stereochemistry

TABLE OF CONTENTS FOR THIS CHAPTER

1. Isomers:Definitions
2. Constitutional Isomers
3. Stereoisomers
4. Chirality
5. Symmetry Elements
6. Nomenclature for Enantiomers
7. Two Stereogenic Centers
8. Two Equivalent Stereogenic Centers
9. Comparative Properties of Enantiomers/Diastereoisomers
10. Optical Activity
11. Racemic Mixtures
12. Optical Purity
13. Resolution of Enantiomers
14. Kinetic Resolution

Isomers:Definitions

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,ie, 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 COC chain, while the latter has a CCO 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.

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Stereoisomers

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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

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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.

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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.

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CHIRALITY

• A molecule or object which is not identical to(ie, 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 (ie, 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.

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Symmetry Elements Which Guarantee Achirality

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R,S Nomenclature

NAMING ENANTIOMERS

Since two enantiomers are different compounds, we will need to have nomenclature which distinguishes them from each other. The convention which is used is called the (R,S) system because one enantiomer is assinged as the R enantiomer and the other as the S enantiomer. What are the rules which govern which is which??

• Priorities are assigned to each of the four different groups attached to a given stereogenic center (one through four, one being the group of highest priority). (It should be understood that each stereogenic center has to be treated separately.)
• Orient the molecule so that the group of priority four (lowest priority) points away from the observer.
• Draw a circular arrow from the group of first priority to the group of second priority.
• If this circular motion is clockwise, the enantiomer is the R enantiomer. If it is counterclockwise, it is the S enantiomer.

HOW TO ASSIGN GROUP PRIORITIES

There is also a set of conventions (rules) which govern the setting of group priorities, which is a part of the R,S system of nomenclature.

• Priority is based upon atomic number , ie, H has the lowest priority, O over C, F over O, and so on. Priority assignment is based upon the four atoms directly attached to the stereogenic center . For example, in 2-butanol, the example we considered previously, the four atoms are H,O, and two C's. Oxygen gets the first priority, and H the fourth. But the methyl and ethyl groups both are attached through carbon , so there is initially a tie for the second and third priorities.
• In this kind of tie situation, priority assignments proceed outward to the next atoms, which we will call the beta atoms.(The directly attached atoms are the alpha atoms). For the methyl group, the alpha atom is carbon and the beta atoms are three H's, while for the ethyl group the alpha atom is also carbon and the beta atoms are two H's and 1 carbon. This beta C of the ethyl group wins the priority competition because there is no beta atom on the methyl group which has an atomic number greater than 1 (all three beta atoms are H). In general, the competition contines from alpha to beta to gamma to delta atoms until a tie-breaker is found.
• Some additional conventions are necessary for handling multiple bonds and aromatic bonds, and these are a little tricky to learn. As an example, take the vinyl group. Each carbon of this double bond is considered to have two bonds to carbon, because of the double bond. In the case of a carbonyl group, the carbon is considered to be bonded to two oxygens, and the oxygen is considered to be bonded to two carbons. For this reason, a vinyl group has priority over an isopropyl group, as shown in the illustration. 

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Two Stereogenic Centers

Non-Equivalent Stereogenic Centers

• When a molecule has two stereogenic centers, each of them can be designated as R or S. Thus there are four possible stereoisomers. If we designate one stereocenter as "a" and the other as "b" just for labelling purposes, the four stereoisomers can be designated as R _a R _b ,R _a S _b ,S _a R _b , and S _a S _b These designations correspond to the cirucumstance theat stereocenter "a" can have the R or S configuration ,and stereocenter "b" can have either configuration.
• In general, if there are n such stereogenic centers , there will be a maximum of 2 ⁿ stereoisomers. For example, with three stereogenic centers, there are eight possible stereoisomers. The maximum of 2 ⁿ occurs when there are all non-equivalent stereocenters. Stereogenic centers are equivalent when all four substituents attached to the center are identical. For example, in 2,3-dibromobutane, both stereogenic carbons have a H, a Br, a methyl, and a 1-bromoethyl substituent. The maximum of four stereoisomers is not observed here, as we saw before. In fact there are three stereoisomers, including one achiral stereoisomer. This is because the 2R,3S molecule is identical to the 2S,3R molecule, since carbons 2 and 3 are equivalent.
• On the other hand, 2,3-dibromopentane has two non-equivalent stereogenic centers and there are four stereoisomers, consisting of two pairs of enantiomers. It should be noted that the relationship between one enantiomeric pair and the other pair of enantiomers is that they are diastereoisomers..

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TWO EQUIVALENT STEREOGENIC CENTERS

• As noted above, when both stereogenic centers are equivalent, the number of stereoisomers is less than the maximum of 2 ⁿ , but in fact is n + 1. In the case of two stereogenic centers (n = 2), there are 3 stereoisomers, as we saw for 2,3-dibromobutane. There is, first of all , a pair of enantiomeers: these are the (2R,3R) and (2S,3S) isomers. Note that the mirror image of 2R,3R is 2S,3S ( ie, the mirror image inverts the configuration at each stereocenter).
• There is also an achiral stereoisomer. A molecule which has stereocenters but is achiral is called a meso compound. We saw in an earlier diagram that this molecule has a point of symmetry in its most stable conformation.
• It should be noted carefully that the meso isomer is a diastereoisomer of the two enantiomers.

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COMPARATIVE PROPERTIES OF ENANTIOMERS AND DIASTEREOISOMERS

DIASTEREOISOMERS

• Diastereoisomers are not mirror image isomers. They are essentially like any other pair of isomers (eg, constitutional isomers) in that they have distinct chemical and physical properties. Since they have the same functional groups, however, they are usually rather similar to one another in their reactions and properties.
• Two diastereoisomers can usually be separated from one another by , eg, recrystallization, since they have different solubilities.
• Although their chemical properties(reactions) are similar, the two diastereoisomers will typically react at different rates .

ENANTIOMERS

• Since two enantiomers are mirror images of each other, they are not distinguished by any physical or chemical means which cannot distinguish mirror images, ie, which are not themselves chiral (handed, meaning can distinguish left from right).
• Therefore 2 enantiomers have exactly the same energy, solubility in typical achiral solvents, boiling and melting points, NMR and IR spectra, etc.
• Their chemical properties, including both the qualitative reactions and the quantitative rates of reaction are identical when reacting with achiral chemical species.
• In general, then, both chemical and physical properties of 2 enantiomers are exactly identical twoard achiral agents,chemical or physical . ,li>It is important to realize, however, that when 2 enantiome4s react with a pure single enantiomer of another chiral compound, the rates of reaction of the 2 enantiomers will be different (more later).
• Also, one physical property which can distinguish them is "optical activity" (see below).

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OPTICAL ACTIVITY

• Since enantiomers are "handed" or "chiral", they can be distinguished by other agents which are chiral. Thus, we can easily tell, in using our right hand to shake hands with another person, whether that person is using his left or right hand. There is a better "fit" of the two right hands than there is of right hand to left hand.
• Chemically this occurs, as noted above, when enantiomers react with another chiral compound. Both the original enantiomer and its reactant distinguish left from right , so then one of the original enantiomers will find a better energetic fit with the chiral compound than will the other.
• One physical property which distinguishes 2 enantiomers is "optical activity". This term refers to the property of chiral compounds (exclusively) of rotating the plane of plane-polarized light to the right (clockwise) or to the left (counterclockwise).
• The two enantiomers have exactly the same ability to rotate this plane, quantitatively, but they rotate it in opposite senses . Thus, if one enantiomer rotates the plane by 10.5 degrees clockwise (considered a positive rotation), the other rotates it by -10.5 degrees (ie, in the counterclockwise direction).
• Since the exact amount of the rotation of the plane by a given enantiomer depends upon how much of that enentiomer the light encounters as it passes through the solution, the measured rotation is divided by the concentration of the enantiomer and by the path length of the polarimeter cell to give a true measure of the inherent ability of the enantiomer to rotate the plane of polarized light. This number is called the specific rotation . Note that in deriving the specific rotation, the concentration is taken in grams per mL, and the path length in decimeters. The magnitude of the rotation also depends upon the wave length of the plane polarized light, so the a single wave length is usually used, ie, the sodium D line (529 nm),the line responsible for the yellow color of sodium-vapor lamps.
• A positive (clockwise) rotation is sometimes called dextrorotation and a ngetaive rotation is sometimes called levorotation

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RACEMIC MIXTURES

• A racemic mixture is a 50:50 mixture of the 2 enantiomers of a chiral compound.
• Because the two enantiomers have equal and opposite specific rotations, a racemic mixture has a specific rotation of zero , ie, it is optically inactive
• In nature, most naturally occurring compounds occur as a single enantiomer , not as racemic mixtures. The importance of racemic mixtures is that ordinary laboratory synthesis which generate a stereogenic center produce a racemic mixture . For example,if 1-butene is converted to 2-butanol by the addition of water catalyzed by acid, a stereogenic center is created in a molecule where none previously existed. Since both enantiomers have equal energy, and since there is nothing in the catalyst or solvent or reactant that is chiral, both enantiomers are formed in equal amounts(for a mechanistic explanation, see later).
• Whereas racemic mixtures are not particularly desirable, they are not problematic in many labaoratory organic syntheses. However, in the manufacture of drugs, usually only a single enantiomer is effective, so that it is desirable to synthesize only a single enaniomer. Nevertheless, racemic drugs are often used anyway because the other enaniomer is harmless, and racemic mixtrues are easier(read, cheaper) to synthesize.

OPTICAL PURITY

• If the specific rotation of a pure single enantiomer is known, it is easy to determine the purity of a sample containing both enantiomers in unequal amounts. The %OPTICAL PURITY = specific rotation of the sample/specific rotation of the pure enantiomer. This particular measure of optical purity is often called ENANTIOMERIC EXCESS( or ee) because it gives %R - %S. A small problem (admittedly very small, mathematically) arises in converted the ee (enantiomeric excess) into a specific composition given in terms of %R and %S. One simple way of doing this is as follows: If the enantiomeric excess of the R enantiomer is, for example, 80%, this means that there is 80% of the R enantiomer plus 20% of the racemic mixture (not 20%S). Since the racemic mixture is 10%R and 10%S, the composition of the mixture is 90% R and 10%S. Remember: ee represents not the % of one of the enantiomers, but the difference between the % of one pure enaniomer and the % of racemic mixture).

SEPARATION OF ENANTIOMERS

• The separation of 2 enantiomers present in a racemic mixture or any mixture of enantiomers, is called resolution .
• Enantiomers are not readily separated by conventional means , such as recrystallization or fractional distillation, since they have the same solubilities, mp's, bp's, etc. So, special means are required for "resolution" of two enantiomers.
• One common strategy for resolution is often to take advantage of the circumstance that, while enatiomers have the same solubilities and cannot be readily separated by simple recrystallization, diastereoisomers have different solubilites. The two enantiomers present in a racemic mixtrue can be reacted with a pure enantiomer of a chiral compound (called a resolving agent) which we have on hand (many occur in pure form in nature). This will form a compound with two chiral centers, and will give rise to 2 different diastereoisomers which can be separated from each other. Following this separation the chiral resolving agent rcan be removed by through some chemical reaction to give the two separate enantiomers. The chiral resolving agentcan also be recovered for re-use.
• As an example, consider the generalized case shown in the illustration below.

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KINETIC RESOLUTION USING ENZYMES

• Enzymes are proteins which have many chiral centers and which occur in nature as a single enantiomer (out of all the myriads of possible stereoisomers).
• The rates of reaction of two enantiomers with a single enantiomer of any chiral substance are different. We can see that the products will be diastereoisomeric, and so of different energies, and the rates of formation of these products will in general be different. In other words, a "handed" molecule can distinguish chemically between 2 mirror image isomers. Enzymes are particularly effective in making this distinction, so that a racemic mixture can often be easily resolved by reaction with some simple substance in the presence of the chiral enzyme as catalyst. The enantiomer whiich reacts faster will be converted to a new compound having an entirely different functional group, while the enantiomer which reacts more slowly will remain unreacted. The separation of the two compounds is then quite easy.
• As an example, if the compound which is the racemic mixture has an alochol function, it can be converted to an acetate ester by reaction with acetic acid in the presence of a suitable esterifying enzyme. The separation of the ester of one enantiomer from the alcohol of the other is then very easy. Then ester can then be hydrolyzed to the alcohol, if desired, by either simple chemical means or by enzyme catalyzed reaction.