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The simplest chiral knot is the trefoil knot, which was shown to be chiral by Max Dehn. All nontrivial torus knots are chiral. The Alexander polynomial cannot distinguish a knot from its mirror image, but the Jones polynomial can in some cases; if V k ( q ) ≠ V k ( q −1 ), then the knot is chiral, however the converse is not true.
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 axial symmetry. [2] (cf. Current algebra.) A scalar field model encoding chiral symmetry and its breaking is the chiral model.
An object that is not chiral is said to be achiral. A chiral object and its mirror image are said to be enantiomorphs. The word chirality is derived from the Greek χείρ (cheir), the hand, the most familiar chiral object; the word enantiomorph stems from the Greek ἐναντίος (enantios) 'opposite' + μορφή (morphe) 'form'.
The four-dimensional point groups (chiral as well as achiral) are listed in Conway and Smith, [1] Section 4, Tables 4.1–4.3. Finite isomorphism and correspondences. The following list gives the four-dimensional reflection groups (excluding those that leave a subspace fixed and that are therefore lower-dimensional reflection groups).
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 plane (σ). Only figures with a point group designation of C 1, C n, D n, T, O, or I can be chiral.
Chirality with hands and two enantiomers of a generic amino acid The direction of current flow and induced magnetic flux follow a "handness" relationship. The term chiral / ˈ k aɪ r əl / describes an object, especially a molecule, which has or produces a non-superposable mirror image of itself.
Enantioselective synthesis, also called asymmetric synthesis, [1] is a form of chemical synthesis.It is defined by IUPAC as "a chemical reaction (or reaction sequence) in which one or more new elements of chirality are formed in a substrate molecule and which produces the stereoisomeric (enantiomeric or diastereomeric) products in unequal amounts."
[4] [5] The configuration of other chiral compounds was then related to that of (+)-glyceraldehyde by sequences of chemical reactions. For example, oxidation of (+)-glyceraldehyde (1) with mercury oxide gives (−)-glyceric acid (2), a reaction that does not alter the stereocenter. Thus the absolute configuration of (−)-glyceric acid must be ...