Achiral

Chiral carbon atoms are common, but they are not the only possible centers of chirality. Other possible chiral tetravalent atoms are Si, Ge, Sn, N, S, and P, while potential trivalent chiral atoms, in which non-bonding electrons occupy the position of the fourth ligand, are N, P, As, Sb, S, Se, and Te. Furthermore, a center of chirality does not even have to be an atom, as shown in the structure represented in Figure 2-70b, where the center of chirality is at the center of the achiral skeleton of adamantane. 

For each combination of atoms i.j, k, and I, c is defined by Eq. (29), where X , y,. and Zj are the coordinates of atom j in Cartesian space defined in such a way that atom i is at position (0, 0, 0), atomj lies on the positive side of the x-axis, and atom k lies on the xy-plaiic and has a positive y-coordinate. On the right-hand side of Eq. (29), the numerator represents the volume of a rectangular prism with edges % , y ., and Zi, while the denominator is proportional to the surface of the same solid. If X . y ., or 2 has a very small absolute value, the set of four atoms is deviating only slightly from an achiral situation. This is reflected in c, which would then take a small absolute value the value of c is conformation-dependent because it is a function of the 3D atomic coordinates. 

Clearly, there is a need for techniques which provide access to enantiomerically pure compounds. There are a number of methods by which this goal can be achieved . One can start from naturally occurring enantiomerically pure compounds (the chiral pool). Alternatively, racemic mixtures can be separated via kinetic resolutions or via conversion into diastereomers which can be separated by crystallisation. Finally, enantiomerically pure compounds can be obtained through asymmetric synthesis. One possibility is the use of chiral auxiliaries derived from the chiral pool. The most elegant metliod, however, is enantioselective catalysis. In this method only a catalytic quantity of enantiomerically pure material suffices to convert achiral starting materials into, ideally, enantiomerically pure products. This approach has found application in a large number of organic... 

The achiral triene chain of (a//-rrans-)-3-demethyl-famesic ester as well as its (6-cis-)-isoiner cyclize in the presence of acids to give the decalol derivative with four chirai centres whose relative configuration is well defined (P.A. Stadler, 1957 A. Escherunoser, 1959 W.S. Johnson, 1968, 1976). A monocyclic diene is formed as an intermediate (G. Stork, 1955). With more complicated 1,5-polyenes, such as squalene, oily mixtures of various cycliz-ation products are obtained. The 18,19-glycol of squalene 2,3-oxide, however, cyclized in modest yield with picric acid catalysis to give a complex tetracyclic natural product with nine chiral centres. Picric acid acts as a protic acid of medium strength whose conjugated base is non-nucleophilic. Such acids activate oxygen functions selectively (K.B. Sharpless, 1970). 

The enantioselective introduction of chiral centres into an achiral molecule can nowadays be achieved most easily using chiral reductants or oxidants. 

Antithesis of Achiral and Chiral Open-Chain Target Molecnles... 

Recent syntheses of steroids apply efficient strategies in which open-chain or monocyclic educts with appropiate side-chains are stereoselectively cyclized in one step to a tri- or tetracyclic steroid precursor. These procedures mimic the biochemical synthesis scheme where acyclic, achiral squalene is first oxidized to a 2,3-epoxide containing one chiral carbon atom and then enzymatically cyclized to lanostetol with no less than seven asymmetric centres (W.S. Johnson, 1%8, 1976 E.E. van Tamden, 1968). 

Achiral molecules which can be converted to chiral molecules by the chemical change of one atom — substitution on an sp -atom or addition on an sp -atom — are called prochiral molecules (Y. Izumi, 1977). The atom involved is a prochiral centre. Pairs of atorns or groups... 

FIGURE 7 2 M irror image forms of chlorodi fluoromethane are superimposable on each other Chlorodifluoro methane is achiral... 

Certain structural features can sometimes help us determine by inspection whether a mol ecule IS chiral or achiral For example a molecule that has a plane of symmetry or a cen ter of symmetry is superimposable on its mirror image and is achiral... 

A plane of symmetry bisects a molecule so that one half of the molecule is the mirror image of the other half The achiral molecule chlorodifluoromethane for exam pie has the plane of symmetry shown m Figure 7 3... 

A point m a molecule is a center of symmetry if any line drawn from it to some element of the structure will when extended an equal distance m the opposite direction encounter an identical element The cyclobutane derivative m Figure 7 4 lacks a plane of symmetry yet is achiral because it possesses a center of symmetry... 

Furthermore (f) 1 2 dichloroethene has a center of symmetry located at the mid t point of the carbon-carbon double bond This too tells us the molecule is achiral... 

Any molecule with a plane of symmetry or a center of symmetry is achiral but their absence is not sufficient for a molecule to be chiral A molecule lacking a center of symmetry or a plane of symmetry is likely to be chiral but the supenmposability test should be applied to be certain... 

To be optically active the sample must contain a chiral substance and one enantiomer must be present in excess of the other A subslance lhal does nol rolale fhe plane of polar ized lighl IS said lo be ophcally maclive All achiral substances are optically inactive... 

In this as m other reactions m which achiral reactants yield chiral products the product IS formed as a racemic mixture and is optically inactive Remember for a substance to be optically active not only must it be chiral but one enantiomer must be present m excess of the other... 

It IS a general principle that optically active products cannot be formed when opti cally inactive substrates react with optically inactive reagents This principle holds irre spective of whether the addition is syn or anti concerted or stepwise No matter how many steps are involved m a reaction if the reactants are achiral formation of one enan tiomer is just as likely as the other and a racemic mixture results... 

In this example addition to the double bond of an alkene converted an achiral mol ecule to a chiral one The general term for a structural feature the alteration of which introduces a chirality center m a molecule is prochiral A chirality center is introduced when the double bond of propene reacts with a peroxy acid The double bond is a prochi ral structural unit and we speak of the top and bottom faces of the double bond as prochiral faces Because attack at one prochiral face gives the enantiomer of the com pound formed by attack at the other face we classify the relationship between the two faces as enantiotopic... 

In a second example addition of hydrogen bromide converts 2 butene which is achiral to 2 bromobutane which is chiral But as before the product is racemic because... 

Addition to double bonds is not the only kind of reaction that converts an achiral molecule to a chiral one Other possibilities include substitution reactions such as the formation of 2 chlorobutane by free radical chlorination of butane Here again the prod uct IS chiral but racemic... 

When a reactant is chiral but optically inactive because it is racemic any products derived from its reactions with optically inactive reagents will be optically inactive For example 2 butanol is chiral and may be converted with hydrogen bromide to 2 bromo butane which is also chiral If racemic 2 butanol is used each enantiomer will react at the same rate with the achiral reagent Whatever happens to (/ ) (—) 2 butanol is mir rored m a corresponding reaction of (5) (+) 2 butanol and a racemic optically inactive product results... 

Optically inactive starting materials can give optically active products only if they are treated with an optically active reagent or if the reaction is catalyzed by an optically active substance The best examples are found m biochemical processes Most bio chemical reactions are catalyzed by enzymes Enzymes are chiral and enantiomerically homogeneous they provide an asymmetric environment m which chemical reaction can take place Ordinarily enzyme catalyzed reactions occur with such a high level of stereo selectivity that one enantiomer of a substance is formed exclusively even when the sub strate is achiral The enzyme fumarase for example catalyzes hydration of the double bond of fumaric acid to malic acid m apples and other fruits Only the S enantiomer of malic acid is formed m this reaction... 

Only three not four stereoisomeric 2 3 butanediols are possible These three are shown m Eigure 7 10 The (2R 3R) and (2S 3S) forms are enantiomers of each other and have equal and opposite optical rotations A third combination of chirality centers (2R 3S) however gives an achiral structure that is superimposable on its (2S 3R) minor image Because it is achiral this third stereoisomer is optically inactive We call achiral mole cules that have chnahty centers meso forms The meso form m Eigure 7 10 is known as meso 2 3 butanediol... 

One way to demonstrate that meso 2 3 butanediol is achiral is to recognize that its eclipsed conformation has a plane of symmetry that passes through and is perpendicular to the C 2-C 3 bond as illustrated m Eigure 7 11a The anti conformation is achiral as... 

FIGURE 7 10 Stereo isomeric 2 3 butanediols shown in their eclipsed con formations for convenience Stereoisomers (a) and (b) are enantiomers of each other Structure (c) is a diastereo mer of (a) and (b) and is achiral It is called meso 2 3 butanediol... 

Disubstituted cyclohexanes present us with a challenging exercise in stereochemistry Con sider the seven possible dichlorocyclohexanes 1 1 as and trans 1 2 as and trans 1 3 and as and trans 1 4 Which are chiral Which are achiral Four isomers—the ones that are achiral be cause they have a plane of symmetry—are relatively easy to identify... 

The same kind of spontaneous racemization oc curs for any as 1 2 disubstituted cyclohexane in which both substituents are the same Because such compounds are chiral it is incorrect to speak of them as meso compounds which are achiral by definition Rapid chair-chair interconversion however converts them to a 1 1 mixture of enantiomers and this mix ture IS optically inactive... 

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