Conformational Analysis

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Chapter: Organic Chemistry : Stereochemical and Conformational Isomerism

In the most basic sense chemical reactions are really only changes in the distribution of electrons. Such changes result in the breaking and making of chemical bonds and cause reactants to be converted to products.


CONFORMATIONAL ANALYSIS

In the most basic sense chemical reactions are really only changes in the distribution of electrons. Such changes result in the breaking and making of chemical bonds and cause reactants to be converted to products. However, before such electronic changes can take place, molecules taking part in the reaction must approach each other within bonding distance or they must undergo a change in geometry which permits overlap between the necessary orbitals to take place which results in electron redistribution. Restated another way, for chemistry to occur, molecules must first interact in a spatial sense. Consequently the shapes of molecules and the surface features they display are an important influence on their interactions with other molecules.

The large number of σ bonds present in organic molecules has a direct bearing on their shapes. Since a σ bond is axially symmetric along the bond, rotations of the groups connected by a σ bond do not cause it to break. (Such cannot be said of π bonds!) Thus molecules with many σ bonds are capable of large numbers of internal rotational motions which largely determine the shape, size, and surface characteristics of the molecule. Conformational analysis is the study of rotational motions in molecules and how they affect molecular properties.

The simplest hydrocarbon capable of internal rotational motion is ethane. Ethane has two tetrahedral methyl groups connected by a carbon – carbon σ bond. As such the methyl groups are free to rotate one relative to the other. However, it is found that the various rotational positions are not equivalent spatially or energetically. In fact, there are two limiting rotational positions for ethane. The lowest energy conformation (synonymous with a conformational isomer) is the one in which the C–H bonds of each methyl group are staggered between the C–H bonds of the other methyl group across the σ bond. This is the lowest energy conformation because the electron clouds of the bonds are the farthest distance apart, and their repulsions are minimized.


The highest energy conformation of ethane is the one in which the C–H bonds of each methyl groups are eclipsed with the C–H bonds of the other methyl group across the σ bond. This is the highest energy because the electron clouds of the C–H bonds are as close as they can be, and their repulsions raise the energy of the molecule.

The staggered and eclipsed forms of ethane are conformational stereoisomers (conformational isomers, conformers) because they have the same molecular for-mulas and sequences of bonded elements but different spatial arrangements due to rotations around single bonds. (Actually there are an infinite number of con-formational isomers (also called conformations) because there are an infinite number of degrees of rotation around the bond, but normally one only needs to be concerned with energy minima and maxima.)

The difference in energy between the higher and lower energy forms of ethane is only 2.9 kcal/mol (12 kJ/mol); thus rotations around the bond are very rapid at room temperature (about 1011 sec1). 

However, if one plots the change in energy as ethane rotates between the staggered and eclipsed forms, a periodic behavior is seen (Figure 6.5). Moreover, if a large number of snapshots of ethane were taken, they would show that most of the time ethane is found in the staggered conformation. The equilibrium between the staggered and eclipsed conformations favors the staggered by 99.2% to 0.8%.


A similar analysis of propane reveals analogous behavior with two major conformations—staggered and eclipsed —and periodic energy changes as rota-tion about a sigma bond occurs (Figure 6.6). There is a difference from ethane, however, in that the energy difference between the staggered and eclipsed con-formations is now 3.3 kcal/mol (14 kJ/mol). This increase means that a hydrogen and methyl group eclipsed across a carbon – carbon bond repel each other more than two hydrogen atoms. This suggests that the electron cloud of the methyl group comes closer to the electron cloud of the C–H bond so the repulsion is greater. Since the electron clouds associated with the methyl group define the space that the methyl group occupies, it is clear that a methyl group occupies more space than a hydrogen, that is, it is “larger.” Thus, it follows that groups in molecules have definite sizes, and the size of these groups is one factor which contributes to the overall shape of the molecule because of its influence on the preferred conformation of the molecule.

Conformational isomerism around the central bond in butane is more com-plex because the various staggered and eclipsed conformations are not equiva-lent as they are in ethane and propane (Figure 6.7). 


Starting with the eclipsed conformation with the dihedral angle between the two methyl groups at 0 , rota-tion around the central bond leads to two different staggered conformations and one additional eclipsed conformation.

The most stable staggered conformation is that in which the methyl groups are antiperiplanar (dihedral angle of 180 ) —called the anti conformation. The other staggered conformation is that in which the dihedral angle between the methyl groups is 60 —called the gauche conformation (there are two of them for rotations of 60 or 300 , respectively). The other eclipsed conformation is that in which the two methyl groups each eclipse a hydrogen (there are two of them for rotations of +120 and 240 , respectively).

From the energy diagram it is seen that the gauche conformation is 0.9 kcal/mol (3.7 kJ/mol) higher than the anticonformation. This must be due to some residual repulsion between the methyl groups when the dihedral angle is only 60 between them. Also the energy difference between the anti conformer and the highest energy eclipsed conformer is 4.5 kcal/mol (18.8 kJ/mol). Thus the greater effective size of the methyl groups results in increased repulsion when they are eclipsed.


In addition to conformational isomerism about the 2,3 bond in butane, rotations about the 1,2 bond and the 3,4 bond are possible. The energy changes here are much smaller and are comparable to those found in propane.

The importance of conformational isomerism lies in the fact that the predom-inant shape that molecules adopt is dependent on the energies of the various staggered and eclipsed conformations. In combination they can be used to pre-dict the probable shapes the molecule normally assumes, and these shapes are those which are presented to reagents in solution.

In contrast to open-chain systems in which groups can rotate through 360 around σ bonds, cyclic systems can undergo conformational change through only limited ranges. Like open-chain systems, however, conformational changes in rings minimize eclipsing interactions across σ bonds. Cyclopropane is a flat ring without conformational motion. Cyclobutane is not planar because, if it were, all the C–H bonds around the ring would be eclipsed. The molecule undergoes a conformational change that bends the molecule out of planarity by about 35 . This reduces eclipsing and leads to a lower overall energy. A similar situation is found in cyclopentane, which adopts an envelope conformation (one ring apex out of plane) which is in equilibrium with four other envelope conformations (each apex up) to avoid the 10 C–H eclipsing interactions that would be present if the molecule were planar.


Saturated six-membered rings are the most common ring systems in nature because they present an optimal conformational situation. As seen in cyclohexane, the molecule adopts a puckered shape called a chair conformation in order to avoid angle strain in the ring bonds. In the chair form, all bond angles are 109 and all the bonds are staggered.


This results in a molecule whose energy is comparable to a completely stag-gered, open-chain alkane. This is easy to see by viewing the molecule in a Newman projection. Viewing the molecule through the ring so that the two side carbon – carbon bonds are seen head on, as in a Newman projection, generates the view in (6.5).

The chair conformer can undergo conformational isomerism to a second chair conformer which is degenerate in energy with the first. Cyclohexane is thus a dynamic molecule which exists largely in one of two chair isomers. These are the lowest energy conformations. Other higher energy conformations of cyclohexane include the boat form, which is 10.1 kcal/mol (42.3 kJ/mol) above the chair form, and the twist boat form, which lies 3.8 kcal/mol (15.9 kJ/mol) above the chair form.


Although these are well-defined conformational isomers, their energies are such that they are virtually unpopulated at room temperature. (The twist boat is an intermediate in the conversion of one chair form to the other.) At the same time the conversion of one chair form to the other occurs rapidly at room temperature, and both chair forms are in rapid equilibrium.

Because cyclohexane exists in the chair form, the C–H bonds of the methylene groups are nonequivalent. There are two types of valences on each CH2 group. One type is perpendicular to a plane loosely defined by the ring carbons and is called axial. The second type falls generally in the plane loosely defined by the ring carbons and is termed equatorial. These are shown both in combination and individually.


Three axial valences on alternate (1,3) carbons point to one side of the ring (up) and the other three axial valences on alternate (1,3) carbons point to the other side of the ring (down). The same is true for equatorial valences; while the directionality is not so obvious for equatorial valences; they still point toward one side of the ring (up) or the other (down).

There are two chair forms and two types of valences (axial and equatorial). The conversion of one chair form to the other interconverts the axial and equatorial valences (i.e., a valence which is axial in one chair form is equatorial in the other chair form and vice versa). In the structures below one of the carbons is indexed with a star ( *) to help keep track of it.


In cyclohexane the chair forms have equal energy, but if groups other than hydrogen are attached to the cyclohexane ring, the two chair forms are no longer equivalent. In one chair isomer the group is equatorial and in the other chair isomer it must be axial. This is shown for methylcyclohexane.


Both conformations have the methyl group staggered between the vicinal pro-tons. When the methyl group is axial, it is sufficiently close to the syn – axial protons to undergo 1,3 diaxial interactions and be repelled by them. This raises the energy of the axial conformer relative to the equatorial conformer. For a methyl group, the energy difference is about 1.8 kcal/mol. (Actually, the rela-tionship of an axial methyl group to the ring bonds is a gauche conformational relationship. Thus the value of 1.8 kcal/mol for an axial methyl group is the value of two gauche butane interactions with the ring bonds!)


Other groups would behave similarly, with the axial isomer being higher in energy (less stable) than the equatorial isomer because of 1,3 diaxial interactions. These two isomers are conformational isomers because they are interconvertible by rotations about C–C single bonds, but they are also called conformational diastereomers since they have different physical properties and are nonsuperim-posable, non-mirror images.

When more than one group is attached to cyclohexane, the stereoisomeric pos-sibilities increase. First, structural isomers of the 1,2, 1,3, or 1,4 type are possible.

Next relative configurations (R,S) are possible for 1,2- or 1,3-disubstituted isomers. (The 1,4 isomer has a plane of symmetry.) The relative stereochemistry can be denoted as cis or trans, depending on whether the substituents point toward the same side or opposite sides of the ring. Finally, the cyclohexane ring can undergo chair – chair interconversion leading to different conformational isomers. These possibilities are shown for methylcyclohexanol in (6.6).

The first three types of isomerism are familiar and have been discussed previ-ously. The conformational isomerism is very understandable if it is remembered that axial and equatorial valences exchange upon chair – chair interconversion. For example, to draw the trans isomer of 3-methylcyclohexanol, one of the groups must be equatorial and the other axial. The other chair form must have the groups in opposite valences. Similarly trans-2-methyl-cyclohexanol has both groups equatorial in one chair form. The other chair form must therefore have both groups axial.




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