivalently, symmetries on the sphere). They are among the crystallographic point groups of the cubic crystal system .