= Chirality
{disambiguate=chemistry}
{wiki}
= Chiral
{synonym}
<Chirality (chemistry)> means that a <molecule> cannot be superposed on its mirror image. A <carbon> attached to four different groups is a common source of <chirality (chemistry)>; the definition concerns the whole <molecule>, rather than requiring this particular structural feature.
The test is spatial: apply a <translation (geometry)> and a <rotation (mathematics)> to the entire <molecule> until corresponding <chemical atoms> coincide, keeping their identities and <chemical bonds>. A mirror operation is a <reflection (mathematics)>; physically turning a model is a <rotation (mathematics)>. They are different operations. If no such superposition exists, the two forms are <enantiomers>; if one succeeds, the <molecule> is <achiral>. A different-looking flat drawing alone establishes neither conclusion.
For a simple <molecule> with exactly one tetrahedral <stereocenter> and four constitutionally different <substituents>, the mirror forms cannot superpose. Compare entire attached groups, including paths around a ring, rather than just the first <chemical atom>. Several tetrahedral <stereocenters> require a whole-<molecule> check: a <meso compound> can be <achiral>. Conversely, <axial chirality> needs no tetrahedral <stereocenter>.<Organic Chemistry by John McMurry/5.2 The Reason for Handedness in Molecules: Chirality>[McMurry, Organic Chemistry, §5.2: whole-molecule chirality, four different groups and equivalent ring paths]{ref}
\Image[/tetrahedral-enantiomer-mirror-geometry.png]
{title=Spatial mirror pair with four distinct substituents}
{description=Ideal <tetrahedral molecular geometry> with distinct <substituents> A, B, C and D. The two models use the same viewing direction and the <reflection (mathematics)> $x\mapsto-x$. Their opposite signed <determinants> exclude superposition by any label-preserving <rotation (mathematics)>. The letters do not denote <R and S configuration> priorities.}
Why care about this distinction? Two <enantiomers> can fit differently into an already <chiral molecule>, just as two opposite hands fit differently into one glove. Thus a <protein>'s spatial arrangement can distinguish a mirror pair even when an <achiral> measurement cannot. <Polarimetry> provides a different kind of test: it measures a sample's net <optical rotation>, which depends on the populations of its <enantiomers>.
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