stereoisomerism

stereoisomerism, the existence of isomers (molecules that have the same numbers of the same kinds of atoms and hence the same formula but differ in chemical and physical properties) that differ in the orientation of their atoms in space. There are two kinds of stereoisomers: enantiomers and diastereomers. Enantiomers are mirror images, like one’s hands, and diastereomers are everything else. However, timescale and energy are important. In order to understand these considerations, it is helpful first to consider a special kind of diastereomer, the conformational isomer.

Conformational isomers

Methane (CH₄) is a molecule that is a perfect tetrahedron, and so it is commonly said that no isomerism is possible with methane. However, the carbon-hydrogen bonds of methane constantly vibrate and bend, so on very short timescales an apparent isomerism can be said to exist. But these structures are not energy minima, and so they do not qualify as isomers.

As complexity increases, isomerism induced by rotations about bonds becomes a bigger factor. In ethane (CH₃CH₃), for example, both carbons are approximately tetrahedral. Thus, there are two limiting structures—staggered ethane, in which the carbon-hydrogen bonds are as far apart as possible, and eclipsed ethane, in which the bonds are as close as possible. These two structures are certainly not the same. Perhaps the best view in which to see the difference is a “Newman projection” (named after American chemist Melvin Newman) in which one sights down the carbon-carbon bond and focuses on the positions of the six hydrogens. In a Newman projection, the front carbon is located at the intersection of the bonds to the three attached hydrogen atoms, and the back carbon is an exploded circle, with the attached bonds emanating from the circumference of the circle.

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isomerism: Stereoisomers

Immediately, questions of energy arise: Which of the two structures is lower in energy and therefore more stable? The staggered form is lower in energy because in the eclipsed form electrons in carbon-hydrogen bonds on the opposite side of the carbon-carbon bond repel each other. The strain that this repulsion creates increases the potential energy of the eclipsed form. The energy difference is not large, about 3 kilocalories per mole (kcal/mol).

If one plots the energy change as ethane rotates around the carbon-carbon bond, another difficulty is revealed. Like the vibrational and rotational “isomers” of methane mentioned above, eclipsed ethane (E) is not even an energy minimum; it is an energy maximum, a transition state between two staggered ethanes (S). Therefore, ethane, like methane, really has only one form.

If substitutions are made in the ethane molecule—for instance, exchanging some of the hydrogen atoms for deuterium atoms to make 1,2-dideuterioethane—isomeric staggered forms become possible. These staggered forms, called “anti” and “gauche,” of 1,2-dideuterioethane are different but are interconverted through rotations around the central carbon-carbon bond and are called “conformational isomers.”

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Whether these different ethanes can be separated depends only on the amount of energy necessary to convert one into the other—that is, to rotate the molecule about the carbon-carbon bond. In the case of 1,2-dideuterioethane, the energy barrier separating the conformational isomers is only 3 kcal/mol, far too low to make them separable under normal conditions.

Butane (C₄H₁₀) has two constitutional isomers, butane and isobutane. Isobutane has no conformational isomers, but butane is closely analogous to 1,2-dideuterioethane, in that a pair of anti and gauche conformational isomers is possible for that molecule. Because a methyl group (CH₃) is much larger than hydrogen or deuterium, the plot of energy versus rotational angle is more complex for butane than it is for ethane or 1,2-dideuterioethane.

Ring compounds often have a particularly rich set of conformational isomers. By far the most interesting of the ring compounds is cyclohexane (C₆H₁₂), shown here with cyclopropane (C₃H₆).

Planar cyclohexane contains 12 pairs of eclipsed carbon-hydrogen bonds and is destabilized by these eclipsing interactions, or torsional strain. There are other problems with the planar form. In a flat hexagon, the C―C―C angles must be 120°, quite far from the optimum for tetrahedral carbons (usually quoted as approximately 109.5°; in fact, the real optimum value for cyclohexane is about 112°, the C―C―C angle in propane). In any event, the planar form of cyclohexane is severely destabilized by both torsional and angle strain.

Lower-energy forms can be made as the cyclohexane ring distorts from planarity. This distortion involves no more than rotations about carbon-carbon bonds, just as occurs in ethane or any other acyclic alkane. The energy minimum for cyclohexane is the chair form. In the chair form, carbon-hydrogen bonds are nicely staggered, and the C―C―C bond angle is 111.5°, very close indeed to the optimum.

Note that there are two kinds of carbon-hydrogen bonds in chair cyclohexane. One set of six parallel carbon-hydrogen bonds is perpendicular to the surface on which the chair apparently sits (these are the axial bonds). The other set of six is roughly in the plane of the ring (equatorial bonds). All six axial hydrogens are equivalent, as are all six equatorial bonds.

Rotations about carbon-carbon bonds interconvert two equally energetic chair forms. This process is colloquially called a ring “flip.”

The axial hydrogens in one chair become the equatorial hydrogens in the other as the ring “flips” from one chair to the other. An implication of this change is that there is more than one monosubstituted cyclohexane. In methylcyclohexane, for example, there are two conformational isomers, one with the methyl group axial and one with the methyl group equatorial. The two interconvert through ring flipping.

Which isomer is more stable? For the axial methyl isomer the methyl group interacts unfavourably with nearby methylene groups. This destabilizing interaction is not present in the equatorial isomer. Axial methylcyclohexane is less stable (higher in energy) than the equatorial isomer by 1.8 kcal/mol.

Cis and trans forms

The examples presented so far have concentrated on the simplest organic molecules, the alkanes. However, stereoisomers crop up in many of the other structural types of organic chemistry. For example, in the alkenes, two versions of 2-butene exist. They are traditionally called cis-2-butene and trans-2-butene or, in slightly more modern terms, (Z)- and (E)-2-butene. The Z and E stand for the German words for “together” (zusammen) and “apart” (entgegen). In principle, cis- and trans-2-butene are conformational isomers; in theory, they could be interconverted by a simple rotation about the central double bond. However, the practical world intrudes into principle, because this rotation would require about 66 kcal/mol, an amount of energy not available under normal conditions.

Other kinds of cis and trans isomers exist in ring compounds. For example, cis- and trans-1,2-dimethylcyclopropane are stereoisomers. (In the figure below, bp stands for “boiling point.”)

This time there is no imaginable rotation about bonds that can equilibrate the two isomers, so these two molecules are not conformational isomers. In addition, because three points determine a plane, the three-membered ring of cyclopropane is necessarily flat; there is no possible out-of-plane distortion.

On the other hand, as is described above, cyclohexane is quite flexible, with one energy-minimum chair form ring-flipping into another through rotations around carbon-carbon bonds. Consider the possible isomers of cis- and trans-1,4-dimethylcyclohexane. If one methyl group is in the lower-energy equatorial position, then the cis compound, with both methyl groups on the same side of the ring, can be made only by placing the second methyl group in the higher-energy axial position. In constructing the trans compound, the second methyl must be placed in the equatorial position. But what happens when the ring flips? Remember that in a ring flip all axial positions become equatorial and vice versa. In the case of the cis-1,4-dimethylcyclohexane isomer, the equatorial-axial version flips into itself, as the axial methyl becomes equatorial and the equatorial methyl becomes axial. The two versions of cis-1,4-dimethylcyclohexane therefore have the same energy.

When the trans isomer flips, however, an equivalent structure is not formed, because each of the two equatorial methyl groups becomes axial. As an equatorial methyl group is more stable than an axial methyl group by 1.74 kcal/mol, the diaxial form would be less stable than the diequatorial form by about twice that amount, or 3.5 kcal/mol. In practice, this energy difference means that far less than 1 percent of the trans-1,4-dimethylcyclohexane present at equilibrium is in the less-stable form.

Enantiomers

One’s hands are related but not the same. Exactly how are they related? Each has a thumb, little finger, and so on. Yet the hands truly are not the same, for they are not superimposable. In effect, the left and right hand are mirror images; the left hand is superimposable on the mirror image of the right hand but not on the right hand itself. Some molecules are related to their mirror images in the same manner. Such molecules are, by definition, stereoisomers, and they go by the special name of enantiomers.

The phenomenon of handedness, or “chirality,” is perhaps the most important phenomenon related to isomerism. Many objects in the macroscopic world are chiral. A pair of scissors and a screw are familiar chiral objects; they are not superimposable on their mirror images. But related objects, a simple knife or a nail, for example, are superimposable on their mirror images and thus are not chiral. The simple test for chirality is the same for objects as it is for molecules: Is the object (or molecule) superimposable on its mirror image? If it is not, it is chiral. If it is, the object is achiral (not chiral).

If each hydrogen atom in a molecule of methane were replaced with a different atom, one possible result would be bromochlorofluoroiodomethane (CBrClFI). The mirror images of this molecule are not superimposable. There are definitely two enantiomers of this molecule.

The molecule, with four different atoms (fluorine, chlorine, bromine, and iodine) attached to what is called a stereogenic carbon, is identified as chiral. Several questions and problems now appear. How are the two enantiomers different physically and chemically? On a more mundane level, how can one specify in words one of the two enantiomers? How is one to differentiate the right-handed molecule of bromochlorofluoroiodomethane from the left-handed version, for example? A rather complex protocol has been devised, and it is worth giving a simplified version of it here. In the so-called Cahn-Ingold-Prelog (CIP) protocol (named after British chemists Robert Cahn and Christopher Ingold and Swiss chemist Vladimir Prelog), one first assigns priorities to the four atoms attached to the stereogenic atom, in this case the carbon at the centre of the tetrahedron. The atom of lowest atomic number is given the lowest priority, 4. In this case that atom is the fluorine (atomic number 9). The atom with the highest atomic number, iodine (atomic number 53), gets the highest priority, 1. Chlorine (atomic number 17) is priority 3, and bromine (atomic number 35) is 2. In the second step of the protocol, one sights down the bond from carbon to the lowest priority (4). Finally, one connects atoms 1 to 2 to 3 with an arrow. If that arrow is clockwise, the molecule is called an R enantiomer. If the arrow is counterclockwise, the molecule is called an S enantiomer. (R comes from rectus, the Latin word for “right,” and S comes from sinister, the Latin word for “left.”) The CIP protocol is simple in the example chosen, but very often more-detailed rules must be applied to assign R and S.

In summary, a molecule with one stereogenic carbon can be either R or S—in a sense, “left-handed” or “right-handed.” One set of such molecules is of profound biological importance: the L-amino acids. The business of the body—biological function—is controlled by proteins, which are polymers of only 20 possible amino acids. All the amino acids but the achiral glycine contain a single stereogenic carbon, and all of them but glycine are left-handed. It is not clear why this sense was selected through evolution; perhaps that selection followed from an initial accident selecting for left-handed amino acids. Extraterrestrial life (should there be any) may well be either left- or right-handed.

All physical attributes of enantiomers are identical except for one rather arcane property: the direction of rotation of the plane of plane-polarized light. If one enantiomer rotates the plane in one direction (say, clockwise) as one views the beam, the other enantiomer will rotate the plane by the same amount in the other direction (in this case, counterclockwise). For example, the rotations of standard solutions of (R)- and (S)-2-aminobutane are −7.4 and +7.4 degrees, respectively.

The chemical properties of enantiomers are also identical, as long as the other reacting molecule is achiral. Chemical reactions of enantiomers are analogous to a hand grasping a ball. If the ball is featureless, one’s right and left hands (enantiomers) have exactly the same interactions with the ball. However, if the ball has the word Label written on it and is thus a chiral object, that labeled ball will be optically active; it will mimic a single enantiomer. The left and right hands will interact differently with the labeled ball. The little finger of the right hand will approach the capital L of Label while the thumb will approach the lowercase l. For the left hand, the interactions will be just the opposite: the little finger will approach the lowercase l and the thumb the capital L.

The figure shows these interactions, as well as a molecular counterpart in which a pair of enantiomers, (R)- and (S)-bromochlorofluoroiodomethane, interacts with a single enantiomer, (S)-2-chlorobutane. In the R enantiomer, the bromine atom approaches the methyl group (―CH₃), and the iodine atom approaches the ethyl group (―CH₂CH₃). In the S enantiomer, the bromine atom approaches the ethyl group, and the iodine atom approaches the methyl group. The figure shows only one of the many possible interactions, every one of which is different.

Stereoisomers of more complex molecules

An atom is stereogenic if switching any two atoms or groups of atoms that are bound to it results in a pair of stereoisomers. So far, molecules with no or only one stereogenic atom have been discussed. Very often the situation is more complex; indeed, there can be several stereogenic atoms in a molecule. A molecule with only one stereogenic atom has only two stereoisomers—the R and S enantiomers. If there are two stereogenic atoms in a molecule, both can be either R or S. Thus, there are four possibilities: RR, SS, RS, and SR. Three stereogenic atoms would lead to eight possibilities: RRR, RRS, RSR, SRR, SSR, SRS, RSS, and SSS. The formula for finding the maximum number of stereoisomers X is X = 2ⁿ, where n is the number of stereogenic atoms in the molecule.

The formula X = 2ⁿ reliably gives the maximum number of stereoisomers, but in situations of high symmetry it fails to give the real number. For example, it fails for 2,3-dichlorobutane [H₂Cl₂(CH₃)₂]. One pair of enantiomers, SS and RR, does appear. But the other combination gives an identical “pair” of SR compounds. This happens because 2,3-dichlorobutane contains an internal plane of symmetry. The result is fewer than the maximum number of stereoisomers predicted by the formula. Three stereoisomers are possible: one pair of enantiomers (A and B) and an achiral molecule C, called a “meso compound.” A meso compound is an achiral molecule that nonetheless contains a stereogenic atom.

In order to find molecules that are enantiomers, one must draw the mirror image of the original and see if they are superimposable. That is the only absolutely safe way to do it. It might be suggested that there is something special about a molecule containing four different groups attached to one carbon. The question now is whether the presence of such an atom (usually carbon) is either sufficient or necessary for the molecule to be chiral. The answer is no in each case. Although looking for such carbons is a good way to start a search for enantiomers, there is no way to avoid the ultimate necessity of writing out the mirror image and checking for superimposability. To test the question of sufficiency, for example, look at the meso compound C of 2,3-dimethylbutane. It certainly does contain a carbon attached to four different groups. The indicated carbon C₂ is attached to hydrogen, a methyl group, a chlorine, and the rest of the molecule. Yet C is achiral.

There are many compounds whose molecular architecture makes them chiral but that do not contain an atom attached to four different groups. One classic example is hexahelicene, a molecule composed of six benzene rings connected to each other. The molecule coils in the form of a spiral so that the atoms of the last ring do not impinge on the atoms of the first ring. The result is a left- or right-handed screw form, and the molecule is chiral.

Diastereomers

Cyclohexane is achiral, as are both axial and equatorial methylcyclohexane. The two methylcyclohexanes (axial and equatorial methyl group) are stereoisomers, but they are not enantiomers. Such isomers—stereoisomers that are not mirror images—are called diastereomers. The molecules cis- and trans-2-butene are diastereomers, as are cis- and trans-1,2-dimethylcyclopropane. However, in dimethylcyclopropane, the cis compound is achiral, but the trans compound exists as a pair of enantiomers. Therefore, there are three stereoisomers of 1,2-dimethylcyclopropane.