Chirality (chemistry)From Wikipedia, the free encyclopedia"L-form" redirects here. For the bacterial strains, seeL-form bacteria.

Two enantiomers of a genericamino acid

(S)-Alanine (left) and (R)-alanine (right) in zwitterionic form at neutral pHAchiral molecule/karl/is a type ofmoleculethat has a non-superposablemirror image. The presence of anasymmetric carbon atomis often the feature that causeschiralityin molecules.[1][2][3][4]Achiralobjects, such as atoms, are symmetrical, identical to their mirror image.Humanhandsare perhaps the most universally recognized example of chirality: the left hand is a non-superposable 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. This difference in symmetry becomes obvious if a left-handed glove is placed on a right hand. The termchiralityis derived from the Greek word for hand, (kheir). It is a mathematical approach to the concept of "handedness".In chemistry, chirality usually refers to molecules. Two mirror images of a chiral molecule are calledenantiomersor opticalisomers. Pairs of enantiomers are often designated as "right-" and "left-handed".Molecular chirality is of interest because of its application tostereochemistryininorganic chemistry,organic chemistry,physical chemistry,biochemistry, andsupramolecular chemistry.Contents[hide] 1History 2Symmetry 3Naming conventions 3.1By configuration:R- andS- 3.2By optical activity: (+)- and ()- ord-andl- 3.3By configuration:D- andL- 4Nomenclature 5Stereogenic centers 5.1The identity of the stereogenic atom 6Properties of enantiomers 7In biology 7.1D-Amino Acid Natural Abundance 8Inorganic chemistry 9Chirality of compounds with a stereogenic "lone pair" 10See also 11References 12External linksHistory[edit]The termoptical activityis derived from the interaction of chiral materials with polarized light. In solution, the ()-form, orlevorotaryform, of an optical isomerrotatesthe plane of a beam ofpolarized lightcounterclockwise. The (+)-form, ordextrorotatoryform, does the opposite. The property was first observed byJean-Baptiste Biotin 1815,[5]and gained considerable importance in the sugar industry, analytical chemistry, and pharmaceuticals.Louis Pasteurdeduced in 1848 that this phenomenon has a molecular basis.[6]Artificial composite materials displaying the analog of optical activity but in themicrowaveregion were introduced byJ.C. Bosein 1898,[7]and gained considerable attention from the mid-1980s.[8]The termchiralityitself was coined byLord Kelvinin 1894.[9]Different enantiomers or diastereomers of a compound were formerly calledoptical isomersdue to their different optical properties.[10]Symmetry[edit]Thesymmetryof a molecule (or any other object) determines whether it is chiral. A molecule isachiral(not chiral) when animproper rotation, that is a combination of arotationand a reflection in a plane, perpendicular to the axis of rotation, results in the same molecule - seechirality (mathematics). Fortetrahedralmolecules, the molecule is chiral if all foursubstituentsare different.A chiral molecule is not necessarily asymmetric (devoid of anysymmetry element), as it can have, for example,rotational symmetry.Naming conventions[edit]By configuration:R- andS-[edit]For chemists, theR / Ssystem is the most important nomenclature system for denoting enantiomers, which does not involve a reference molecule such asglyceraldehyde. It labels each chiral centerRorSaccording to a system by which its substituents are each assigned apriority, according to theCahnIngoldPrelog priority rules(CIP), based on atomic number. If the center is oriented so that the lowest-priority of the four is pointed away from a viewer, the viewer will then see two possibilities: If the priority of the remaining three substituents decreases in clockwise direction, it is labeledR(forRectus, Latin for right), if it decreases in counterclockwise direction, it isS(forSinister, Latin for left).[11]This system labels each chiral center in a molecule (and also has an extension to chiral molecules not involving chiral centers). Thus, it has greater generality than thed/lsystem, and can label, for example, an (R,R) isomer versus an (R,S) diastereomers.TheR / Ssystem has no fixed relation to the (+)/() system. AnRisomer can be either dextrorotatory or levorotatory, depending on its exact substituents.TheR / Ssystem also has no fixed relation to thed/lsystem. For example, the side-chain one ofserinecontains a hydroxyl group, -OH. If a thiol group, -SH, were swapped in for it, thed/llabeling would, by its definition, not be affected by the substitution. But this substitution would invert the molecule'sR / Slabeling, because the CIP priority of CH2OH is lower than that for CO2H but the CIP priority of CH2SH is higher than that for CO2H.For this reason, thed/lsystem remains in common use in certain areas of biochemistry, such as amino acid and carbohydrate chemistry, because it is convenient to have the same chiral label for all of the commonly occurring structures of a given type of structure in higher organisms. In thed/lsystem, they are nearly all consistent - naturally occurring amino acids are alll, while naturally occurring carbohydrates are nearly alld. In theR / Ssystem, they are mostlyS, but there are some common exceptions.By optical activity: (+)- and ()- ord-andl-[edit]An enantiomer can be named by the direction in which it rotates the plane of polarized light. If it rotates the light clockwise (as seen by a viewer towards whom the light is traveling), that enantiomer is labeled (+). Its mirror-image is labeled (). The (+) and () isomers have also been termedd-andl-, respectively (fordextrorotatoryandlevorotatory). Naming withd-andl-is easy to confuse withd- andl- labeling and is therefore strongly discouraged byIUPAC.[12]By configuration:d- andl-[edit]An optical isomer can be named by the spatial configuration of its atoms. Thed/lsystem, not to be confused with thed-andl-system,see above, does this by relating the molecule toglyceraldehyde. Glyceraldehyde is chiral itself, and its two isomers are labeleddandl(typically typeset insmall capsin published work). Certain chemical manipulations can be performed on glyceraldehyde without affecting its configuration, and its historical use for this purpose (possibly combined with its convenience as one of the smallest commonly used chiral molecules) has resulted in its use for nomenclature. In this system, compounds are named by analogy to glyceraldehyde, which, in general, produces unambiguous designations, but is easiest to see in the small biomolecules similar to glyceraldehyde. One example is the amino acidalanine, which has two optical isomers, and they are labeled according to which isomer of glyceraldehyde they come from. On the other hand,glycine, the amino acid derived from glyceraldehyde, has no optical activity, as it is not chiral (achiral). Alanine, however, is chiral.Thed/llabeling is unrelated to (+)/(); it does not indicate which enantiomer is dextrorotatory and which is levorotatory. Rather, it says that the compound's stereochemistry is related to that of thedextrorotatoryorlevorotatoryenantiomer of glyceraldehydethe dextrorotatory isomer of glyceraldehyde is, in fact, thed-isomer. Nine of the nineteenl-amino acids commonly found in proteins are dextrorotatory (at a wavelength of 589nm), andd-fructose is also referred to as levulose because it is levorotatory.A rule of thumb for determining thed/lisomeric form of an amino acid is the "CORN" rule. The groups:COOH,R,NH2and H (where R is the side-chain)are arranged around the chiral center carbon atom. With the hydrogen atom away from the viewer, if the arrangement of theCORNgroups around the carbon atom is center is clockwise, then it is thedform.[13]If the arrangement is counter-clockwise, it is thelform. Thelform is the usual one found in natural proteins. For most amino acids, thelform corresponds to anSabsolute stereochemistry, but isRinstead for certain side-chains.Nomenclature[edit] Any non-racemicchiral substance is calledscalemic.[14] A chiral substance isenantiopureorhomochiralwhen only one of two possible enantiomers is present. A chiral substance isenantioenrichedorheterochiralwhen an excess of one enantiomer is present but not to the exclusion of the other. Enantiomeric excessoreeis a measure for how much of one enantiomer is present compared to the other. For example, in a sample with 40% ee inR, the remaining 60% is racemic with 30% ofRand 30% ofS, so that the total amount ofRis 70%.Stereogenic centers[edit]Main article:Stereogenic centerIn general, chiral molecules havepoint chiralityat a singlestereogenicatom, which has four different substituents. The two enantiomers of such compounds are said to have differentabsolute configurationsat this center. This center is thus stereogenic (i.e., a grouping within a molecular entity that may be considered a focus of stereoisomerism).Normally when an atom has four different substituents, it is chiral. However in rare cases, two of the ligands differ from each other by being mirror images of each other. When this happens, the mirror image of the molecule is identical to the original, and the molecule is achiral. This is calledpseudochirality.A molecule can have multiple stereogenic centers without being chiral overall if there is a symmetry between the two (or more) stereocenters themselves. Such a molecule is called ameso compound.It is also possible for a molecule to be chiral without having actual point chirality. Common examples include1,1'-bi-2-naphthol(BINOL), 1,3-dichloro-allene, andBINAP, which haveaxial chirality, (E)-cyclooctene, which hasplanar chirality, and certaincalixarenesandfullerenes, which haveinherent chirality.A form of point chirality can also occur if a molecule contains a tetrahedral subunit which cannot easily rearrange, for instance 1-bromo-1-chloro-1-fluoroadamantaneand methylethylphenyltetrahedrane.It is important to keep in mind that molecules have considerable flexibility and thus, depending on the medium, may adopt a variety of different conformations. These various conformations are themselves almost always chiral. When assessing chirality, a time-averaged structure is considered and for routine compounds, one should refer to the most symmetric possible conformation.When the opticalrotationfor an enantiomer is too low for practical measurement, it is said to exhibitcryptochirality.Even isotopic differences must be considered when examining chirality. Replacing one of the two1H atoms at the CH2position ofbenzyl alcoholwith adeuterium(2H) makes that carbon a stereocenter. The resulting benzyl--dalcohol exists as two distinct enantiomers, which can be assigned by the usual stereochemical naming conventions. TheSenantiomer has []D= +0.715.[15]The identity of the stereogenic atom[edit]The stereogenic atom in chiral molecules is usually carbon, as in many biological molecules. However, it may also be a metal atom (as in many chiralcoordination compounds), nitrogen, phosphorus, or sulfur.The chiral atomCarbonNitrogenPhosphorus (phosphates)Phosphorus (phosphines)SulfurMetal (type of metal)

1 stereogenic centerSerine,glyceraldehydeSarin,VXEsomeprazole,armodafinilTris(bipyridine)ruthenium(II)(ruthenium),cis-Dichlorobis(ethylenediamine)cobalt(III)(cobalt),hexol(cobalt)

2 stereogenic centersThreonine,isoleucineTrger's baseAdenosine triphosphateDIPAMPDithionous acid

3 or more stereogenic centersMet-enkephalin,leu-enkephalinDNA

Properties of enantiomers[edit]Normally, the two enantiomers of a molecule behave identically to each other. For example, they will migrate with identical Rfinthin layer chromatographyand have identical retention time inHPLC. TheirNMRandIRspectra are identical. However, enantiomers behave differently in the presence of other chiral molecules or objects. For example, enantiomers do not migrate identically on chiral chromatographic media, such asquartzor standard media that have been chirally modified. The NMR spectra of enantiomers are affected differently by single-enantiomer chiral additives such asEuFOD.Chiral compounds rotate plane polarized light. Each enantiomer will rotate the light in a different sense, clockwise or counterclockwise. Molecules that do this are said to beoptically active.Characteristically, different enantiomers of chiral compounds often taste and smell differently and have different effects as drugs see below. These effects reflect the chirality inherent in biological systems.One chiral 'object' that interacts differently with the two enantiomers of a chiral compound is circularly polarised light: An enantiomer will absorb left- and right-circularly polarised light to differing degrees. This is the basis ofcircular dichroism(CD) spectroscopy. Usually the difference in absorptivity is relatively small (parts per thousand).CD spectroscopy[16]is a powerful analytical technique for investigating the secondary structure of proteins and for determining the absolute configurations of chiral compounds, in particular, transition metal complexes. CD spectroscopy is replacingpolarimetryas a method for characterising chiral compounds, although the latter is still popular with sugar chemists.In biology[edit]Many biologically active molecules are chiral, including the naturally occurringamino acids(the building blocks ofproteins) andsugars. In biological systems, most of these compounds are of the same chirality: most amino acids areland sugars ared. Typical naturally occurring proteins, made oflamino acids, are known asleft-handed proteins, whereasdamino acids produceright-handed proteins.The origin of thishomochiralityinbiologyis the subject of much debate.[17]Most scientists believe that Earth life's "choice" of chirality was purely random, and that if carbon-based life forms exist elsewhere in the universe, their chemistry could theoretically have opposite chirality. However, there is some suggestion that early amino acids could have formed in comet dust. In this case, circularly polarised radiation (which makes up 17% of stellar radiation) could have caused the selective destruction of one chirality of amino acids, leading to a selection bias which ultimately resulted in all life on Earth being homochiral.[18]Enzymes, which are chiral, often distinguish between the two enantiomers of a chiral substrate. Imagine an enzyme as having a glove-like cavity that binds a substrate. If this glove is right-handed, then one enantiomer will fit inside and be bound, whereas the other enantiomer will have a poor fit and is unlikely to bind.d-form amino acids tend to taste sweet, whereasl-forms are usually tasteless.[19]Spearmintleaves andcarawayseeds, respectively, containR-()-carvoneandS-(+)-carvone - enantiomers of carvone.[20]These smell different to most people because our olfactoryreceptorsalso contain chiral molecules that behave differently in the presence of different enantiomers.Chirality is important in context of ordered phases as well, for example the addition of a small amount of an optically active molecule to a nematic phase (a phase that has long range orientational order of molecules) transforms that phase to a chiral nematic phase (or cholesteric phase). Chirality in context of such phases in polymeric fluids has also been studied in this context.[21]d-Amino Acid Natural Abundance[edit]The relative abundances of each of the differentd-isomers of several amino acids have recently been quantified by collecting experimentally reported data from the proteome across all organisms in the Swiss-Prot database. Thed-isomers observed experimentally were found to occur very rarely as shown in the following table in the database of protein sequences containing over 187 million amino acids.[22]d-amino acid# of Times Experimentally Observed

d-alanine664

d-serine114

d-methionine19

d-phenylalanine15

d-valine8

d-tryptophan7

d-leucine6

d-asparagine2

d-threonine2

However, thed-isomers are not uncommon as free amino acids. Humans have special enzymes to process then,d-amino acid oxidaseandd-aspartate oxidase.d-glutamic acid,d-glutamin, andd-alanine are also extremely common at a part of thepeptidoglycanlayer in the bacterial cell wall. In addition,d-serine is a neurotransmitter, and produced in humans byserine racemase.Inorganic chemistry[edit]

Delta-ruthenium-tris(bipyridine) cationMain article:Complex (chemistry): IsomerismManycoordination compoundsare chiral. At one time, chirality was only associated with organic chemistry, but this misconception was overthrown by the resolution of a purely inorganic compound,hexol, byAlfred Werner. A famous example istris(bipyridine)ruthenium(II)complex in which the three bipyridine ligands adopt a chiral propeller-like arrangement.[23]In this case, theRuatom is the stereogenic center. The two enantiomers of complexes such as [Ru(2,2-bipyridine)3]2+may be designated as (capitallambda, the Greek version of "L") for a left-handed twist of the propeller described by the ligands, and (capitaldelta, Greek "D") for a right-handed twist pictured.Chirality of compounds with a stereogenic "lone pair"[edit]When a nonbonding pair of electrons, a lone pair, occupies space, chirality can result. The effect is pervasive in certainamines,phosphines,[24]sulfoniumandoxoniumions,sulfoxides, and evencarbanions. The main requirement is that aside from the lone pair, the other three substituents differ mutually. Chiral phosphine ligands are useful inasymmetric synthesis.

Geometric inversion among the lone pair and three bonded groups on a tetrahedral amineChiralaminesare special in the sense that the enantiomers can rarely be separated. The energy barrier fornitrogen inversionof the stereocenter is generally only about 30kJ/mol, which means that the two stereoisomers rapidly interconvert at room temperature. As a result, such chiral amines cannot be resolved into individual enantiomers unless some of the substituents are constrained in cyclic structures as inTrger's base.

See also[edit] Stereochemistryfor overview of stereochemistry in general Supramolecular chirality Chirality (physics) Chirality (mathematics) Pfeiffer Effect Chemical chirality in popular fiction BROWSE >HOME/ALPHABETICAL SEARCH/C-D/ CHIRAL MOLECULE Print This Page Chiral Molecule A chiral molecule is a molecule that is not superimposable on its mirror image. eg. 1: Molecule1is not superimposable on its mirror image and, therefore, is chiral. eg. 2: Molecule2is not superimposable on its mirror image and, therefore, is chiral. An achiral molecule is a molecule that is superimposable on its mirror image. eg.1: Molecule3is superimposable on its mirror image and, therefore, is achiral. eg. 2: Molecule4is superimposable on its mirror image and, therefore, is achiral. Alternatively, an achiral molecule is a molecule that has at least one plane of symmetry. eg. 1: The vertical plane that bisects the bromine atom and the methyl group, which is the plane of the screen, is a plane of symmetry. Thus,3is achiral. eg. 2: The vertical plane that bisects the molecule perpendicular to the plane of the screen is a plane of symmetry. Thus,4is achiral. A chiral molecule has no plane of symmetry. eg. 1 1is chiral and has no plane of symmetry. eg. 2: 2is chiral and has no plane of symmetry. Although relatively rare, molecules do exist that have no plane of symmetry but is achiral. eg: Thus, presence of a plane of symmetry is not a foolproof method to determine whether a molecule is chiral or achiral. Discussion:Chiralobjects are not superposable with their mirror images. An excellent example of this is your hands. Hold your hands out in front of you, with the palms facing together. Neglecting unnatural additions such as jewelry, note that your hands are mirror images. Now turn your hands so that both palms face the same direction. Note that the thumbs now point in opposite directions. When the thumbs point in the same direction, the palms are opposite. Your hands are mirror images, but not superposable. Each hand is therefore chiral. Achiralobjects may be superposed on their mirror image. Examine two sheets of blank paper in the same way as you experimented with your hands. Notice the sheets of paper are mirror images, but superposable. The sheets of paper are therefore achiral. All objects can be classified as chiral or achiral, including molecules. If our hands were molecules, they would be a pair ofenantiomers. We know from basic biology that interaction of molecules, such as the docking of a substrate to an enzyme, is vital to living organisms. Because enzymes and their substrates may be chiral, it is useful to understand how achiral and chiral molecules can interact. (enzymes are constructed from a group of about 20 small molecules called amino acids. All amino acids except one are chiral, so the enzymes they make are chiral as well.) The way a hand slips into a glove provides a useful way to model this effect. The glove is the enzyme, and the hand is the substrate that must fit properly into the enzyme pocket for the enzyme to be able to act upon the substrate. (Verify that a pair of gloves are chiral in the same way you explored the chirality of your hands.) Your right hand fits nicely into the right handed glove, but does not fit well into the left-handed glove. Likewise, your left hand fits well into the left-handed glove, but the right hand does not. Imagine the glove represents an enzyme and your hand the substrate. The left-handed enzyme/glove would accept the left-handed substrate/hand readily, and would be able to act upon the substrate. The left-handed enzyme/glove cannot readily accept the right hand/substrate, as so this enzyme cannot readily act upon this substrate. This simple model implies that an enzyme will act on one enantiomer more readily than another. Thus, enantiomers of drugs can have different effects in the body, because they are acted upon differently by enzymes, despite the fact that they have the same set of functional groups. That enantiomers of drugs can have different biological effects has been demonstrated in many instances, but perhaps none so dramatically as the in the case of the drug thalidomide. In the late 1950s, theracemicform of this drug was prescribed as a sedative or hypnotic for pregnant women. Some women who took the drug delivered children with severe birth defects. A substance that causes fetal abnormalities is called a teratogen. Further research revealed that one enantiomer of thalidomide has the desired sedative effects, while the other enantiomer was teratogenic. The enantiomers of thalidomide were acting differently in the body, because they interacted differently with chiral biomolecules such as enzymes. The drug was quickly removed from the market. Chiral molecules are nonsuperposable with their mirror images. This can be tested on paper or with molecular models using the two methods described below. Internal mirror plane. We can look for a plane of symmetry in the molecule. Imagine this plane as a mirror through the middle of the molecule. If one half of the molecule is reflected into the other half, then the molecule is achiral. If no such mirror plane exist, the molecule is usually chiral. (There are symmetry elements other than a mirror plane that may render a molecule achiral, but these are rarely encountered and thus beyond the scope of an introductory organic chemistry course.) Molecular models can be used in the same way. Example 1: Using the method of an internal mirror plane, determine if cyclohexanol is chiral or achiral. Solution 1: To determine if cyclohexanol is chiral using the internal mirror method, draw a mirror plane through the middle of molecule. If there are any unique functional groups or atoms within the molecule, these must lie within the mirror plane, so that one half of the atom or functional group is reflected into the other half. In this case, there is only one alcohol functional group, so it must be contained in the mirror plane. Figure 1 shows that the mirror plane bisects the molecule into two equivalent halves, so cyclohexanol is achiral. Figure 1. Two views of cyclohexanol showing the internal mirror plane. The mirror plane is indicated by the dashed line. Figure 2. Cyclohexanol molecular model. A vertical mirror plane bisects the molecule through the middle of the picture. Superposable models. To determine if a molecule is chiral using the superposability requirement, build a molecular model of the molecule in question, then a build a mirror image of this model. Now try to superpose the models by aligning them so that all the atoms match up. The models may be manipulated in any way, such as rotation around single bonds (changing molecular conformation) or changing perspective, but bonds cannot be broken. If all the atoms can be made to line up, the molecule is achiral. If they cannot be aligned, the molecule is chiral. Example 2: Using the method of superposable molecular models, determine if cyclopentanol and 2-chlorobutane are chiral or achiral. Solution 2: Figure 3.Left: Molecular model of cyclopentanol and its mirror image. Right: A top view showing that these cyclopentanol models can be aligned (superposed), so cyclopentanol is achiral. Figure 4. Left: Molecular model of 2-chlorobutane and its mirror image. Right: The same models stacked. The Cl-C-H portions of the models can be made to superpose, but at the same time the methyl and ethyl groups do not. The 2-chlorobutane models cannot be superposed, so the molecule is chiral. Exercises: Using either method discussed above, determine if the molecules shown below are chiral or achiral. Link to: Definitions: Chiral

A molecule ischiralif it is not superimposable on its mirror image. Mostchiralmolecules can be identified by their lack of aplane of symmetryor acenter of symmetry. Your hand is a chiral object, as it does not have either of these types of symmetry.

The molecule on the left has aplane of symmetrythrough the center carbon. This is amirror plane; in other words, one half of the molecule is a perfect reflection of the other half of the molecule. This molecule isnotchiralbecause of itsmirror plane.

Molecules which areidentical(superimposable) with their mirror image geometries are alwaysoptically inactive(achiral); whereas the non-superimposability of a structure with its mirror image results inchirality(optical activity, see below). A simple, but not always accurate test whether a molecule is achiral or not is the presence of amirror plane(equal to aplane of reflectionorplane of symmetry, symmetry element) in the structure of a molecule. Compounds possessing mirror symmetry are always optically inactive, such as, for example,cis- andtrans-1,4-disubstituted cyclohexane derivatives, or symmetricallycis-1,2-disubstituted cyclohexanes (see also the 3D structures at'Cycloalkanes').

In addition, compounds which posses acenter of inversion(equal to acenter of symmetry, symmetry elementi) are also always achiral (see the above example of -truxillic acid which is ofCisymmetry, but does not have a mirror plane of symmetry).However, there are molecules featuring neither a mirror planenor a center of inversioni, but which are still achiral.Most accurately, all molecules which have an-foldalternating axisof symmetry (equal to animproper rotation axisor arotary-reflection axis, symmetry elementSn) are achiral (and thus superimposable with their mirror images).ASnaxis is composed of two successive transformations, first a rotation through 360/n, followed by a reflection through a plane perpendicular to that axis; neither operation alone (rotation or reflection) is a valid symmetry operation for these molecules, but only the combination of both. Note, that aS1axis is identical to a simple mirror plane, and aS2axis is equivalent to a center of inversioni.

Molecules which do not posses a mirror planeor a center of inversioni, but aS4axis are not very common, the examples given below are 1,3,5,7-tetrabromo-2,4,6,8-tetramethyl-cyclooctane and 2,3,7,8-tetramethyl-spiro[4.4]nonane (bothS4symmetry only). Combinations ofS4axis with other symmetry elements are common, e.g. methane CH4possess threeS4axis along with six mirror planes, fourC3and threeC2axis; in total the over-all symmetry of methane is described by theTdpoint group.

On some rare occasions molecules possessingSnaxis with n > 4 are found, the one example above is provided by [6.5]coronane (low-energy solid-state conformation of point groupS6) which also has the symmetry elementsiandC3.NOTE: In many cases the modern drawings of chemical formulas may erroneously suggest a compound to be of different (i.e. wrong) symmetry than it really is. In all cases, the actually prevailing geometry (very often, but not necessarily the low-energy conformation) of a molecule must be considered when establishing the symmetry of a molecule. Below examples are given, in which chirality results from conformational effects, whereas chemical formulas at first sight suggest planar conformations of molecules (see'Helical Chirality'below). Chemical formulas are very often helpful, but not always accurate. For example, the above formula of [6.5]coronane virtually implies aD3dpoint group (symmetry elementsi, three mirror planes, oneC3, threeC2, and oneS6axis), but the solid-state conformation actually is ofS6symmetry (still achiral) only.

Chiral Compounds-3D Structures

The ultimate criterion forchirality(handedness) of a molecule is the non-superimposability of a structure with its mirror image geometry through pure translation and/or rotation only. Chiral molecules related to each other as mutual mirror images may be separated into twoenantiomers(reflection isomers,mirror images) with identical chemical (stability and reactivity in achiral environments) and physical (scalar) properties (melting and boiling point, spectroscopic data, etc.), except for their specific optical rotation (the optical activity ofenantiomersis of equal absolute magnitude, but of opposite sign).Chirality of molecules may originate from configurational or conformational effects of structures. This differentiation of configurational and conformational stereoisomers is not allways unambiguous, but generally conformational isomers may interconvert in each other through rotations about C-C single bonds only (this will not interconvert configurational isomers). Below, numerous examples for the different origins of chirality of organic compounds are given.The formal maxmimum number ofconfigurational stereoisomers(includingE/Z-isomers for double bonds) of any compound may be calculated from the number ofstereocenters(see'Asymmetric Substituted Atoms'below) and the number ofstereogenic double bonds(double bonds carrying different substitutents at either end,E/Z-isomerism) present in the molecule:Maxmimum number ofconfigurational stereoisomers:Nmax= 2(n+m)wheren= the number ofstereocentersandm= the number ofstereogenic double bonds.This includesE/Z-isomers of alkenes which may be regared as configurational isomers (not interconvertible through rotation about C-C single bonds), and which are not superimposable to each other. These isomers are not related to each other as mirror images, and thus they are in factdiastereomers(see also below'Two or More Asymmetric Substituted Atoms'). For eachstereocenterandstereogenic double bondpresent in a molecule a pair of stereoisomers may be generated (enantiomersordiastereomers).The actual number of differentstereocentermay be smaller than the formal maximum numberNmaxas defined above ifconstitutional symmetryis present in the molecule (see below'Two or More Asymmetric Substituted Atoms'formeso-compounds). Steric strain and geometrical limitations may also reduce the number of possible stereoisomers (e.g. double bonds in small and normal rings may only adoptZ-configuration, or bridged and bicyclic ring systems may require certain rigid linkage geometries and relative configurations of stereocenters - see also below for'Substituted Adamantane Derivatives').On the other hand, this maximum number may be exceeded if hindered rotation about C-C single bonds results in additional stereoisomers (see below'Biphenyls and Binaphthyls').

Chiral Compounds - Asymmetric Substituted Atoms-3D Structures

Any molecule with a singlechirality center(any atom holding a set of ligands in a spatial arrangement which is not superimposable on its mirror image) must bechiral. This is the generalized extension of the traditional concept of the asymmetrically substituted carbon atom (van't Hoff): any tetrahedral carbon atom that is attached to four different entities (atoms or groups, e.g. CR1R2R3R4) acts as a chirality center, and the corresponding compound may be separated intoenantiomers. Thus 2-bromo-butane is chiral (four different substituents -Br, -C2H5, -CH3, and -H at C-2). This rule applies no matter how slight the differences between the four groups are, including isotopic substitution: 1-butanol-1-dis also a chiral compound.

The above defintion is not only restricted to tetrahedral carbon atoms, but to any other type of central atom with an appropriate set of bound groups or ligands. Numerous sulfur derivatives exhibit pyramidal bonding where the non-bonded electron pair located at the sulfur atom acts as a fourth ligand. In many cases these compounds are configurationally sufficiently stable to be separated into enantiomers.

The same would apply to nitrogen derivatives (tertiary amines), but usually these compounds rapidly interconvert through an trigonal planar transition state (pyramidal inversion) and thus prevent separation into enantiomers. Ammonia interconverts 2*1011times per second, and although this process is slower for substituted amines it is still very fast at room temperature. Exceptions are provided by nitrogen atoms in small rings such as aziridines (for which the trigonal planar transition state of inversion builds up strain energy in the ring), or nitrogen bonded to other atoms with non-bonded electron pairs (such as oxygen). Compounds of these types may be resolved into optically pure enantiomers.

Other examples of configurationally stable amines are bicyclic ring systems with nitrogen located at the bridgehead positions. The geometrical restrictions operative in these ring systems may also prevent inversion. As an typical example, Trger's base has been separated into enantiomers (see above).Phosphorous inverts less rapid than nitrogen and arsenic still more slowly. The above rules are not only restricted to tetrahedral centers, but also apply to octahedral and other coordination geometries of appropriate substitution, including metal complexes and inorganic structures.

The above example of a chiral substituted ferrocene may also be classified as beingplanar chiral(see below'Planar Chirality').

Chiral Compounds - Two or More Asymmetric Substituted Atoms-3D Structures

Compunds with two or more asymmetrically substituted atoms (chiral centers) may be optically active. Typical examples are (2S,3S)- and (2R,3R)-2,3-dibromo-butane, or (2S,3S)- and (2R,3R)-tartaric acid (german:Weinsure). However, if pairs of equivalentstereocentersof opposite configuration are present in the molecule, the compounds are optically inactive (achiralmeso-compounds) as both chiral centers neutralize each other (internal compensation). For example, (2S,3R)- and (2R,3S)-2,3-dibromo-butane are identical (meso) as both structures can be superimposed through simple rotations and translations only. The same applies tomeso-tartaric acid.

Stereoisomers of compunds which are not not related as mirror images are calleddiastereoisomers. Structures of this type cannot be interconverted into each other through translation, rotation, and mirror symmetry operations. In contrast toenantiomers,diastereoisomershave different chemical (towards achiral as well as chiral reagents) and physical properties (including totally independent values for their specific optical rotation).trans-1,2-Disubstituted cyclohexanes ofC2symmetry are chiral compounds, whereas symmetricallycis-1,2-disubstituted cyclohexanes are optically inactive as they posses a mirror planeof symmetry. However, the latter type compounds exist inchiral conformationswhich interconvert rapidly into each other throughchair-antichairinversions of the cyclohexane ring (see also the 3D structures at'Achiral Compounds'and the chapter'Ring Pseudorotation'in theMolArch+- Moviessection of this web-site).

Chiral Compounds - Substituted Adamantane Derivatives-3D Structures

Adamantane derivates of suitable substitution may also be chiral compounds. In these structures, not a single atom, but an entire group (the adamantyl residue) holds four substituents (adamantane derivative on the left below) in a spatial arrangement that causes the compound to be non-superimposable with its mirror image geometry. The central adamantyl residue may be regarded as an extended tetrahedron.

This example demonstrates that thestereogenic centerof a moleucle needs not to be located on a specific atom. In this case, the stereogenic center is located in the center of the adamantyl cage. Disubstituted adamantanes (note the different substitution positions and pattern) are also chiral compounds - they do not feature achiral centerbut anaxis of chirality(see below'Axial Chirality').In fact, the above (left) adamantane derivative features fourasymmetric substituted carbon atoms(the four tertiary carbon atoms of adamantane backbone). As derived above, the formal maximum number of stereoisomers (see abvoe'Chiral Compounds') would beNmax= 24= 16. However, in this case only two stereoisomers actually exist, as the steric strain and geometrical limitations of the adamantane resdiue require all substituent to point towards the outside of the molecule (in fact, once the first stereocenter is defined, the remaining three are determined by their relative configuration, and thus the number of observed stereoisomers is 2).Similar limitations on the number of stereoisomers are observed in almost all bi- and polycyclic systems with small rings. Twistanes (even the unsubstituted parent hydrocarbon) are chiral. As another example, camphor yields two stereoisomers only, although it features two stereocenters in position 1 and 4 (but the relative configuration of both centers is constrained in the bicyclic ring system):

Chiral Compounds - Axial Chirality-3D Structures

Some compounds which do not have asymmetrically substituted carbon atoms (or any other atom type) may still be chiral if they feature two perpendicular planes which are not symmetry planes. If thesedisymmetric(chiral) planes cannot freely rotate against each other, the corresponding compounds are chiral. Compounds of this type are said to beaxially chiral(they feture anaxis of chiralityinstead acenter of chirality)Typical examples are allenes in which the central atom issp-hybridized, and the planes containing the substitutents on either end of the double bonds are aligned perpendicular to each other (in contrast to simple olefines where all substituents are contained in a single plane of the-bond; note the difference toE/Z-isomerism of alkenes). For an even number of double bonds in the allene, and if neither side of it is symmetrically substituted, these compounds are optically active and thus chiral.

Very similar arrangements are observed in chiralspiro-annelated ring systems and compounds with exocyclic double-bonds (see examples below).

As demonstrated above, suitably disubstituted adamantane derivatives also show axial chirality (see above'Substituted Adamantane Derivatives').

Chiral Compounds - Biphenyls and Binaphthyls-3D Structures

The same rules as outlined above for the allenes and spiranes apply also to biphenyl- and binaphtyl-derivatives. If both aromatic ring systems are asymmetrically substituted, the compounds are chiral. As the chirality of these structures originates not from an asymmetrically substituted atom center, but from an asymmetric axis around which rotation is hindered, these enantiomers are also calledatropisomers. In the biphenyls, theortho-substitutents must be large enough to prevent rotation around the central single bond; if hydrogen atoms are present in these positions the barrier of rotation may be too small to prevent interconversion of the enantiomeric forms at room temperature and the two structures may not be separated, or may racemize slowly on standing.

Please note, that for the biphenyls and binaphtyls derivatives the formal maximum number of stereoisomers (see above'Chiral Compounds') is exceeded. As these moleucles do neither feature astereocenteror astereogenic double bond, no stereoisomers would be expected. Only the hindered rotation about the central C-C single bond leads to the stereoisomerism of these compounds. Therefore, biphenyl- and binaphtyl-derivatives areconformational stereoisomers(notconfigurational stereoisomers).In particular the enentiomerically pure binaphthyl derivatives are of great use in asymmetric catalysis. For some animations of the dynamic behavior of biphenyls and binaphthyls and the process of racemization see the chapter'Atropsiomers'in theMolArch+- Moviessection of this web-site.

Chiral Compounds - Helical Chirality-3D Structures

Helices are chiral as they can exist in enantiomeric left- or right-handed forms. Typical examples for helical strutures are provided by the helicenes (benzologues of phenanthrene). With four or more rings, steric hinderance at both ends of these molecule prevents the formation of planar conformations, and helicenes rather adopt non-planar, but helical and enantiomeric structures withC2symmetry (see also the 3D structures at'Helicenes'and the chapter'Racemization of [8]Helicene'in theMolArch+- Moviessection of this web-site).

Other examples of chiral helical structures are provided bytrans-cyclooctene and suitably substituted heptalenes. Heptalene is not planar, and its twisted structure results in chirality. Although these conformations generally interconvert rapidly, bulky substituents may sufficiently slow down this process to optically resolve and separate these compounds.

The above example of the chirality of (E)-cyclooctene is also example for'Planar Chirality'(see below).

Chiral Compounds - Planar Chirality-3D Structures

Planar chirality may arise if an appropriately substituted planar group of atoms or ring system is bridged by a linker-chain extending into the space above or below of this plane. Commmon examples are the planar chirality of cyclophanes or alkenes as shown below. Even (E)-cyclooctene is a planar chiral compound (see also above'Helical Chirality'):

The above mentioned suitably substituted ferrocenes are also planar chiral compounds (see'Asymmetric Substituted Atoms').

Chiral Compounds - Other Examples-3D Structures

There are many more examples known for which chirality of molecules results from hindered rotation of groups or spatial arrangements of chemical moieties, a few examples are listed below:

Even catenanes and molecular knots made up from achiral molecules are chiral.

For more informations on other research topics, please refer to the completelist of publicationsand to thegallery of graphics and animations.Molecules which areidentical(superimposable) with their mirror image geometries are alwaysoptically inactive(achiral); whereas the non-superimposability of a structure with its mirror image results inchirality(optical activity, see below). A simple, but not always accurate test whether a molecule is achiral or not is the presence of amirror plane(equal to aplane of reflectionorplane of symmetry, symmetry element) in the structure of a molecule. Compounds possessing mirror symmetry are always optically inactive, such as, for example,cis- andtrans-1,4-disubstituted cyclohexane derivatives, or symmetricallycis-1,2-disubstituted cyclohexanes (see also the 3D structures at'Cycloalkanes').

In addition, compounds which posses acenter of inversion(equal to acenter of symmetry, symmetry elementi) are also always achiral (see the above example of -truxillic acid which is ofCisymmetry, but does not have a mirror plane of symmetry).However, there are molecules featuring neither a mirror planenor a center of inversioni, but which are still achiral.Most accurately, all molecules which have an-foldalternating axisof symmetry (equal to animproper rotation axisor arotary-reflection axis, symmetry elementSn) are achiral (and thus superimposable with their mirror images).ASnaxis is composed of two successive transformations, first a rotation through 360/n, followed by a reflection through a plane perpendicular to that axis; neither operation alone (rotation or reflection) is a valid symmetry operation for these molecules, but only the combination of both. Note, that aS1axis is identical to a simple mirror plane, and aS2axis is equivalent to a center of inversioni.

Molecules which do not posses a mirror planeor a center of inversioni, but aS4axis are not very common, the examples given below are 1,3,5,7-tetrabromo-2,4,6,8-tetramethyl-cyclooctane and 2,3,7,8-tetramethyl-spiro[4.4]nonane (bothS4symmetry only). Combinations ofS4axis with other symmetry elements are common, e.g. methane CH4possess threeS4axis along with six mirror planes, fourC3and threeC2axis; in total the over-all symmetry of methane is described by theTdpoint group.

On some rare occasions molecules possessingSnaxis with n > 4 are found, the one example above is provided by [6.5]coronane (low-energy solid-state conformation of point groupS6) which also has the symmetry elementsiandC3.NOTE: In many cases the modern drawings of chemical formulas may erroneously suggest a compound to be of different (i.e. wrong) symmetry than it really is. In all cases, the actually prevailing geometry (very often, but not necessarily the low-energy conformation) of a molecule must be considered when establishing the symmetry of a molecule. Below examples are given, in which chirality results from conformational effects, whereas chemical formulas at first sight suggest planar conformations of molecules (see'Helical Chirality'below). Chemical formulas are very often helpful, but not always accurate. For example, the above formula of [6.5]coronane virtually implies aD3dpoint group (symmetry elementsi, three mirror planes, oneC3, threeC2, and oneS6axis), but the solid-state conformation actually is ofS6symmetry (still achiral) only.

Chiral Compounds-3D Structures

The ultimate criterion forchirality(handedness) of a molecule is the non-superimposability of a structure with its mirror image geometry through pure translation and/or rotation only. Chiral molecules related to each other as mutual mirror images may be separated into twoenantiomers(reflection isomers,mirror images) with identical chemical (stability and reactivity in achiral environments) and physical (scalar) properties (melting and boiling point, spectroscopic data, etc.), except for their specific optical rotation (the optical activity ofenantiomersis of equal absolute magnitude, but of opposite sign).Chirality of molecules may originate from configurational or conformational effects of structures. This differentiation of configurational and conformational stereoisomers is not allways unambiguous, but generally conformational isomers may interconvert in each other through rotations about C-C single bonds only (this will not interconvert configurational isomers). Below, numerous examples for the different origins of chirality of organic compounds are given.The formal maxmimum number ofconfigurational stereoisomers(includingE/Z-isomers for double bonds) of any compound may be calculated from the number ofstereocenters(see'Asymmetric Substituted Atoms'below) and the number ofstereogenic double bonds(double bonds carrying different substitutents at either end,E/Z-isomerism) present in the molecule:Maxmimum number ofconfigurational stereoisomers:Nmax= 2(n+m)wheren= the number ofstereocentersandm= the number ofstereogenic double bonds.This includesE/Z-isomers of alkenes which may be regared as configurational isomers (not interconvertible through rotation about C-C single bonds), and which are not superimposable to each other. These isomers are not related to each other as mirror images, and thus they are in factdiastereomers(see also below'Two or More Asymmetric Substituted Atoms'). For eachstereocenterandstereogenic double bondpresent in a molecule a pair of stereoisomers may be generated (enantiomersordiastereomers).The actual number of differentstereocentermay be smaller than the formal maximum numberNmaxas defined above ifconstitutional symmetryis present in the molecule (see below'Two or More Asymmetric Substituted Atoms'formeso-compounds). Steric strain and geometrical limitations may also reduce the number of possible stereoisomers (e.g. double bonds in small and normal rings may only adoptZ-configuration, or bridged and bicyclic ring systems may require certain rigid linkage geometries and relative configurations of stereocenters - see also below for'Substituted Adamantane Derivatives').On the other hand, this maximum number may be exceeded if hindered rotation about C-C single bonds results in additional stereoisomers (see below'Biphenyls and Binaphthyls').

Chiral Compounds - Asymmetric Substituted Atoms-3D Structures

Any molecule with a singlechirality center(any atom holding a set of ligands in a spatial arrangement which is not superimposable on its mirror image) must bechiral. This is the generalized extension of the traditional concept of the asymmetrically substituted carbon atom (van't Hoff): any tetrahedral carbon atom that is attached to four different entities (atoms or groups, e.g. CR1R2R3R4) acts as a chirality center, and the corresponding compound may be separated intoenantiomers. Thus 2-bromo-butane is chiral (four different substituents -Br, -C2H5, -CH3, and -H at C-2). This rule applies no matter how slight the differences between the four groups are, including isotopic substitution: 1-butanol-1-dis also a chiral compound.

The above defintion is not only restricted to tetrahedral carbon atoms, but to any other type of central atom with an appropriate set of bound groups or ligands. Numerous sulfur derivatives exhibit pyramidal bonding where the non-bonded electron pair located at the sulfur atom acts as a fourth ligand. In many cases these compounds are configurationally sufficiently stable to be separated into enantiomers.

The same would apply to nitrogen derivatives (tertiary amines), but usually these compounds rapidly interconvert through an trigonal planar transition state (pyramidal inversion) and thus prevent separation into enantiomers. Ammonia interconverts 2*1011times per second, and although this process is slower for substituted amines it is still very fast at room temperature. Exceptions are provided by nitrogen atoms in small rings such as aziridines (for which the trigonal planar transition state of inversion builds up strain energy in the ring), or nitrogen bonded to other atoms with non-bonded electron pairs (such as oxygen). Compounds of these types may be resolved into optically pure enantiomers.

Other examples of configurationally stable amines are bicyclic ring systems with nitrogen located at the bridgehead positions. The geometrical restrictions operative in these ring systems may also prevent inversion. As an typical example, Trger's base has been separated into enantiomers (see above).Phosphorous inverts less rapid than nitrogen and arsenic still more slowly. The above rules are not only restricted to tetrahedral centers, but also apply to octahedral and other coordination geometries of appropriate substitution, including metal complexes and inorganic structures.

The above example of a chiral substituted ferrocene may also be classified as beingplanar chiral(see below'Planar Chirality').

Chiral Compounds - Two or More Asymmetric Substituted Atoms-3D Structures

Compunds with two or more asymmetrically substituted atoms (chiral centers) may be optically active. Typical examples are (2S,3S)- and (2R,3R)-2,3-dibromo-butane, or (2S,3S)- and (2R,3R)-tartaric acid (german:Weinsure). However, if pairs of equivalentstereocentersof opposite configuration are present in the molecule, the compounds are optically inactive (achiralmeso-compounds) as both chiral centers neutralize each other (internal compensation). For example, (2S,3R)- and (2R,3S)-2,3-dibromo-butane are identical (meso) as both structures can be superimposed through simple rotations and translations only. The same applies tomeso-tartaric acid.

Stereoisomers of compunds which are not not related as mirror images are calleddiastereoisomers. Structures of this type cannot be interconverted into each other through translation, rotation, and mirror symmetry operations. In contrast toenantiomers,diastereoisomershave different chemical (towards achiral as well as chiral reagents) and physical properties (including totally independent values for their specific optical rotation).trans-1,2-Disubstituted cyclohexanes ofC2symmetry are chiral compounds, whereas symmetricallycis-1,2-disubstituted cyclohexanes are optically inactive as they posses a mirror planeof symmetry. However, the latter type compounds exist inchiral conformationswhich interconvert rapidly into each other throughchair-antichairinversions of the cyclohexane ring (see also the 3D structures at'Achiral Compounds'and the chapter'Ring Pseudorotation'in theMolArch+- Moviessection of this web-site).

Chiral Compounds - Substituted Adamantane Derivatives-3D Structures

Adamantane derivates of suitable substitution may also be chiral compounds. In these structures, not a single atom, but an entire group (the adamantyl residue) holds four substituents (adamantane derivative on the left below) in a spatial arrangement that causes the compound to be non-superimposable with its mirror image geometry. The central adamantyl residue may be regarded as an extended tetrahedron.

This example demonstrates that thestereogenic centerof a moleucle needs not to be located on a specific atom. In this case, the stereogenic center is located in the center of the adamantyl cage. Disubstituted adamantanes (note the different substitution positions and pattern) are also chiral compounds - they do not feature achiral centerbut anaxis of chirality(see below'Axial Chirality').In fact, the above (left) adamantane derivative features fourasymmetric substituted carbon atoms(the four tertiary carbon atoms of adamantane backbone). As derived above, the formal maximum number of stereoisomers (see abvoe'Chiral Compounds') would beNmax= 24= 16. However, in this case only two stereoisomers actually exist, as the steric strain and geometrical limitations of the adamantane resdiue require all substituent to point towards the outside of the molecule (in fact, once the first stereocenter is defined, the remaining three are determined by their relative configuration, and thus the number of observed stereoisomers is 2).Similar limitations on the number of stereoisomers are observed in almost all bi- and polycyclic systems with small rings. Twistanes (even the unsubstituted parent hydrocarbon) are chiral. As another example, camphor yields two stereoisomers only, although it features two stereocenters in position 1 and 4 (but the relative configuration of both centers is constrained in the bicyclic ring system):

Chiral Compounds - Axial Chirality-3D Structures

Some compounds which do not have asymmetrically substituted carbon atoms (or any other atom type) may still be chiral if they feature two perpendicular planes which are not symmetry planes. If thesedisymmetric(chiral) planes cannot freely rotate against each other, the corresponding compounds are chiral. Compounds of this type are said to beaxially chiral(they feture anaxis of chiralityinstead acenter of chirality)Typical examples are allenes in which the central atom issp-hybridized, and the planes containing the substitutents on either end of the double bonds are aligned perpendicular to each other (in contrast to simple olefines where all substituents are contained in a single plane of the-bond; note the difference toE/Z-isomerism of alkenes). For an even number of double bonds in the allene, and if neither side of it is symmetrically substituted, these compounds are optically active and thus chiral.

Very similar arrangements are observed in chiralspiro-annelated ring systems and compounds with exocyclic double-bonds (see examples below).

As demonstrated above, suitably disubstituted adamantane derivatives also show axial chirality (see above'Substituted Adamantane Derivatives').

Chiral Compounds - Biphenyls and Binaphthyls-3D Structures

The same rules as outlined above for the allenes and spiranes apply also to biphenyl- and binaphtyl-derivatives. If both aromatic ring systems are asymmetrically substituted, the compounds are chiral. As the chirality of these structures originates not from an asymmetrically substituted atom center, but from an asymmetric axis around which rotation is hindered, these enantiomers are also calledatropisomers. In the biphenyls, theortho-substitutents must be large enough to prevent rotation around the central single bond; if hydrogen atoms are present in these positions the barrier of rotation may be too small to prevent interconversion of the enantiomeric forms at room temperature and the two structures may not be separated, or may racemize slowly on standing.

Please note, that for the biphenyls and binaphtyls derivatives the formal maximum number of stereoisomers (see above'Chiral Compounds') is exceeded. As these moleucles do neither feature astereocenteror astereogenic double bond, no stereoisomers would be expected. Only the hindered rotation about the central C-C single bond leads to the stereoisomerism of these compounds. Therefore, biphenyl- and binaphtyl-derivatives areconformational stereoisomers(notconfigurational stereoisomers).In particular the enentiomerically pure binaphthyl derivatives are of great use in asymmetric catalysis. For some animations of the dynamic behavior of biphenyls and binaphthyls and the process of racemization see the chapter'Atropsiomers'in theMolArch+- Moviessection of this web-site.

Chiral Compounds - Helical Chirality-3D Structures

Helices are chiral as they can exist in enantiomeric left- or right-handed forms. Typical examples for helical strutures are provided by the helicenes (benzologues of phenanthrene). With four or more rings, steric hinderance at both ends of these molecule prevents the formation of planar conformations, and helicenes rather adopt non-planar, but helical and enantiomeric structures withC2symmetry (see also the 3D structures at'Helicenes'and the chapter'Racemization of [8]Helicene'in theMolArch+- Moviessection of this web-site).

Other examples of chiral helical structures are provided bytrans-cyclooctene and suitably substituted heptalenes. Heptalene is not planar, and its twisted structure results in chirality. Although these conformations generally interconvert rapidly, bulky substituents may sufficiently slow down this process to optically resolve and separate these compounds.

The above example of the chirality of (E)-cyclooctene is also example for'Planar Chirality'(see below).

Chiral Compounds - Planar Chirality-3D Structures

Planar chirality may arise if an appropriately substituted planar group of atoms or ring system is bridged by a linker-chain extending into the space above or below of this plane. Commmon examples are the planar chirality of cyclophanes or alkenes as shown below. Even (E)-cyclooctene is a planar chiral compound (see also above'Helical Chirality'):

The above mentioned suitably substituted ferrocenes are also planar chiral compounds (see'Asymmetric Substituted Atoms').

Chiral Compounds - Other Examples-3D Structures

There are many more examples known for which chirality of molecules results from hindered rotation of groups or spatial arrangements of chemical moieties, a few examples are listed below:

Even catenanes and molecular knots made up from achiral molecules are chiral.

For more informations on other research topics, please refer to the completelist of publicationsand to thegallery of graphics and animations.Molecules which areidentical(superimposable) with their mirror image geometries are alwaysoptically inactive(achiral); whereas the non-superimposability of a structure with its mirror image results inchirality(optical activity, see below). A simple, but not always accurate test whether a molecule is achiral or not is the presence of amirror plane(equal to aplane of reflectionorplane of symmetry, symmetry element) in the structure of a molecule. Compounds possessing mirror symmetry are always optically inactive, such as, for example,cis- andtrans-1,4-disubstituted cyclohexane derivatives, or symmetricallycis-1,2-disubstituted cyclohexanes (see also the 3D structures at'Cycloalkanes').

In addition, compounds which posses acenter of inversion(equal to acenter of symmetry, symmetry elementi) are also always achiral (see the above example of -truxillic acid which is ofCisymmetry, but does not have a mirror plane of symmetry).However, there are molecules featuring neither a mirror planenor a center of inversioni, but which are still achiral.Most accurately, all molecules which have an-foldalternating axisof symmetry (equal to animproper rotation axisor arotary-reflection axis, symmetry elementSn) are achiral (and thus superimposable with their mirror images).ASnaxis is composed of two successive transformations, first a rotation through 360/n, followed by a reflection through a plane perpendicular to that axis; neither operation alone (rotation or reflection) is a valid symmetry operation for these molecules, but only the combination of both. Note, that aS1axis is identical to a simple mirror plane, and aS2axis is equivalent to a center of inversioni.

Molecules which do not posses a mirror planeor a center of inversioni, but aS4axis are not very common, the examples given below are 1,3,5,7-tetrabromo-2,4,6,8-tetramethyl-cyclooctane and 2,3,7,8-tetramethyl-spiro[4.4]nonane (bothS4symmetry only). Combinations ofS4axis with other symmetry elements are common, e.g. methane CH4possess threeS4axis along with six mirror planes, fourC3and threeC2axis; in total the over-all symmetry of methane is described by theTdpoint group.

On some rare occasions molecules possessingSnaxis with n > 4 are found, the one example above is provided by [6.5]coronane (low-energy solid-state conformation of point groupS6) which also has the symmetry elementsiandC3.NOTE: In many cases the modern drawings of chemical formulas may erroneously suggest a compound to be of different (i.e. wrong) symmetry than it really is. In all cases, the actually prevailing geometry (very often, but not necessarily the low-energy conformation) of a molecule must be considered when establishing the symmetry of a molecule. Below examples are given, in which chirality results from conformational effects, whereas chemical formulas at first sight suggest planar conformations of molecules (see'Helical Chirality'below). Chemical formulas are very often helpful, but not always accurate. For example, the above formula of [6.5]coronane virtually implies aD3dpoint group (symmetry elementsi, three mirror planes, oneC3, threeC2, and oneS6axis), but the solid-state conformation actually is ofS6symmetry (still achiral) only.

Chiral Compounds-3D Structures

The ultimate criterion forchirality(handedness) of a molecule is the non-superimposability of a structure with its mirror image geometry through pure translation and/or rotation only. Chiral molecules related to each other as mutual mirror images may be separated into twoenantiomers(reflection isomers,mirror images) with identical chemical (stability and reactivity in achiral environments) and physical (scalar) properties (melting and boiling point, spectroscopic data, etc.), except for their specific optical rotation (the optical activity ofenantiomersis of equal absolute magnitude, but of opposite sign).Chirality of molecules may originate from configurational or conformational effects of structures. This differentiation of configurational and conformational stereoisomers is not allways unambiguous, but generally conformational isomers may interconvert in each other through rotations about C-C single bonds only (this will not interconvert configurational isomers). Below, numerous examples for the different origins of chirality of organic compounds are given.The formal maxmimum number ofconfigurational stereoisomers(includingE/Z-isomers for double bonds) of any compound may be calculated from the number ofstereocenters(see'Asymmetric Substituted Atoms'below) and the number ofstereogenic double bonds(double bonds carrying different substitutents at either end,E/Z-isomerism) present in the molecule:Maxmimum number ofconfigurational stereoisomers:Nmax= 2(n+m)wheren= the number ofstereocentersandm= the number ofstereogenic double bonds.This includesE/Z-isomers of alkenes which may be regared as configurational isomers (not interconvertible through rotation about C-C single bonds), and which are not superimposable to each other. These isomers are not related to each other as mirror images, and thus they are in factdiastereomers(see also below'Two or More Asymmetric Substituted Atoms'). For eachstereocenterandstereogenic double bondpresent in a molecule a pair of stereoisomers may be generated (enantiomersordiastereomers).The actual number of differentstereocentermay be smaller than the formal maximum numberNmaxas defined above ifconstitutional symmetryis present in the molecule (see below'Two or More Asymmetric Substituted Atoms'formeso-compounds). Steric strain and geometrical limitations may also reduce the number of possible stereoisomers (e.g. double bonds in small and normal rings may only adoptZ-configuration, or bridged and bicyclic ring systems may require certain rigid linkage geometries and relative configurations of stereocenters - see also below for'Substituted Adamantane Derivatives').On the other hand, this maximum number may be exceeded if hindered rotation about C-C single bonds results in additional stereoisomers (see below'Biphenyls and Binaphthyls').

Chiral Compounds - Asymmetric Substituted Atoms-3D Structures

Any molecule with a singlechirality center(any atom holding a set of ligands in a spatial arrangement which is not superimposable on its mirror image) must bechiral. This is the generalized extension of the traditional concept of the asymmetrically substituted carbon atom (van't Hoff): any tetrahedral carbon atom that is attached to four different entities (atoms or groups, e.g. CR1R2R3R4) acts as a chirality center, and the corresponding compound may be separated intoenantiomers. Thus 2-bromo-butane is chiral (four different substituents -Br, -C2H5, -CH3, and -H at C-2). This rule applies no matter how slight the differences between the four groups are, including isotopic substitution: 1-butanol-1-dis also a chiral compound.

The above defintion is not only restricted to tetrahedral carbon atoms, but to any other type of central atom with an appropriate set of bound groups or ligands. Numerous sulfur derivatives exhibit pyramidal bonding where the non-bonded electron pair located at the sulfur atom acts as a fourth ligand. In many cases these compounds are configurationally sufficiently stable to be separated into enantiomers.

The same would apply to nitrogen derivatives (tertiary amines), but usually these compounds rapidly interconvert through an trigonal planar transition state (pyramidal inversion) and thus prevent separation into enantiomers. Ammonia interconverts 2*1011times per second, and although this process is slower for substituted amines it is still very fast at room temperature. Exceptions are provided by nitrogen atoms in small rings such as aziridines (for which the trigonal planar transition state of inversion builds up strain energy in the ring), or nitrogen bonded to other atoms with non-bonded electron pairs (such as oxygen). Compounds of these types may be resolved into optically pure enantiomers.

Other examples of configurationally stable amines are bicyclic ring systems with nitrogen located at the bridgehead positions. The geometrical restrictions operative in these ring systems may also prevent inversion. As an typical example, Trger's base has been separated into enantiomers (see above).Phosphorous inverts less rapid than nitrogen and arsenic still more slowly. The above rules are not only restricted to tetrahedral centers, but also apply to octahedral and other coordination geometries of appropriate substitution, including metal complexes and inorganic structures.

The above example of a chiral substituted ferrocene may also be classified as beingplanar chiral(see below'Planar Chirality').

Chiral Compounds - Two or More Asymmetric Substituted Atoms-3D Structures

Compunds with two or more asymmetrically substituted atoms (chiral centers) may be optically active. Typical examples are (2S,3S)- and (2R,3R)-2,3-dibromo-butane, or (2S,3S)- and (2R,3R)-tartaric acid (german:Weinsure). However, if pairs of equivalentstereocentersof opposite configuration are present in the molecule, the compounds are optically inactive (achiralmeso-compounds) as both chiral centers neutralize each other (internal compensation). For example, (2S,3R)- and (2R,3S)-2,3-dibromo-butane are identical (meso) as both structures can be superimposed through simple rotations and translations only. The same applies tomeso-tartaric acid.

Stereoisomers of compunds which are not not related as mirror images are calleddiastereoisomers. Structures of this type cannot be interconverted into each other through translation, rotation, and mirror symmetry operations. In contrast toenantiomers,diastereoisomershave different chemical (towards achiral as well as chiral reagents) and physical properties (including totally independent values for their specific optical rotation).trans-1,2-Disubstituted cyclohexanes ofC2symmetry are chiral compounds, whereas symmetricallycis-1,2-disubstituted cyclohexanes are optically inactive as they posses a mirror planeof symmetry. However, the latter type compounds exist inchiral conformationswhich interconvert rapidly into each other throughchair-antichairinversions of the cyclohexane ring (see also the 3D structures at'Achiral Compounds'and the chapter'Ring Pseudorotation'in theMolArch+- Moviessection of this web-site).

Chiral Compounds - Substituted Adamantane Derivatives-3D Structures

Adamantane derivates of suitable substitution may also be chiral compounds. In these structures, not a single atom, but an entire group (the adamantyl residue) holds four substituents (adamantane derivative on the left below) in a spatial arrangement that causes the compound to be non-superimposable with its mirror image geometry. The central adamantyl residue may be regarded as an extended tetrahedron.

This example demonstrates that thestereogenic centerof a moleucle needs not to be located on a specific atom. In this case, the stereogenic center is located in the center of the adamantyl cage. Disubstituted adamantanes (note the different substitution positions and pattern) are also chiral compounds - they do not feature achiral centerbut anaxis of chirality(see below'Axial Chirality').In fact, the above (left) adamantane derivative features fourasymmetric substituted carbon atoms(the four tertiary carbon atoms of adamantane backbone). As derived above, the formal maximum number of stereoisomers (see abvoe'Chiral Compounds') would beNmax= 24= 16. However, in this case only two stereoisomers actually exist, as the steric strain and geometrical limitations of the adamantane resdiue require all substituent to point towards the outside of the molecule (in fact, once the first stereocenter is defined, the remaining three are determined by their relative configuration, and thus the number of observed stereoisomers is 2).Similar limitations on the number of stereoisomers are observed in almost all bi- and polycyclic systems with small rings. Twistanes (even the unsubstituted parent hydrocarbon) are chiral. As another example, camphor yields two stereoisomers only, although it features two stereocenters in position 1 and 4 (but the relative configuration of both centers is constrained in the bicyclic ring system):

Chiral Compounds - Axial Chirality-3D Structures

Some compounds which do not have asymmetrically substituted carbon atoms (or any other atom type) may still be chiral if they feature two perpendicular planes which are not symmetry planes. If thesedisymmetric(chiral) planes cannot freely rotate against each other, the corresponding compounds are chiral. Compounds of this type are said to beaxially chiral(they feture anaxis of chiralityinstead acenter of chirality)Typical examples are allenes in which the central atom issp-hybridized, and the planes containing the substitutents on either end of the double bonds are aligned perpendicular to each other (in contrast to simple olefines where all substituents are contained in a single plane of the-bond; note the difference toE/Z-isomerism of alkenes). For an even number of double bonds in the allene, and if neither side of it is symmetrically substituted, these compounds are optically active and thus chiral.

Very similar arrangements are observed in chiralspiro-annelated ring systems and compounds with exocyclic double-bonds (see examples below).

As demonstrated above, suitably disubstituted adamantane derivatives also show axial chirality (see above'Substituted Adamantane Derivatives').

Chiral Compounds - Biphenyls and Binaphthyls-3D Structures

The same rules as outlined above for the allenes and spiranes apply also to biphenyl- and binaphtyl-derivatives. If both aromatic ring systems are asymmetrically substituted, the compounds are chiral. As the chirality of these structures originates not from an asymmetrically substituted atom center, but from an asymmetric axis around which rotation is hindered, these enantiomers are also calledatropisomers. In the biphenyls, theortho-substitutents must be large enough to prevent rotation around the central single bond; if hydrogen atoms are present in these positions the barrier of rotation may be too small to prevent interconversion of the enantiomeric forms at room temperature and the two structures may not be separated, or may racemize slowly on standing.

Please note, that for the biphenyls and binaphtyls derivatives the formal maximum number of stereoisomers (see above'Chiral Compounds') is exceeded. As these moleucles do neither feature astereocenteror astereogenic double bond, no stereoisomers would be expected. Only the hindered rotation about the central C-C single bond leads to the stereoisomerism of these compounds. Therefore, biphenyl- and binaphtyl-derivatives areconformational stereoisomers(notconfigurational stereoisomers).In particular the enentiomerically pure binaphthyl derivatives are of great use in asymmetric catalysis. For some animations of the dynamic behavior of biphenyls and binaphthyls and the process of racemization see the chapter'Atropsiomers'in theMolArch+- Moviessection of this web-site.

Chiral Compounds - Helical Chirality-3D Structures

Helices are chiral as they can exist in enantiomeric left- or right-handed forms. Typical examples for helical strutures are provided by the helicenes (benzologues of phenanthrene). With four or more rings, steric hinderance at both ends of these molecule prevents the formation of planar conformations, and helicenes rather adopt non-planar, but helical and enantiomeric structures withC2symmetry (see also the 3D structures at'Helicenes'and the chapter'Racemization of [8]Helicene'in theMolArch+- Moviessection of this web-site).

Other examples of chiral helical structures are provided bytrans-cyclooctene and suitably substituted heptalenes. Heptalene is not planar, and its twisted structure results in chirality. Although these conformations generally interconvert rapidly, bulky substituents may sufficiently slow down this process to optically resolve and separate these compounds.

The above example of the chirality of (E)-cyclooctene is also example for'Planar Chirality'(see below).

Chiral Compounds - Planar Chirality-3D Structures

Planar chirality may arise if an appropriately substituted planar group of atoms or ring system is bridged by a linker-chain extending into the space above or below of this plane. Commmon examples are the planar chirality of cyclophanes or alkenes as shown below. Even (E)-cyclooctene is a planar chiral compound (see also above'Helical Chirality'):

The above mentioned suitably substituted ferrocenes are also planar chiral compounds (see'Asymmetric Substituted Atoms').

Chiral Compounds - Other Examples-3D Structures

There are many more examples known for which chirality of molecules results from hindered rotation of groups or spatial arrangements of chemical moieties, a few examples are listed below:

Even catenanes and molecular knots made up from achiral molecules are chiral.

For more informations on other research topics, please refer to the completelist of publicationsand to thegallery of graphics and animations.Compunds with two or more asymmetrically substituted atoms (chiral centers) may be optically active. Typical examples are (2S,3S)- and (2R,3R)-2,3-dibromo-butane, or (2S,3S)- and (2R,3R)-tartaric acid (german:Weinsure). However, if pairs of equivalentstereocentersof opposite configuration are present in the molecule, the compounds are optically inactive (achiralmeso-compounds) as both chiral centers neutralize each other (internal compensation). For example, (2S,3R)- and (2R,3S)-2,3-dibromo-butane are identical (meso) as both structures can be superimposed through simple rotations and translations only. The same applies tomeso-tartaric acid.

Stereoisomers of compunds which are not not related as mirror images are calleddiastereoisomers. Structures of this type cannot be interconverted into each other through translation, rotation, and mirror symmetry operations. In contrast toenantiomers,diastereoisomershave different chemical (towards achiral as well as chiral reagents) and physical properties (including totally independent values for their specific optical rotation).trans-1,2-Disubstituted cyclohexanes ofC2symmetry are chiral compounds, whereas symmetricallycis-1,2-disubstituted cyclohexanes are optically inactive as they posses a mirror planeof symmetry. However, the latter type compounds exist inchiral conformationswhich interconvert rapidly into each other throughchair-antichairinversions of the cyclohexane ring (see also the 3D structures at'Achiral Compounds'and the chapter'Ring Pseudorotation'in theMolArch+- Moviessection of this web-site).

Chiral Compounds - Substituted Adamantane Derivatives-3D Structures

Adamantane derivates of suitable substitution may also be chiral compounds. In these structures, not a single atom, but an entire group (the adamantyl residue) holds four substituents (adamantane derivative on the left below) in a spatial arrangement that causes the compound to be non-superimposable with its mirror image geometry. The central adamantyl residue may be regarded as an extended tetrahedron.

This example demonstrates that thestereogenic centerof a moleucle needs not to be located on a specific atom. In this case, the stereogenic center is located in the center of the adamantyl cage. Disubstituted adamantanes (note the different substitution positions and pattern) are also chiral compounds - they do not feature achiral centerbut anaxis of chirality(see below'Axial Chirality').In fact, the above (left) adamantane derivative features fourasymmetric substituted carbon atoms(the four tertiary carbon atoms of adamantane backbone). As derived above, the formal maximum number of stereoisomers (see abvoe'Chiral Compounds') would beNmax= 24= 16. However, in this case only two stereoisomers actually exist, as the steric strain and geometrical limitations of the adamantane resdiue require all substituent to point towards the outside of the molecule (in fact, once the first stereocenter is defined, the remaining three are determined by their relative configuration, and thus the number of observed stereoisomers is 2).Similar limitations on the number of stereoisomers are observed in almost all bi- and polycyclic systems with small rings. Twistanes (even the unsubstituted parent hydrocarbon) are chiral. As another example, camphor yields two stereoisomers only, although it features two stereocenters in position 1 and 4 (but the relative configuration of both centers is constrained in the bicyclic ring system):

Chiral Compounds - Axial Chirality-3D Structures

Some compounds which do not have asymmetrically substituted carbon atoms (or any other atom type) may still be chiral if they feature two perpendicular planes which are not symmetry planes. If thesedisymmetric(chiral) planes cannot freely rotate against each other, the corresponding compounds are chiral. Compounds of this type are said to beaxially chiral(they feture anaxis of chiralityinstead acenter of chirality)Typical examples are allenes in which the central atom issp-hybridized, and the planes containing the substitutents on either end of the double bonds are aligned perpendicular to each other (in contrast to simple olefines where all substituents are contained in a single plane of the-bond; note the difference toE/Z-isomerism of alkenes). For an even number of double bonds in the allene, and if neither side of it is symmetrically substituted, these compounds are optically active and thus chiral.

Very similar arrangements are observed in chiralspiro-annelated ring systems and compounds with exocyclic double-bonds (see examples below).

As demonstrated above, suitably disubstituted adamantane derivatives also show axial chirality (see above'Substituted Adamantane Derivatives').

Chiral Compounds - Biphenyls and Binaphthyls-3D Structures

The same rules as outlined above for the allenes and spiranes apply also to biphenyl- and binaphtyl-derivatives. If both aromatic ring systems are asymmetrically substituted, the compounds are chiral. As the chirality of these structures originates not from an asymmetrically substituted atom center, but from an asymmetric axis around which rotation is hindered, these enantiomers are also calledatropisomers. In the biphenyls, theortho-substitutents must be large enough to prevent rotation around the central single bond; if hydrogen atoms are present in these positions the barrier of rotation may be too small to prevent interconversion of the enantiomeric forms at room temperature and the two structures may not be separated, or may racemize slowly on standing.

Please note, that for the biphenyls and binaphtyls derivatives the formal maximum number of stereoisomers (see above'Chiral Compounds') is exceeded. As these moleucles do neither feature astereocenteror astereogenic double bond, no stereoisomers would be expected. Only the hindered rotation about the central C-C single bond leads to the stereoisomerism of these compounds. Therefore, biphenyl- and binaphtyl-derivatives areconformational stereoisomers(notconfigurational stereoisomers).In particular the enentiomerically pure binaphthyl derivatives are of great use in asymmetric catalysis. For some animations of the dynamic behavior of biphenyls and binaphthyls and the process of racemization see the chapter'Atropsiomers'in theMolArch+- Moviessection of this web-site.

Chiral Compounds - Helical Chirality-3D Structures

Helices are chiral as they can exist in enantiomeric left- or right-handed forms. Typical examples for helical strutures are provided by the helicenes (benzologues of phenanthrene). With four or more rings, steric hinderance at both ends of these molecule prevents the formation of planar conformations, and helicenes rather adopt non-planar, but helical and enantiomeric structures withC2symmetry (see also the 3D structures at'Helicenes'and the chapter'Racemization of [8]Helicene'in theMolArch+- Moviessection of this web-site).

Other examples of chiral helical structures are provided bytrans-cyclooctene and suitably substituted heptalenes. Heptalene is not planar, and its twisted structure results in chirality. Although these conformations generally interconvert rapidly, bulky substituents may sufficiently slow down this process to optically resolve and separate these compounds.

The above example of the chirality of (E)-cyclooctene is also example for'Planar Chirality'(see below).

Chiral Compounds - Planar Chirality-3D Structures

Planar chirality may arise if an appropriately substituted planar group of atoms or ring system is bridged by a linker-chain extending into the space above or below of this plane. Commmon examples are the planar chirality of cyclophanes or alkenes as shown below. Even (E)-cyclooctene is a planar chiral compound (see also above'Helical Chirality'):

The above mentioned suitably substituted ferrocenes are also planar chiral compounds (see'Asymmetric Substituted Atoms').

Chiral Compounds - Other Examples-3D Structures

There are many more examples known for which chirality of molecules results from hindered rotation of groups or spatial arrangements of chemical moieties, a few examples are listed below:

Even catenanes and molecular knots made up from achiral molecules are chiral.

For more informations on other research topics, please refer to the completelist of publicationsand to thegallery of graphics and animations.Compunds with two or more asymmetrically substituted atoms (chiral centers) may be optically active. Typical examples are (2S,3S)- and (2R,3R)-2,3-dibromo-butane, or (2S,3S)- and (2R,3R)-tartaric acid (german:Weinsure). However, if pairs of equivalentstereocentersof opposite configuration are present in the molecule, the compounds are optically inactive (achiralmeso-compounds) as both chiral centers neutralize each other (internal compensation). For example, (2S,3R)- and (2R,3S)-2,3-dibromo-butane are identical (meso) as both structures can be superimposed through simple rotations and translations only. The same applies tomeso-tartaric acid.

Stereoisomers of compunds which are not not related as mirror images are calleddiastereoisomers. Structures of this type cannot be interconverted into each other through translation, rotation, and mirror symmetry operations. In contrast toenantiomers,diastereoisomershave different chemical (towards achiral as well as chiral reagents) and physical properties (including totally independent values for their specific optical rotation).trans-1,2-Disubstituted cyclohexanes ofC2symmetry are chiral compounds, whereas symmetricallycis-1,2-disubstituted cyclohexanes are optically inactive as they posses a mirror planeof symmetry. However, the latter type compounds exist inchiral conformationswhich interconvert rapidly into each other throughchair-antichairinversions of the cyclohexane ring (see also the 3D structures at'Achiral Compounds'and the chapter'Ring Pseudorotation'in theMolArch+- Moviessection of this web-site).

Chiral Compounds - Substituted Adamantane Derivatives-3D Structures

Adamantane derivates of suitable substitution may also be chiral compounds. In these structures, not a single atom, but an entire group (the adamantyl residue) holds four substituents (adamantane derivative on the left below) in a spatial arrangement that causes the compound to be non-superimposable with its mirror image geometry. The central adamantyl residue may be regarded as an extended tetrahedron.

This example demonstrates that thestereogenic centerof a moleucle needs not to be located on a specific atom. In this case, the stereogenic center is located in the center of the adamantyl cage. Disubstituted adamantanes (note the different substitution positions and pattern) are also chiral compounds - they do not feature achiral centerbut anaxis of chirality(see below'Axial Chirality').In fact, the above (left) adamantane derivative features fourasymmetric substituted carbon atoms(the four tertiary carbon atoms of adamantane backbone). As derived above, the formal maximum number of stereoisomers (see abvoe'Chiral Compounds') would beNmax= 24= 16. However, in this case only two stereoisomers actually exist, as the steric strain and geometrical limitations of the adamantane resdiue require all substituent to point towards the outside of the molecule (in fact, once the first stereocenter is defined, the remaining three are determined by their relative configuration, and thus the number of obser