Nonsuperimposability

Structures A and A are nonsuperimposable mirror images of each other Thus although as 1 2 dichloro cyclohexane is chiral it is optically inactive when chair-chair interconversion occurs Such interconver Sion IS rapid at room temperature and converts opti cally active A to a racemic mixture of A and A Because A and A are enantiomers interconvertible by a conformational change they are sometimes re ferred to as conformational enantiomers... 

Section 7 1 A molecule is chiral if it cannot be superimposed on its mirror image Nonsuperimposable mirror images are enantiomers of one another Mol ecules m which mirror images are superimposable are achiral... 

Enantiomers. Two nonsuperimposable structures that are mirror images of each other are known as enantiomers. Enantiomers are related to each other in the same way that a right hand is related to a left hand. Except for the direction in which they rotate the plane of polarized light, enantiomers are identical in all physical properties. Enantiomers have identical chemical properties except in their reactivity toward optically active reagents. 

Compounds in which one or more carbon atoms have four nonidentical substituents are the largest class of chiral molecules. Carbon atoms with four nonidentical ligands are referred to as asymmetric carbon atoms because the molecular environment at such a carbon atom possesses no element of symmetry. Asymmetric carbons are a specific example of a stereogenic center. A stereogenic center is any structural feature that gives rise to chirality in a molecule. 2-Butanol is an example of a chiral molecule and exists as two nonsuperimposable mirror images. Carbon-2 is a stereogenic center. 

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. 

Enantiomers (Section 7.1) Stereoisomers that are related as an object and its nonsuperimposable mirror image. 

Enantiotopic (Section 7.9) Describing two atoms or groups in a molecule whose environments are nonsuperimposable mirror images of each other. The two protons shown in bold in CH3CH2CI, for example, are enantiotopic. Replacement of first one, then the other, by some arbitrary test group yields compounds that are enantiomers of each other. 

FIGURE 4.12 Enantiomeric molecules based on a chiral carbon atom. Enantiomers are nonsuperimposable mirror images of each other. 

Same atoms, same partners nonsuperimposable mirror images... 

The C atom marked with a is chiral therefore the molecule is nonsuperimposable on its mirror image. 

If a molecule is nonsuperimposable on its miixor image, the mirror image must be a different molecule, since superimposability is the same as identity. In each case of optical activity of a pure compound there are two and only two isomers, called enantiomers (sometimes enantiomorphs), which differ in structure only in the left-and right-handedness of their orientations (Fig. 4.1). Enantiomers have identical physical and chemical properties except in two important respects ... 

Although the ultimate criterion is, of course, nonsuperimposability on the mirror image (chirality), other tests may be used that are simpler to apply but not always accurate. One such test is the presence of a plane of symmetry A plane of symmetry (also called a mirror plane) is a plane passing through an object such that the part on one side of the plane is the exact reflection of the part on the other side (the plane acting as a mirror). Compounds possessing such a plane are always optically inactive, but there are a few cases known in which compounds lack a plane of symmetry and are nevertheless inactive. Such compounds possess a center of symmetry, such as in a-truxillic acid, or an alternating axis of symmetry as in 1. A... 

This molecule has no chiral carbons, nor does it have a rigid shape, but it too has neither a plane nor an alternating axis of symmetry. Compound 32 has been synthesized and has, in fact, been shown to be chiral. Rings containing 50 or more members should be able to exist as knots (33, and see 37 on p. 114 in Chapter 3). Such a knot would be nonsuperimposable on its mirror image. Calixarenes, ° crown ethers, catenanes, and rotaxanes (see p. 113) can also be chiral if suitably substituted. For example, A and B are nonsuperimposable mirror images. 

We mentioned before that enantiomers are two compounds that are nonsuperim-posable mirror images. Let s first clear up the term enantiomers, since students will often use this word incorrectly in a sentence. Let s compare it to people again. If two boys are born to the same parents, those boys are called brothers. Each one is the brother of the other. If you had to describe both of them, you say that they are brothers. Similarly, when you have two compounds that are non-superimposable mirror images, they are called enantiomers. Each one is the enantiomer of the other. Together, they are a pair of enantiomers. But what do we mean by nonsuperimposable mirror images Let s go back to the brother analogy to explain it. 

The first thing you need to realize is that enantiomers always come in pairs. Remember that they are mirror images of each other. There are only two sides to a mirror, so there can be only two different compounds that have this relationship (nonsuperimposable mirror images). This is very much like the twin brothers. Each brother only has one twin brother, not more. 

We can clearly see that they are not the same compound. In other words, they are nonsuperimposable. But, they are not mirror images of each other. The top stereocenter has the same configuration in both compounds. If they are not mirror images, then they are not enantiomers. So what is their relationship They are called di-astereomers. Diastereomers are any compounds that are nonsuperimposable stereoisomers that are not mirror images of each other. 

One of the fundamental concepts of structural chemistry is that of molecular asymmetry or chirality. The most typical example is that of a tetrahedral carbon atom with four different substituents, C(abcd), which can produce two different arrangements, which are nonsuperimposable mirror images of one another. Such a carbon atom is usually called asymmetric or chiral. In contrast, when two of the substituents are alike, as in C(abc2), the system is usually termed symmetrical or achiral, except for a special class of compounds... 

In recent years, stereochemistry, dealing with the three-dimensional behavior of chiral molecules, has become a significant area of research in modern organic chemistry. The development of stereochemistry can, however, be traced as far back as the nineteenth century. In 1801, the French mineralogist Haiiy noticed that quartz crystals exhibited hemihedral phenomena, which implied that certain facets of the crystals were disposed as nonsuperimposable species showing a typical relationship between an object and its mirror image. In 1809, the French physicist Malus, who also studied quartz crystals, observed that they could induce the polarization of light. 

If a molecule contains more than one chiral center, there are other forms of stereoisomerism. As mentioned in Section 1.1, nonsuperimposable mirror images are called enantiomers. However, substances with the same chemical constitution may not be mirror images and may instead differ from one another... 

Enantiomer Two stereoisomers that are nonsuperimposable mirror images of each other. 

Enantiomers are stereoisomers which are mirror images of one another, but these images are nonsuperimposable, i.e., they do not fit over one another (e.g., like left- and right-handed gloves). This occurs when a central carbon... 

An example is l-methyl-2-chlorocyclopropane which exists as a pair of geometric isomers and since each isomer has a nonsuperimposable mirror image, it has a pair of enantiomers. Thus its forms are ... 

---