Stereochemistry

Isomers

You are already familiar with the concept of isomers: different compounds which have the same molecular formula. In this chapter we learn to make distinctions between various kinds of isomers, especially the more subtle kind of isomers which we call stereoisomers.

Constitutional Isomers: Isomers which differ in "connectivity". The latter term means that the difference is in the sequence in which atoms are attached to one another. Examples of isomers pairs which are consitutional isomers are (1)butane and methylpropane,i.e., isobutane, which are different in that butane has a sequence of four carbon atoms in a row, but isobutane has a three carbon chain with a branch (2)dimethyl ether and ethanol--the former has a C-O-C chain, while the latter has a C-C-O chain (3) 1-pentene and cyclopentane--the former has an acylic chain of 5 carbons, while the latter has a 5-membered ring.
Stereoisomers: Isomers which have the same connectivity. Thus all isomers are either constitutional or stereoisomers. Stereoisomerism is a more subtle kind of isomerism in which the isomers differ only in their spatial arrangement, not in their connectivity. Cis- and Trans-1,4-dimethylcyclohexane are a good example of a pair of stereoisomers.

Stereoisomers

We have just seen that there are two major types of isomer, but now it is necessary to further notice that their are two sub-types of stereoisomers:
Enantiomers: Stereoisomers which are mirror images
Diastereoisomers: Stereoisomers which are not mirror images
The examples of cis- and trans-1,4-dimethylcyclohexane are of the latter type, that is , they are diastereoisomers. Cis- and trans-isomers in general are diastereoisomers. They have the same connectivity but are not mirror images of each other. Enantiomers are mirror image isomers. This is the very most subtle way in which two chemical compounds can differ:In an overal sense, then , there are three types of isomers: (1)constitutional isomers (2)diastereoisomers and (3)enantiomers in order of increasing subtlety of difference. Since we have previously considered constitutional isomerism, and since the difference between diastereoisomers and enantiomers rests upon the concept of mirror image isomerism, we must now consider this latter phenomenon in greater detail.

Mirror Image Isomerism

To be isomers, molecules must not be identical. The test for "identicality" is one of superimposability. In a sample of butane, all of the molecules are identical because they can be superimposed upon one another in some conformation. The same is true of ethanol or propanol or 1-butanol, but in the case of 2-butanol there are two isomeric forms which can not be superimposed. They do not differ in connectivity, obviously, or they wouldn't both be called by the same name (2-butanol). They also don't have a cis or trans prefix, to indicate that they are diastereoisomers. They have a very specific, unique relationship to one another, the same relationship which exists between an object and its mirror image. A key aspect of this difference, as we all know, is that a mirror acts to interchange left and right hands.

CHIRALITY

A molecule or object which is not identical to(i.e., non-superimposable upon) its mirror image molecule or object is said to be chiral. This means it resembles a human hand in that the left and right hands are not superimposabile but can be readily distinguished (at least by some of us). By the same token, a molecule or any object is said to be achiral if it is identical to (superimposable upon) its mirror image molecule or object. Many molecules are achiral, but many are chiral, especially complex molecules such as are found in biological systems.How can we anticipate when a molecule is chiral and therefore has an isomer (an enantiomer) or when it is achiral and has no enantiomer?
Consider 2-butanol, which is an example of a chiral molecule. The illustration below (hopefully) shows that the mirror image of one 2-butanol isomer is non-superimposable upon the original molecule. Your can verify this by making models, but you can also visualize trying to superimpose the two by sliding one structure over (mentally) on top of the other.We can, for example, slide B over to A and superimpose the OH, the central C, and its attached H of the B molecule over the corresponding gorups of the A molecule, but the ethyl group on B sits over the methyl group of A, and the methyl group on B superimposes upon the ethyl group of A. The two molecules have all the same kinds of bonds and are extremely similar, but are mirror image isomers. We will learn how to name the two different enantiomers shortly.
Although 2-butanol is a chiral molecule and therefore has two enantiomers, the very similar molecule 2-propanol is achiral and does not exist as an enantiomeric pair. In the illustration, you can see that B slides over onto A with all corresponding groups superimposing perfectly. Many simple molecules are of this kind. How can we predict whether a molecule is chiral or achiral?
One of the simple ways is to use the concept of a stereogenic center. If a molecule has a single stereogenic center it will necessarily be chiral. The most common kind of stereogenic center is a carbon (or other atom) which has four different atoms or groups directly attached to it. You can see that the central carbon of 2-butanol (the one marked by an asterisk) is a stereogenic center, having H,OH,methyl, and ethyl groups attached. Since it has just a single stereogenic center , it must be chiral. On the other hand, 2-propanol has no stereogenic center and is achiral. The corresponding carbon atom of 2-propanol has an OH,H, and two methyl groups attached. Of course, no methyl carbon atom or methylene carbon can be chiral since these groups automatically have at least two identical groups (H's) attached. We will see a little later what happens when we have more than one stereogenic center.
The second method, especially useful when there is more than one stereogenic center, is the use of symmetry elements.If the molecule or object has either a plane of symmetry or a center of symmetry it is achiral. The examples shown below refer to cis- and trans-1,2-dimethylcyclobutane, The former of which is achiral and the latter chiral. They both have two stereogenic centers, viz., the ring carbons which have the methyl and hydrogen groups attached, but one molecule is chiral and the other achiral. This emphasizes the point that a molecule or object is guaranteed to be chiral only if it has a single stereogenic center. If it has more than one stereogenic center, it may be either chiral or achiral. Note that in the cis isomer, the two methyls are on the same side of the ring and are equidistant from the plane of symmtery which runs through the center of the ring perpendicular to the ring. In the trans isomer, the methyls are on opposite sides of the ring, so that where there is a methyl group on the right there is a H on the left.
What is the relationship between the cis and trans isomers of 1,2-dimethylcyclobutane??? They are diastereoisomers, having the same connectivity but obviously not being mirror images of each other. To sum up, there are three isomers of 2,3-dimethylcyclobutane, a single cis isomer, and two enantiomeric trans isomers.
The plane of symmetry is relatively easy to find and is the most common one to look for, but one other element of symmetry also guarantees an achiral molecule, and that is the center of symmetry. This is a point in the molecule for which any line drawn through the point will encounter identical components of the object at equal distances from the center of symmetry.In the case illustrated, 2,3-dimethylbutane (the so-called meso isomer), the center of symmetry is at the center point of the C2-C3 carbon-carbon bond. One of the dotted lines shown connects the equivalent bromines on of the two carbons,another connects equivalent methyl groups, and a third connects equivalent hydrogens (not shown).The meso isomer is just one of the three stereoisomers of this system. Again, there is one enantiomeric pair plus this meso isomer, which is achiral. A center of symmetry will be encountered in any molecule which has two equivalent chiral centers (i.e., both carbons have the same set of four distinct substituents) and in a conformation of such a molecule in which all identical groups are anti to one another. The two carbons of this molecule both have H,methyl,bromine, and 1-bromoethyl substituents.

Please note that the stereogenic center need not be carbon. It can be a quaternary nitrogen atom ( the nitrogen of an ammonium salt, if there are four different groups attached to the nitrogen.