Chirality is a property that describes how an object is not the same as its mirror image. If an object cannot be matched exactly with its mirror image, it is called chiral. This means the object cannot be overlapped completely with its mirror image. If an object can be overlapped with its mirror image, it is called achiral, like a sphere. A chiral object and its mirror image are called enantiomorphs, or enantiomers when referring to molecules. Chirality is a type of asymmetry that is important in many areas of science.
Human hands are a well-known example of chirality. The left hand is a mirror image of the right hand that cannot be overlapped completely. No matter how the hands are positioned, their features do not match perfectly across all directions. This difference is clear when trying to shake hands with someone using the opposite hand or when wearing a left-handed glove on a right hand.
The word "chirality" comes from the Greek word χείρ (kheir), meaning "hand," which is a common chiral object. The term was first used by Lord Kelvin in 1893 during a lecture at Oxford University, which was published in 1894.
Mathematics
In mathematics, a figure is chiral if it cannot be made to look like its mirror image by just turning or moving it. For example, a right shoe is different from a left shoe, and S-twist yarn is different from Z-twist. For a full mathematical definition, see the explanation provided.
A chiral object and its mirror image are called enantiomorphs. The word "enantiomorph" comes from Greek words meaning "opposite" and "form." A figure that is not chiral is called achiral or amphichiral.
A helix (and objects like a spun string, a screw, or a propeller) and a Möbius strip are chiral two-dimensional shapes in three-dimensional space. In the video game Tetris, the J, L, S, and Z-shaped tetrominoes also show chirality, but only in two dimensions.
Many everyday objects, like gloves, shoes, and sometimes glasses, share the same chiral symmetry as the human body. A similar idea of chirality is studied in knot theory, as explained below.
Some chiral three-dimensional objects, like a helix, can be described as right-handed or left-handed based on the right-hand rule.
In geometry, a figure is achiral if its symmetry group includes at least one way to reverse direction. In two dimensions, any shape with an axis of symmetry is achiral, and all bounded achiral shapes must have an axis of symmetry. In three dimensions, any shape with a plane of symmetry or a center of symmetry is achiral. However, some achiral shapes may lack both. In terms of point groups, chiral figures do not include an improper axis of rotation (Sₙ). This means they cannot have a center of inversion (i) or a mirror plane (σ). Only figures with point groups like C₁, Cₙ, Dₙ, T, O, or I can be chiral.
A knot is achiral if it can be reshaped into its mirror image without breaking. If it cannot, the knot is chiral. For example, the unknot and the figure-eight knot are achiral, but the trefoil knot is chiral.
Physics
In physics, chirality can be seen in the spin of a particle. The handedness of a particle is determined by the direction it spins. This should not be confused with helicity, which describes how the spin direction aligns with the movement of the particle. Chirality is an intrinsic property, like spin, and does not depend on the particle’s motion. Both chirality and helicity can be left-handed or right-handed. However, they are only the same for massless particles. For massless particles, helicity matches chirality, but for antiparticles, their signs are opposite.
The handedness in chirality and helicity relates to how a particle rotates while moving in a straight line. Imagine pointing your thumb in the direction of motion and curling your fingers; this shows the rotation direction (clockwise or counterclockwise). Depending on how the particle moves and rotates, it can be left-handed or right-handed. A change between left-handed and right-handed is called a parity transformation. When a Dirac fermion remains unchanged under a parity transformation, this is known as chiral symmetry.
Electromagnetic waves can have handedness based on their polarization. Polarization describes the direction and strength of the electric field in a wave over time. For example, left-handed or right-handed circularly polarized waves create helical patterns in space with opposite handedness.
Circularly polarized waves with opposite handedness move at different speeds and experience different losses in chiral materials. These effects, called circular birefringence and circular dichroism, are together known as optical activity. Circular birefringence causes the polarization direction of electromagnetic waves to change in chiral materials. In some cases, this can result in a negative index of refraction for waves of one handedness.
Optical activity is linked to three-dimensional chiral structures, like helices. However, chirality can also exist in two dimensions. In two dimensions, patterns such as flat spirals cannot be matched with their mirror images through movement or rotation in a flat plane. Two-dimensional chirality is connected to how circularly polarized waves are transmitted, reflected, or absorbed differently depending on their direction. Two-dimensional chiral materials, which are not uniform and absorb energy, show different transmission levels for the same wave hitting their front or back. This happens because the efficiency of converting left-handed to right-handed polarization varies depending on the wave’s direction. As a result, the properties of left-handed and right-handed waves are swapped when the wave hits the front or back of the material.
While optical activity relates to three-dimensional chirality and circular conversion relates to two-dimensional chirality, both effects can also occur in non-chiral materials. This happens when the direction of the electromagnetic wave and the structure of a non-chiral material create a chiral setup. This type of setup, where non-chiral parts form a chiral arrangement, is called extrinsic chirality.
Chiral mirrors are a type of metamaterial that reflects circularly polarized light with a specific spin direction without changing its spin. They absorb light with the opposite spin. However, most chiral mirrors only work well in a narrow range of frequencies due to the causality principle. A different design allows unwanted waves to pass through instead of being absorbed, enabling chiral mirrors to perform well across a wide range of frequencies.
Chemistry
A chiral molecule is a type of molecule that has mirror images that cannot be matched exactly. The most common reason for chirality in molecules is the presence of a carbon atom that has four different groups attached to it.
The term "chiral" is used to describe objects that cannot be matched exactly with their mirror images. In chemistry, chirality usually refers to molecules. Two mirror images of a chiral molecule are called enantiomers or optical isomers. These pairs are often described as "right-handed" or "left-handed." If a molecule has no handedness, it is called achiral. When polarized light passes through a chiral molecule, the light’s direction of polarization is rotated either clockwise (to the right) or counterclockwise (to the left). A right-handed rotation is called dextrorotary (d), and a left-handed rotation is called levorotary (l). The d- and l-isomers are the same compound but are named as enantiomers. A mixture that has equal amounts of both optical isomers is called a racemic mixture, and it does not change the direction of polarized light. Left-handed molecules have the letter "l-" added to their names, and right-handed molecules have "d-." However, the d- and l- system does not explain the exact arrangement of groups around the special carbon atom, which is called the configuration. Another system for naming configurations is the Fischer convention, also known as the D- and L-system. This system uses D-(+)-Glyceraldehyde and L-(−)-Glyceraldehyde as standards for comparison. The Fischer convention is often used in the study of sugars and amino acids. Because of its limitations, the Fischer system is mostly replaced by the Cahn-Ingold-Prelog convention, also called the R and S system. This system is used to describe the exact arrangement of groups in molecules, including cis-trans isomers, using the E-Z notation.
Molecular chirality is important because it affects many areas of chemistry, including inorganic, organic, physical, biochemical, and supramolecular chemistry. Recent advances in chiral chemistry include the creation of chiral inorganic nanoparticles that have a shape similar to the tetrahedral geometry of traditional chiral centers found in carbon atoms. These nanoparticles are larger than typical chiral molecules. Other chiral nanomaterials have been developed with helical or other symmetrical shapes.
Biology
All living things show specific mirror-image traits in their chemical structures, body parts, growth, and actions. In any organism or group of related organisms, most chemicals, organs, or behaviors are found in the same mirror-image form. Some chemicals, organs, or behaviors may appear in the opposite mirror-image form, but this depends on the organism’s genes. At the molecular level, living systems act very specifically with mirror-image forms in how they make chemicals, take in nutrients, sense things, and process food. Living systems often treat the two mirror-image forms of the same chemical very differently.
In biology, most amino acids and carbohydrates have mirror-image traits. The amino acids used to build proteins, which are made by cells based on genetic instructions, are usually in the L form. However, D-form amino acids also exist in nature. Simple sugar units are often found in the D form. The DNA double helix has a mirror-image shape, and the B-form of DNA twists to the right.
Sometimes, the two mirror-image forms of a chemical can have very different tastes, smells, or effects in the body. For example, (+)-carvone smells like caraway seeds, while (–)-carvone smells like spearmint. A common mistake is thinking that (+)-limonene is in oranges and (–)-limonene is in lemons. However, in 2021, scientists discovered that all citrus fruits only contain (+)-limonene, and the smell differences come from other factors.
For man-made chemicals, such as medicines, the two mirror-image forms of a drug can have very different effects. Dextropropoxyphene (Darvon) is used to relieve pain, while its mirror-image form, levopropoxyphene (Novrad), is used to stop coughs. In penicillamine, the S form helps treat a type of arthritis, but the R form is harmful and has no medical use. In some cases, the less effective mirror-image form can cause health problems. For example, the S form of naproxen helps with pain, but the R form can harm the kidneys. When one mirror-image form of a drug is helpful and the other is harmful, scientists may switch to using only the helpful form. This change is called a chiral switch.
The natural form of alpha-tocopherol (vitamin E) is RRR-α-tocopherol. The man-made form, dl-tocopherol, is a mix of different mirror-image forms. The natural form is more effective than the man-made form, so 1.36 mg of dl-tocopherol is equal to 1.0 mg of the natural form.
Mirror-image traits appear in plants, animals, and all living things. For example, climbing plants can grow in either a left- or right-handed spiral.
In anatomy, many animals have body parts that are not perfect mirror images. For example, some snails have shells that twist to the right or left. Over 90% of snail species have right-handed shells, but a few have left-handed shells. Some species, like Amphidromus perversus, have individuals with both right- and left-handed shells.
In humans, mirror-image traits are called handedness. People who use their right hand more are right-handed, and those who use their left hand more are left-handed. Mirror-image traits also appear in facial asymmetry, known as aurofacial asymmetry.
According to the Axial Twist theory, some animals develop with a left-handed twist. This causes the brain, heart, and intestines to rotate slightly.
In situs inversus totalis, a condition where all internal organs are mirrored, patients may face challenges if they need a liver or heart transplant. This is because organs are mirror-image structures, and blood vessels would need to be rearranged if a normal organ is used.
In the bloodroot plant family, some species have flowers that twist to the left or right. This helps increase genetic diversity. A related plant, Dilatris, has flowers that twist both ways on the same plant. In flatfish, summer flounder have eyes on the left side, while halibut have eyes on the right side.