Minor image

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... 

As shown in Figure 7.1, the two minor images of bromochlorofluoromethane cannot be superimposed on each other. Because the two mirror images of bromochlorofluoromethane are not superimposable, BrClFCH is chiral. 

The minor images of bromochlorofluoromethane have the sane constitution. That is, the atoms are connected in the sane order. But they differ in the anangement of then-atoms in space they are stereoisomers. Stereoisomers that are related as an object and its nonsuperimposable minor image are classified as enantiomers. The word enantiomer describes a paiticulai- relationship between two objects. One cannot look at a single molecule in isolation and ask if it is an enantiomer any more than one can look at an individual human being and ask, Is that person a cousin Fuithennore, just as an object has one, and only one, minor image, a chiral molecule can have one, and only one, enantiomer. 

The surest test for chirality is a careful examination of minor-image forms for superimposability. Working with models provides the best practice in dealing with molecules as three-dimensional objects and is strongly recommended. 

Certain structural features can sometimes help us detennine by inspection whether a molecule is chir al or achiral. For example, a molecule that has a plane of symmetry or a center of symmetry is superimposable on its minor image and is achiral. 

A plane of symmetry bisects a molecule so that one half of the molecule is the minor image of the other half. The achiral molecule chlorodifluoromethane, for example, has the plane of symmetry shown in Figure 7.3. 

As outlined in Table 7.1, (+)-2-butanol has the S configuration. Its minor image is (—)-2-butanol, which has the R configuration. 

We can view this reaction as the replacement of one or the other of the two methylene protons at C-2 of butane. These protons are prochiral atoms and, as the red and blue protons in the Newman projection indicate, occupy minor-image environments. 

Stereoisomer I is not a minor image of III or IV, so it is not an enantiomer of either one. Stereoisomers that are not related as an object and its minor image are called diastereomers diastereomers are stereoisomers that are not enantiomers. Thus, stereoisomer I is a diastereomer of III and a diastereomer of IV. Similarly, II is a diaste-reomer of III and IV. 

Because diastereomers are not minor images of each other, they can have quite different physical and chemical properties. For example, the (2R,3R) stereoisomer of 3-fflnino-2-butanoI is a liquid, but the (2R,3S) diastereomer is a crystalline solid. 

Fischer projection fonnulas can help us identify meso fonns. Of the three stereoisomeric 2,3-butanediols, notice that only in the meso stereoisomer does a dashed line through the center of the Fischer projection divide the molecule into two minor-image halves. 

Steroids are another class of natural products with multiple chirality centers. One such compound is cholic acid, which can be obtained from bile. Its structural formula is given in Figure 7.12. Cholic acid has 11 chirality centers, and so a total (including cholic acid) of 2, or 2048, stereoisomers have this constitution. Of these 2048 stereoisomers, how many are diastereomers of cholic acid Remember Diastereomers are stereoisomers that are not enantiomers, and any object can have only one minor image. Therefore, of the 2048 stereoisomers, one is cholic acid, one is its enantiomer, and the other 2046 are diastereomers of cholic acid. Only a small fraction of these compounds are known, and (-l-)-cholic acid is the only one ever isolated from natural sources. 

Occasionally, an optically inactive sfflnple of tartaric acid was obtained. Pasteur-noticed that the sodium ammonium salt of optically inactive tartaric acid was a mixture of two minor-image crystal forms. With microscope and tweezers, Pasteur carefully separated the two. He found that one kind of crystal (in aqueous solution) was dextrorotatory, whereas the minor-image crystals rotated the plane of polarized light an equal fflnount but were levorotatory. 

Section 7.1 A molecule is chiral if it cannot be superimposed on its minor image. 

Nonsriperimposable mirror images are enantiomers of one another. Molecules in which minor images are superimposable are achiral. 

The nonplanarity of allenes has an interesting stereochemical consequence. 1,3-Disubstituted allenes are chiral they are not superimposable on their minor images. Even an allene as simple as 2,3-pentadiene (CH3CH=C=CHCH3) has been obtained as separate enantiomers. 

Fluorescence always occurs from the lowest singlet state even if the initial excitation is to higher energy state (Kasha s rule). Azulene and some of its derivatives are exceptions to this rule. Because of vibrational relaxation of initially excited vibronic state, the fluorescence spectrum may appear as a minor image of the absorption spectrum for large polyatomic molecules. The shape of the emission spectrum is independent of the exciting wavelength. 

PLANES OF SYMMETRY. The plane of symmetry is reflection in the plane. Planes of symmetry are often called mirror planes or reflection planes. Some examples of planes of symmetry are shown in Fig. 5.3. Note that it is not sufficient for the two halves of the body to be identical. They must be exact minor images of one another in the plane. Fig. 5.4 illustrates a plane dividing a body into two identical halves which are not minor images of one another in the plane so that the plane is not a plane of symmetry. 

From its definition, the P-polynomial appears to depend on the particular projection of the link which we are working with. However, when this polynomial was defined it was proven that given any oriented link, no matter how it is deformed or projected, the link will always have the same P-polynomial [5, 6]. This means that two oriented links which are topologically equivalent have the same P-polynomial. In particular, if an oriented link can be deformed to its minor image then it and its minor image will have the same P-polynomial. 

One delntion of cWraSly is that the molecule be nonstfmrinipgsaUe CO its minor image. An equivalent criterion is (hat it not possess an crnpiupcr axis of eolation (page 52). The absence of a minor plane does not insure optical activity because a molecule may have no mirror plane, yet may possess an improper rotational axis. We can, however, be sure that the molecule with a minor plane will be optically inactive. 

Enantiomeric purity, measured as the enantiomeric excess (ee) of an isomer, is determined by the formula (% major isomer)—(% minor isomer). Thus, if a chiral drag is said to be or 50% ee, the composite mixture contains 75% of one enantiomer and 25% of the other. Enantioselectivity refers to the greater activity of one enantiomer over its minor image. Enantiospecificily is rarely observed and implies that one enantiomer possesses 100% of the observed activity in most cases it is more accurate to use the term highly enantioselective. The pharmacologically more active enantiomer is termed the eulomei and the less active enantiomer is referred to as tire distomer. 

Meso compounds can be recognized by the faetjhat half tlie molecule is a minor image of the other half. 

Since each carbon of 1 is the minor-image configuration of the carbons in 4 (i.e., C-2 of 1 is R and C-2 of 4 is S C-3 of 1 is S and C-3 of 4 is R), dien the molecules diemselves are minor images, but dtey are nonsuperimposable. They are thus enantiomers. This relationship can also be shown by reorienting the molecules to see diat dtey are mirror images,... 

The irons isomer and its minor image are identical. They are not isomers of each other. 

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