# Chirality

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Chirality is a property of asymmetry important in several branches of science. The word chirality is derived from the Greek χειρ (kheir), "hand", a familiar chiral object.

## Contents

An object or a system is chiral if it is distinguishable from its mirror image; that is, it cannot be superimposed onto it. Conversely, a mirror image of an achiral object, such as a sphere, cannot be distinguished from the object. A chiral object and its mirror image are called enantiomorphs (Greek, "opposite forms") or, when referring to molecules, enantiomers . A non-chiral object is called achiral (sometimes also amphichiral) and can be superposed on its mirror image.

The term was first used by Lord Kelvin in 1893 in the second Robert Boyle Lecture at the Oxford University Junior Scientific Club which was published in 1894:

I call any geometrical figure, or group of points, 'chiral', and say that it has chirality if its image in a plane mirror, ideally realized, cannot be brought to coincide with itself. [1]

Human hands are perhaps the most recognized example of chirality. The left hand is a non-superimposable mirror image of the right hand; no matter how the two hands are oriented, it is impossible for all the major features of both hands to coincide across all axes. [2] This difference in symmetry becomes obvious if someone attempts to shake the right hand of a person using their left hand, or if a left-handed glove is placed on a right hand. In mathematics, chirality is the property of a figure that is not identical to its mirror image.

## Mathematics

In mathematics, a figure is chiral (and said to have chirality) if it cannot be mapped to its mirror image by rotations and translations alone. For example, a right shoe is different from a left shoe, and clockwise is different from anticlockwise. See [3] for a full mathematical definition.

A chiral object and its mirror image are said to be enantiomorphs. The word enantiomorph stems from the Greek ἐναντίος (enantios) 'opposite' + μορφή (morphe) 'form'. A non-chiral figure is called achiral or amphichiral.

The helix (and by extension a spun string, a screw, a propeller, etc.) and Möbius strip are chiral two-dimensional objects in three-dimensional ambient space. The J, L, S and Z-shaped tetrominoes of the popular video game Tetris also exhibit chirality, but only in a two-dimensional space.

Many other familiar objects exhibit the same chiral symmetry of the human body, such as gloves, glasses (sometimes), and shoes. A similar notion of chirality is considered in knot theory, as explained below.

Some chiral three-dimensional objects, such as the helix, can be assigned a right or left handedness, according to the right-hand rule.

### Geometry

In geometry, a figure is achiral if — and only if — its symmetry group contains at least one orientation-reversing isometry. In two dimensions, every figure that possesses an axis of symmetry is achiral, and it can be shown that every bounded achiral figure must have an axis of symmetry. 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 (Sn). This means that they cannot contain a center of inversion (i) or a mirror plane (σ). Only figures with a point group designation of C1, Cn, Dn, T, O, or I can be chiral.

### Knot theory

A knot is called achiral if it can be continuously deformed into its mirror image, otherwise it is called chiral. For example, the unknot and the figure-eight knot are achiral, whereas the trefoil knot is chiral.

## Physics

In physics, chirality may be found in the spin of a particle, where the handedness of the object is determined by the direction in which the particle spins. [4] Not to be confused with helicity, which is the projection of the spin along the linear momentum of a subatomic particle, chirality is an intrinsic quantum mechanical property, like spin. Although both chirality and helicity can have left-handed or right-handed properties, only in the massless case are they identical. [5] In particular for a massless particle the helicity is the same as the chirality while for an antiparticle they have opposite sign.

The handedness in both chirality and helicity relate to the rotation of a particle while it proceeds in linear motion with reference to the human hands. The thumb of the hand points towards the direction of linear motion whilst the fingers curl into the palm, representing the direction of rotation of the particle (i.e. clockwise and counterclockwise). Depending on the linear and rotational motion, the particle can either be defined by left-handedness or right-handedness. [5] A symmetry transformation between the two is called parity. Invariance under parity by a Dirac fermion is called chiral symmetry.

### Electromagnetism

Electromagnetic waves can have handedness associated with their polarization. Polarization of an electromagnetic wave is the property that describes the orientation, i.e., the time-varying direction and amplitude, of the electric field vector. For example, the electric field vectors of left-handed or right-handed circularly polarized waves form helices of opposite handedness in space.

Circularly polarized waves of opposite handedness propagate through chiral media at different speeds (circular birefringence) and with different losses (circular dichroism). Both phenomena are jointly known as optical activity. Circular birefringence causes rotation of the polarization state of electromagnetic waves in chiral media and can cause a negative index of refraction for waves of one handedness when the effect is sufficiently large. [6] [7]

While optical activity occurs in structures that are chiral in three dimensions (such as helices), the concept of chirality can also be applied in two dimensions. 2D-chiral patterns, such as flat spirals, cannot be superimposed with their mirror image by translation or rotation in two-dimensional space (a plane). 2D chirality is associated with directionally asymmetric transmission (reflection and absorption) of circularly polarized waves. 2D-chiral materials, which are also anisotropic and lossy exhibit different total transmission (reflection and absorption) levels for the same circularly polarized wave incident on their front and back. The asymmetric transmission phenomenon arises from different, e.g. left-to-right, circular polarization conversion efficiencies for opposite propagation directions of the incident wave and therefore the effect is referred to as circular conversion dichroism. Like the twist of a 2d-chiral pattern appears reversed for opposite directions of observation, 2d-chiral materials have interchanged properties for left-handed and right-handed circularly polarized waves that are incident on their front and back. In particular left-handed and right-handed circularly polarized waves experience opposite directional transmission (reflection and absorption) asymmetries. [8] [9]

While optical activity is associated with 3d chirality and circular conversion is associated with 2d chirality, both effects have also been observed in structures that are not chiral by themselves. For the observation of these chiral electromagnetic effects, chirality does not have to be an intrinsic property of the material that interacts with the electromagnetic wave. Instead, both effects can also occur when the propagation direction of the electromagnetic wave together with the structure of an (achiral) material form a chiral experimental arrangement. [10] [11] This case, where the mutual arrangement of achiral components forms a chiral (experimental) arrangement, is known as extrinsic chirality. [12] [13]

Chiral mirrors are a class of metamaterials that reflect circularly polarized light of a certain helicity in a handedness-preserving manner, while absorbing circular polarization of the opposite handedness. [14] However, most absorbing chiral mirrors operate only in a narrow frequency band, as limited by the causality principle. Employing a different design methodology that allows undesired waves to pass through instead of absorbing the undesired waveform, chiral mirrors are able to show good broadband performance. [15]

## Chemistry

A chiral molecule is a type of molecule that has a non-superposable mirror image. The feature that is most often the cause of chirality in molecules is the presence of an asymmetric carbon atom. [16] [17]

The term "chiral" in general is used to describe the object that is non-superposable on its mirror image. [18]

In chemistry, chirality usually refers to molecules. Two mirror images of a chiral molecule are called enantiomers or optical isomers. Pairs of enantiomers are often designated as "right-", "left-handed" or, if they have no bias, "achiral". As polarized light passes through a chiral molecule, the plane of polarization, when viewed along the axis toward the source, will be rotated clockwise (to the right) or anticlockwise (to the left). A right handed rotation is dextrorotary (d); that to the left is levorotary (l). The d- and l-isomers are the same compound but are called enantiomers. An equimolar mixture of the two optical isomers, which is called a racemic mixture, will produce no net rotation of polarized light as it passes through. [19] Left handed molecules have l- prefixed to their names; d- is prefixed to right handed molecules. However, this d- and l- notation of distinguishing enantiomers does not say anything about the actual spatial arrangement of the ligands/substituents around the stereogenic center, which is defined as configuration. Another nomenclature system employed to specify configuration is Fischer convention. [20] This is also referred to as the D- and L-system. Here the relative configuration is assigned with reference to D-(+)-Glyceraldehyde and L-(-)-Glyceraldehyde, being taken as standard. Fischer convention is widely used in sugar chemistry and for α-amino acids. Due to the drawbacks of Fischer convention, it is almost entirely replaced by Cahn-Ingold-Prelog convention, also known as the sequence rule or R and S nomenclature. [21] [22] This was further extended to assign absolute configuration to cis-trans isomers with the E-Z notation.

Molecular chirality is of interest because of its application to stereochemistry in inorganic chemistry, organic chemistry, physical chemistry, biochemistry, and supramolecular chemistry.

More recent developments in chiral chemistry include the development of chiral inorganic nanoparticles that may have the similar tetrahedral geometry as chiral centers associated with sp3 carbon atoms traditionally associated with chiral compounds, but at larger scale. [23] [24] Helical and other symmetries of chiral nanomaterials were also obtained. [25]

## Biology

R-(+)-Limonene found in all citrus fruits
S-(–)-Limonene found in only trace amounts in lemongrass and citronella
(S)-(+)-Carvone occurs in caraway seed oil, and (R)-(-)-carvone occurs in spearmint
Dextropropoxyphene or Darvon, a painkiller
Levopropoxyphene or Novrad, an anticough agent
A natural left-handed helix, made by a certain climber plant's tendril
Shells of two different species of sea snail: on the left is the normally sinistral (left-handed) shell of Neptunea angulata , on the right is the normally dextral (right-handed) shell of Neptunea despecta
Wachendorfia paniculata flower with style left

All of the known life-forms show specific chiral properties in chemical structures as well as macroscopic anatomy, development and behavior. [26] In any specific organism or evolutionarily related set thereof, individual compounds, organs, or behavior are found in the same single enantiomorphic form. Deviation (having the opposite form) could be found in a small number of chemical compounds, or certain organ or behavior but that variation strictly depends upon the genetic make up of the organism. From chemical level (molecular scale), biological systems show extreme stereospecificity in synthesis, uptake, sensing, metabolic processing. A living system usually deals with two enantiomers of the same compound in drastically different ways.

In biology, homochirality is a common property of amino acids and carbohydrates. The chiral protein-making amino acids, which are translated through the ribosome from genetic coding, occur in the L form. However, D-amino acids are also found in nature. The monosaccharides (carbohydrate-units) are commonly found in D-configuration. DNA double helix is chiral (as any kind of helix is chiral), and B-form of DNA shows a right-handed turn.

Sometimes, when two enantiomers of a compound found in organisms, they significantly differ in their taste, smell and other biological actions. For example,(+)-Carvone is responsible for the smell of caraway seed oil, whereas (–)-carvone is responsible for smell of spearmint oil. [27] . However, it is a commonly held misconception that (+)-limonene is found in oranges (causing its smell), and (–)-limonene is found in lemons (causing its smell). In 2021, after rigorous experimentation, it was found that all citrus fruits contain only (+)-limonene and the odor difference is because of other contributing factors [28] .

Also, for artificial compounds, including medicines, in case of chiral drugs, the two enantiomers sometimes show remarkable difference in effect of their biological actions. [29] Darvon (dextropropoxyphene) is a painkiller, whereas its enantiomer, Novrad (levopropoxyphene) is an anti-cough agent. In case of penicillamine, the (S-isomer is used in the treatment of primary chronic arthritis, whereas the (R)-isomer has no therapeutic effect, as well as being highly toxic. [30] In some cases, the less therapeutically active enantiomer can cause side effects. For example, (S-naproxen is an analgesic but the (R-isomer causes renal problems. [31] In such situations where one of the enantiomers of a racemic drug is active and the other partner has undesirable or toxic effect one may switch from racemate to a single enantiomer drug for a better therapeutic value. Such a switching from a racemic drug to an enantiopure drug is called a chiral switch.

The naturally occurring plant form of alpha-tocopherol (vitamin E) is RRR-α-tocopherol whereas the synthetic form (all-racemic vitamin E, or dl-tocopherol) is equal parts of the stereoisomers RRR, RRS, RSS, SSS, RSR, SRS, SRR, and SSR with progressively decreasing biological equivalency, so that 1.36 mg of dl-tocopherol is considered equivalent to 1.0 mg of d-tocopherol. [32]

Macroscopic examples of chirality are found in the plant kingdom, the animal kingdom and all other groups of organism. A simple example is the coiling direction of any climber plant, which can grow to form either a left- or right-handed helix.

In anatomy, chirality is found in the imperfect mirror image symmetry of many kinds of animal bodies. Organisms such as gastropods exhibit chirality in their coiled shells, resulting in an asymmetrical appearance. Over 90% of gastropod species [33] have dextral (right-handed) shells in their coiling, but a small minority of species and genera are virtually always sinistral (left-handed). A very few species (for example Amphidromus perversus [34] ) show an equal mixture of dextral and sinistral individuals.

In humans, chirality (also referred to as handedness or laterality) is an attribute of humans defined by their unequal distribution of fine motor skill between the left and right hands. An individual who is more dexterous with the right hand is called right-handed , and one who is more skilled with the left is said to be left-handed . Chirality is also seen in the study of facial asymmetry.

In the case of the health condition situs inversus totalis , in which all the internal organs are flipped horizontally (i.e. the heart placed slightly to the right instead of the left), chirality poses some problems should the patient require a liver or heart transplant, as these organs are chiral, thus meaning that the blood vessels which supply these organs would need to be rearranged should a normal, non situs inversus ( situs solitus ) organ be required.

In the monocot bloodroot family, the species of the genera Wachendorfia and Barberetta have only individuals that either have the style points to the right or the style pointed to the left, with both morphs appearing within the same populations. This is thought to increase outcrossing and so boost genetic diversity, which in turn may help to survive in a changing environment. Remarkably, the related genus Dilatris also has chiraly dimorphic flowers, but here both morphs occur on the same plant. [35] In flatfish, the summer flounder or fluke are left-eyed, while halibut are right-eyed.

## Related Research Articles

In organic chemistry, the Cahn–Ingold–Prelog (CIP) sequence rules are a standard process to completely and unequivocally name a stereoisomer of a molecule. The purpose of the CIP system is to assign an R or S descriptor to each stereocenter and an E or Z descriptor to each double bond so that the configuration of the entire molecule can be specified uniquely by including the descriptors in its systematic name. A molecule may contain any number of stereocenters and any number of double bonds, and each usually gives rise to two possible isomers. A molecule with an integer n describing the number of stereocenters will usually have 2n stereoisomers, and 2n−1 diastereomers each having an associated pair of enantiomers. The CIP sequence rules contribute to the precise naming of every stereoisomer of every organic molecule with all atoms of ligancy of fewer than 4.

In stereochemistry, stereoisomerism, or spatial isomerism, is a form of isomerism in which molecules have the same molecular formula and sequence of bonded atoms (constitution), but differ in the three-dimensional orientations of their atoms in space. This contrasts with structural isomers, which share the same molecular formula, but the bond connections or their order differs. By definition, molecules that are stereoisomers of each other represent the same structural isomer.

Stereochemistry, a subdiscipline of chemistry, involves the study of the relative spatial arrangement of atoms that form the structure of molecules and their manipulation. The study of stereochemistry focuses on the relationships between stereoisomers, which by definition have the same molecular formula and sequence of bonded atoms (constitution), but differ in structural formula. For this reason, it is also known as 3D chemistry—the prefix "stereo-" means "three-dimensionality".

Optical rotation, also known as polarization rotation or circular birefringence, is the rotation of the orientation of the plane of polarization about the optical axis of linearly polarized light as it travels through certain materials. Circular birefringence and circular dichroism are the manifestations of optical activity. Optical activity occurs only in chiral materials, those lacking microscopic mirror symmetry. Unlike other sources of birefringence which alter a beam's state of polarization, optical activity can be observed in fluids. This can include gases or solutions of chiral molecules such as sugars, molecules with helical secondary structure such as some proteins, and also chiral liquid crystals. It can also be observed in chiral solids such as certain crystals with a rotation between adjacent crystal planes or metamaterials.

In electrodynamics, circular polarization of an electromagnetic wave is a polarization state in which, at each point, the electromagnetic field of the wave has a constant magnitude and is rotating at a constant rate in a plane perpendicular to the direction of the wave.

In chemistry, a racemic mixture, or racemate, is one that has equal amounts of left- and right-handed enantiomers of a chiral molecule or salt. Racemic mixtures are rare in nature, but many compounds are produced industrially as racemates.

Circular dichroism (CD) is dichroism involving circularly polarized light, i.e., the differential absorption of left- and right-handed light. Left-hand circular (LHC) and right-hand circular (RHC) polarized light represent two possible spin angular momentum states for a photon, and so circular dichroism is also referred to as dichroism for spin angular momentum. This phenomenon was discovered by Jean-Baptiste Biot, Augustin Fresnel, and Aimé Cotton in the first half of the 19th century. Circular dichroism and circular birefringence are manifestations of optical activity. It is exhibited in the absorption bands of optically active chiral molecules. CD spectroscopy has a wide range of applications in many different fields. Most notably, UV CD is used to investigate the secondary structure of proteins. UV/Vis CD is used to investigate charge-transfer transitions. Near-infrared CD is used to investigate geometric and electronic structure by probing metal d→d transitions. Vibrational circular dichroism, which uses light from the infrared energy region, is used for structural studies of small organic molecules, and most recently proteins and DNA.

In chemistry, an enantiomer – also called optical isomer, antipode, or optical antipode – is one of two stereoisomers that are non-superposable onto their own mirror image. Enantiomers are much like one's right and left hands, when looking at the same face, they cannot be superposed onto each other. No amount of reorientation in three spatial dimensions will allow the four unique groups on the chiral carbon to line up exactly. The number of stereoisomers a molecule has can be determined by the number of chiral carbons it has. Stereoisomers include both enantiomers and diastereomers.

In stereochemistry, a stereocenter of a molecule is an atom (center), axis or plane that is the focus of stereoisomerism; that is, when having at least three different groups bound to the stereocenter, interchanging any two different groups creates a new stereoisomer. Stereocenters are also referred to as stereogenic centers.

A meso compound or meso isomer is a non-optically active member of a set of stereoisomers, at least two of which are optically active. This means that despite containing two or more stereocenters, the molecule is not chiral. A meso compound is "superposable" on its mirror image. Two objects can be superposed if all aspects of the objects coincide and it does not produce a "(+)" or "(-)" reading when analyzed with a polarimeter. The name is derived from the Greek mésos meaning “middle”.

A metamaterial is any material engineered to have a property that is not found in naturally occurring materials. They are made from assemblies of multiple elements fashioned from composite materials such as metals and plastics. These materials are usually arranged in repeating patterns, at scales that are smaller than the wavelengths of the phenomena they influence. Metamaterials derive their properties not from the properties of the base materials, but from their newly designed structures. Their precise shape, geometry, size, orientation and arrangement gives them their smart properties capable of manipulating electromagnetic waves: by blocking, absorbing, enhancing, or bending waves, to achieve benefits that go beyond what is possible with conventional materials.

In geometry, a figure is chiral if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. An object that is not chiral is said to be achiral.

In chemistry, a molecule or ion is called chiral if it cannot be superposed on its mirror image by any combination of rotations, translations, and some conformational changes. This geometric property is called chirality. The terms are derived from Ancient Greek χείρ (cheir) 'hand'; which is the canonical example of an object with this property.

Planar chirality, also known as 2D chirality, is the special case of chirality for two dimensions.

Homochirality is a uniformity of chirality, or handedness. Objects are chiral when they cannot be superposed on their mirror images. For example, the left and right hands of a human are approximately mirror images of each other but are not their own mirror images, so they are chiral. In biology, 19 of the 20 natural amino acids are homochiral, being L-chiral (left-handed), while sugars are D-chiral (right-handed). Homochirality can also refer to enantiopure substances in which all the constituents are the same enantiomer, but some sources discourage this use of the term.

Negative refraction is the electromagnetic phenomenon where light rays become refracted at an interface that is opposite to their more commonly observed positive refractive properties. Negative refraction can be obtained by using a metamaterial which has been designed to achieve a negative value for (electric) permittivity (ε) and (magnetic) permeability (μ); in such cases the material can be assigned a negative refractive index. Such materials are sometimes called "double negative" materials.

Raman optical activity (ROA) is a vibrational spectroscopic technique that is reliant on the difference in intensity of Raman scattered right and left circularly polarised light due to molecular chirality.

Absolute configuration refers to the spatial arrangement of atoms within a chiral molecular entity and its resultant stereochemical description. Absolute configuration is typically relevant in organic molecules, where carbon is bonded to four different substituents. This type of construction creates two possible enantiomers. Absolute configuration uses a set of rules to describe the relative positions of each bond around the chiral center atom. The most common labeling method uses the descriptors R or S is based on the Cahn–Ingold–Prelog priority rules. R and S refer to Rectus and Sinister, which are Latin for right and left, respectively.

The term chiral describes an object, especially a molecule, which has or produces a non-superposable mirror image of itself. In chemistry, such a molecule is called an enantiomer or is said to exhibit chirality or enantiomerism. The term "chiral" comes from the Greek word for the human hand, which itself exhibits such non-superimposeability of the left hand precisely over the right. Due to the opposition of the fingers and thumbs, no matter how the two hands are oriented, it is impossible for both hands to exactly coincide. Helices, chiral characteristics (properties), chiral media, order, and symmetry all relate to the concept of left- and right-handedness.

Mirror life is a hypothetical form of life with mirror-reflected molecular building blocks. The possibility of mirror life was first discussed by Louis Pasteur. Although this alternative life form has not been discovered in nature, efforts to build a mirror-image version of biology's molecular machinery are already underway.

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