Take bromochlorofluoromethane, CHBrClF: one carbon bonded to a hydrogen, a fluorine, a bromine and a chlorine. Hold a model of it up to a mirror. The reflection is a second molecule with the same four atoms on the same carbon. Now try to turn that reflection until it matches the original. You can always bring two of the groups into line, but the other two then come out swapped.
So CHBrClF and its mirror image are two different molecules. They have the same formula and the same bonds, yet neither can be laid on top of the other. That property is chirality. Living things are built from molecules like this and can tell the two mirror forms apart, which is why chirality sits near the center of organic chemistry.
The definition
An object is chiral if it is not superimposable on its mirror image. To superimpose two objects is to lay one on the other so that every part meets its counterpart, using only turning and sliding. Bending the object or breaking bonds is not allowed. An object that can be superimposed on its mirror image is achiral.
Replace the fluorine of CHBrClF with a second hydrogen and you have bromochloromethane, CH₂BrCl. Run the same test on it. This time the turned mirror image matches the original group for group. The two hydrogens have traded places, and since they are identical, nothing has changed. CH₂BrCl is achiral.
Every object has a mirror image, so the question is never whether one exists. The question is whether the mirror image is the same object. For CH₂BrCl it is, and for CHBrClF it is not.
Hands, mugs and screws
Your left and right hands are mirror images. However you turn your left hand, you cannot make it match your right: the thumb always ends up on the wrong side. Hands are the classic chiral object, and they gave the property its name, from the Greek cheir, hand.
A plain coffee mug is achiral. A plane through the middle of the mug and its handle cuts it into two halves that are mirror images of each other, so reflecting the mug gives back the same mug.
A screw is chiral. Its thread winds around it as a coil, and a right-handed coil and a left-handed coil are mirror images that no turning can match. That is why a screw with a right-hand thread will not go into a nut with a left-hand thread. Scissors are chiral too, which is why left-handed scissors are sold, and so is a spiral seashell. A sphere, a cube and a plain pencil are achiral.
The symmetry shortcut
The mug suggests a faster test than turning mirror images in your head. Draw 2-chloropropane, CH₃CHClCH₃, with Cl and H on plain bonds in the page and the two methyl groups on a solid wedge and a dashed wedge. The page itself now cuts the molecule into two mirror halves. The carbon, the chlorine and the hydrogen lie in it, and it reflects the wedged methyl onto the dashed one.
A flat plane that cuts a molecule into two halves that are mirror images of each other is a plane of symmetry, also called an internal mirror plane. Reflecting a molecule through such a plane gives back the same molecule. So the test is: if a molecule has a plane of symmetry, it is achiral.
Change one methyl of 2-chloropropane to an ethyl group and you have 2-chlorobutane. Drawn the same way, the page would now reflect a methyl onto an ethyl, which is a different group. 2-Chlorobutane has no plane of symmetry in any shape it can take, and it is chiral.
Strictly, a plane is only one of the symmetries that make a molecule achiral. A molecule is achiral if it has any improper symmetry element, meaning any symmetry operation that includes a reflection. A plane of symmetry is one such element. A center of symmetry is another: a point in the molecule such that every atom has an identical twin directly across that point, the same distance away.
Take CHBrCl–CHBrCl. It has more than one stereoisomer: forms with the same bonds that differ only in how the atoms are arranged in space. (Isomers with the same formula but different bonds, such as butane and 2-methylpropane, are constitutional isomers instead.) The figure below shows one of them, viewed along the carbon–carbon bond as in Newman projections. The front bromine's twin is the back bromine, directly across the center. The two chlorines pair up the same way, and so do the two hydrogens. In this conformation the molecule has no plane of symmetry, but the center is enough to make it achiral. (Its eclipsed conformation, with the back bromine directly behind the front one, also has a plane.)
In this course, the full test is: look for a plane of symmetry, and if there is none, look for a center of symmetry.
Checking the right conformation
Butane shows why the shape you check matters. A molecule that can turn about its single bonds takes many shapes, called conformations. In the anti conformation of butane, a plane passes through both methyl groups and the C2–C3 bond, and it is a plane of symmetry. In a gauche conformation there is no plane, and the mirror image of one gauche conformation is the other gauche conformation.
Butane is still one achiral compound. A turn about the C2–C3 bond carries one gauche conformation into the other, and into the anti conformation, many times a second at room temperature.
Chirality without a stereocenter
Most chiral molecules in this course owe their chirality to a carbon with four different groups. There are other routes, and knowing them keeps you from treating "stereocenter" and "chiral" as the same word. In each of them the handedness comes from a twist in the molecule rather than from one atom.
Start with penta-2,3-diene, CH₃–CH=C=CH–CH₃. Its middle carbon forms two double bonds, one to each neighbor. Two double bonds that share a carbon like this are cumulated, and a compound with the C=C=C unit is an allene. The middle carbon is bonded to only two atoms, so it is sp, and the three carbons of the C=C=C unit lie in a straight line.
The two ends of an allene are twisted a quarter turn from each other. The middle carbon has two p orbitals at right angles. One overlaps a p orbital on the left carbon to make the left π bond, and the other overlaps a p orbital on the right carbon to make the right π bond. Each end carbon holds its two groups in the plane at right angles to its own p orbital. So the groups on the left end lie in one plane, and the groups on the right end lie in a plane at right angles to it.
That twist makes penta-2,3-diene chiral, although it has no stereocenter. Turn its mirror image half a turn about the C=C=C axis and the right-hand end matches the original, but the methyl and the hydrogen on the left-hand end come out swapped.
An allene is chiral only when each end carbon carries two different groups. Buta-1,2-diene, CH₂=C=CH–CH₃, has two hydrogens on one end. The plane that holds the C=C=C unit and the CH₃ end reflects one of those hydrogens onto the other, so it is a plane of symmetry, and the molecule is achiral. The same condition decides whether a double bond has two stereoisomers, as Cis/trans and E/Z, later in this chapter, shows.
The second route is a blocked single bond. A biaryl is two benzene rings joined by a single bond. Turning about a single bond is normally free, as in butane, but in 6,6′-dinitro[1,1′-biphenyl]-2,2′-dicarboxylic acid it is not. Each ring carries a nitro group, –NO₂, and a carboxylic acid group, –CO₂H, on the two carbons beside the joint. To turn, the rings would have to pass through the arrangement where both lie in one plane, and there those four groups would run into one another.
So the rings stay twisted, and the molecule is chiral. Stereoisomers that exist only because turning about a single bond is blocked are called atropisomers. This compound was separated into its two mirror-image forms in 1922.
As with allenes, each ring must carry two different groups beside the joint. If one ring carried two identical groups there, the plane of the other ring would reflect them onto each other, and the molecule would be achiral.
How well the turning is blocked depends on how big the groups beside the joint are. With only hydrogens there, as in plain biphenyl, the rings turn freely. If the groups are only moderately large, the rings can still squeeze past each other slowly, and each form gradually turns into its mirror image. The sample ends up as a 50:50 mixture of the two forms, called a racemic mixture, and the process is called racemization. Bulky groups beside the joint slow the turning enough that the two forms can be separated and kept.
The best-known atropisomers are built on naphthalene, two benzene rings that share one edge. A 1,1′-binaphthyl joins two naphthalenes by a single bond. On each naphthalene, the ring that is not bonded to the joint has a hydrogen right beside the joint. That hydrogen is called the peri hydrogen. It slows the turning but does not stop it: plain 1,1′-binaphthyl slowly racemizes at room temperature. One more group beside the joint on each naphthalene locks the twist.
In BINOL, that group is an OH, on the side of the joint opposite the peri hydrogen, as the figure shows. BINAP has a PPh₂ group there instead: a phosphorus bonded to two benzene rings. Both are ligands, molecules that bind to a metal atom, and they are two of the most used ligands in asymmetric catalysis, where a chiral catalyst makes more of one mirror-image form of a product than of the other. Their OH and PPh₂ groups do two jobs at once: they lock the twist, and they bind the metal.
The third route is a helix. A molecule shaped as a helix has a handedness for the same reason a screw does, and its mirror image is a helix of the opposite hand. DNA's double helix is right-handed.
Why this matters biologically
Nineteen of the twenty amino acids that build proteins are chiral, and living things use the same one of the two mirror forms, the one called L, for all nineteen. Natural sugars are almost all the D form. D and L are older labels for the two mirror forms, explained in Fischer projections.
The receptors, enzymes and transport proteins of a living system are built from these chiral pieces, so they are chiral too. That lets them tell mirror images apart, the way a right-handed glove fits only a right hand.
Two molecules that are mirror images and cannot be superimposed, like the two forms of CHBrClF, are called enantiomers. They have a section of their own, Enantiomers. Most physical measurements cannot tell two enantiomers apart, but one can. A sample that contains more of one enantiomer than the other rotates polarized light, a property called optical activity. Optical activity is how chirality was first discovered, and it is still a standard way to detect it. A racemic mixture shows no rotation, and neither does an achiral compound.
Your nose can tell enantiomers apart, because its smell receptors are chiral. One enantiomer of carvone smells of spearmint and the other of caraway. The two enantiomers of limonene smell of oranges and of pine.
In drugs the difference can matter more. Each enantiomer can be named with a letter, R or S, by the rules in R/S configuration. Here the letters serve only as names. Ibuprofen is sold as a racemic mixture, but only the (S) enantiomer is active, and the body slowly converts the (R) form into it. Naproxen's anti-inflammatory action comes from its (S) enantiomer, and naproxen is sold as that enantiomer alone.
Thalidomide is the best-known case, and it is often told wrongly. The (R) enantiomer is an effective sedative and the (S) enantiomer causes birth defects, but the two interconvert in the body. Selling the pure (R) form would not have prevented the disaster. The real lesson is not "separate your enantiomers" but "know what each one does", and drug regulators now require exactly that.
What carries forward
Chirality is the organizing idea of this chapter. The sections that follow give you the tools: how to spot the atoms that cause it, how to name the two mirror forms, how to sort the relationships between several stereoisomers of one compound, and how to draw them all without ambiguity. From Substitution & Elimination onward, what a reaction does to the arrangement at a carbon, whether it inverts it, keeps it or scrambles it into a racemic mixture, becomes a standard part of describing its mechanism.