Chapter 4

Chapter 4: Conformational Stereoisomers Of Alkanes

Structural formulas show the manner in which the atoms of a molecule are bonded together (its constitution), but do not generally describe the three-dimensional shape of a molecule, unless special bonding notations (e.g. wedge and hatched lines) are used. The importance of such three-dimensional descriptive formulas became clear in discussing configurational stereoisomerism, where the relative orientation of atoms in space is fixed by a molecule's bonding constitution (e.g. double-bonds and rings). Here too it was noted that nomenclature prefixes must be used when naming specific stereoisomers. In this section we shall extend our three-dimensional view of molecular structure to include compounds that normally assume an array of equilibrating three-dimensional spatial orientations, which together characterize the same isolable compound. We call these different spatial orientations of the atoms of a molecule that result from rotations or twisting about single bonds conformations.

In the case of hexane, we have an unbranched chain of six carbons which is often written as a linear formula: CH₃CH₂CH₂CH₂CH₂CH₃. We know this is not strictly true, since the carbon atoms all have a tetrahedral configuration. The actual shape of the extended chain is therefore zig-zag in nature. However, there is facile rotation about the carbon-carbon bonds, and the six-carbon chain easily coils up to assume a rather different shape. Many conformations of hexane are possible and two are illustrated below.

Extended Chain	Coiled Chain

For a Chime-based animation of conformational motion in hexane .

Ethane Conformers

Ethane Conformations

The simple alkane ethane provides a good introduction to conformational analysis. Here there is only one carbon-carbon bond, and the rotational structures (rotamers) that it may assume fall between two extremes, staggered and eclipsed. In the following description of these conformers, several structural notations are used. The first views the ethane molecule from the side, with the carbon-carbon bond being horizontal to the viewer. The hydrogens are then located in the surrounding space by wedge (in front of the plane) and hatched (behind the plane) bonds. If this structure is rotated so that carbon #1 is canted down and brought closer to the viewer, the "sawhorse" projection is presented. Finally, if the viewer looks down the carbon-carbon bond with carbon #1 in front of #2, the Newman projection is seen.

Extreme Conformations of Ethane
Name of Conformer	Wedge-Hatched Bond Structure	Sawhorse Structure	Newman Projection

Bond Repulsions in Ethane

As a result of bond-electron repulsions, illustrated on the right above, the eclipsed conformation is less stable than the staggered conformation by roughly 3 kcal / mol (eclipsing strain). The most severe repulsions in the eclipsed conformation are depicted by the red arrows. There are six other less strong repulsions that are not shown. In the staggered conformation there are six equal bond repusions, four of which are shown by the blue arrows, and these are all substantially less severe than the three strongest eclipsed repulsions. Consequently, the potential energy associated with the various conformations of ethane varies with the dihedral angle of the bonds, as shown below. Although the conformers of ethane are in rapid equilibrium with each other, the 3 kcal/mol energy difference leads to a substantial preponderance of staggered conformers (> 99.9%) at any given time.

Potential Energy Profile for Ethane Conformers		Dihedral Angle

The above animation illustrates the relationship between ethane's potential energy and its dihedral angle

Butane Conformers

Butane Conformations

The hydrocarbon butane has a larger and more complex set of conformations associated with its constitution than does ethane. Of particular interest and importance are the conformations produced by rotation about the central carbon-carbon bond. Among these we shall focus on two staggered conformers (A & C) and two eclipsed conformers (B & D), shown below in several stereo-representations. As in the case of ethane, the staggered conformers are more stable than the eclipsed conformers by 2.8 to 4.5 kcal/mol. Since the staggered conformers represent the chief components of a butane sample they have been given the identifying prefix designations anti for A and gauche for C.

Four Conformers of Butane

Potential Energy Profile for Butane Conformers

It is useful to summarize some important aspects of conformational stereoisomerism at this time.

Most conformational interconversions in simple molecules occur rapidly at room temperature. Consequently, isolation of pure conformers is usually not possible.
Specific conformers require special nomenclature terms such as staggered, eclipsed, gauche and anti when they are designated.
Specific conformers may also be designated by dihedral angles. In the butane conformers shown above, the dihedral angles formed by the two methyl groups about the central double bond are: A 180°, B 120°, C 60° & D 0°.
Staggered conformations about carbon-carbon single bonds are more stable (have a lower potential energy) than the corresponding eclipsed conformations. The higher energy of eclipsed bonds is known as eclipsing strain.
In butane the gauche-conformer is less stable than the anti-conformer by about 0.9 kcal/mol. This is due to a crowding of the two-methyl groups in the gauche structure, and is called steric strain or steric hindrance.
Butane conformers B and C have non-identical mirror image structures in which the clockwise dihedral angles are 240° & 300° respectively. These pairs are energetically the same, and have not been distinguished in the potential energy diagram shown here.

Ring Conformers

Ring Conformations

Although the customary line drawings of simple cycloalkanes are geometrical polygons, the actual shape of these compounds in most cases is very different.

Cyclopropane is necessarily planar (flat), with the carbon atoms at the corners of an equilateral triangle. The 60° bond angles are much smaller than the optimum 109.5° angles of a normal tetrahedral carbon atom, and the resulting angle strain dramatically influences the chemical behavior of this cycloalkane. Cyclopropane also suffers substantial eclipsing strain, since all the carbon-carbon bonds are fully eclipsed. Cyclobutane reduces some bond-eclipsing strain by folding (the out-of-plane dihedral angle is about 25°), but the total eclipsing and angle strain remains high. Cyclopentane has very little angle strain (the angles of a pentagon are 108°), but its eclipsing strain would be large (about 10 kcal/mol) if it remained planar. Consequently, the five-membered ring adopts non-planar puckered conformations whenever possible. Rings larger than cyclopentane would have angle strain if they were planar. However, this strain, together with the eclipsing strain inherent in a planar structure, can be relieved by puckering the ring. Cyclohexane is a good example of a carbocyclic system that virtually eliminates eclipsing and angle strain by adopting non-planar conformations, such as those shown below.

Some Conformations of Cyclohexane Rings

A planar structure for cyclohexane is clearly improbable. The bond angles would necessarily be 120°, 10.5° larger than the ideal tetrahedral angle. Also, every carbon-carbon bond in such a structure would be eclipsed. The resulting angle and eclipsing strains would severely destabilize this structure. If two carbon atoms on opposite sides of the six-membered ring are lifted out of the plane of the ring, much of the angle strain can be eliminated. This boat structure still has two eclipsed bonds (colored magenta in the drawing) and severe steric crowding of two hydrogen atoms on the "bow" and "stern" of the boat. This steric crowding is often called steric hindrance. By twisting the boat conformation, the steric hindrance can be partially relieved, but the twist-boat conformer still retains some of the strains that characterize the boat conformer. Finally, by lifting one carbon above the ring plane and the other below the plane, a relatively strain-free chair conformer is formed. This is the predominant structure adopted by molecules of cyclohexane.

On careful examination of a chair conformation of cyclohexane, we find that the twelve hydrogens are not structurally equivalent. Six of them are located about the periphery of the carbon ring, and are termed equatorial. The other six are oriented above and below the approximate plane of the ring (three in each location), and are termed axial because they are aligned parallel to the symmetry axis of the ring. In the stick model shown on the left below, the equatorial hydrogens are colored blue, and the axial hydrogens are red. Since there are two equivalent chair conformations of cyclohexane in rapid equilibrium, all twelve hydrogens have 50% equatorial and 50% axial character.

Because axial bonds are parallel to each other, substituents larger than hydrogen generally suffer greater steric crowding when they are oriented axial rather than equatorial. Consequently, substituted cyclohexanes will preferentially adopt conformations in which large substituents assume equatorial orientation. In the two methylcyclohexane conformers shown above, the methyl carbon is colored blue. When the methyl group occupies an axial position it suffers steric crowding by the two axial hydrogens located on the same side of the ring. This crowding or steric hindrance is associated with the red-colored hydrogens in the structure. A careful examination of the axial conformer shows that this steric hindrance is due to two gauche-like orientations of the methyl group with ring carbons #3 and #5. The use of models, including Chime, is particularly helpful in recognizing and evaluating these relationships.

Substituted Cyclohexanes

Substituted Cyclohexane Compounds

Because it is so common among natural and synthetic compounds, and because its conformational features are rather well understood, we shall focus on the six-membered cyclohexane ring in this discussion. In a sample of cyclohexane, the two identical chair conformers are present in equal concentration, and the hydrogens are all equivalent (50% equatorial & 50% axial) due to rapid interconversion of the conformers. When the cyclohexane ring bears a substituent, the two chair conformers are not the same. In one conformer the substituent is axial, in the other it is equatorial. Due to steric hindrance in the axial location, substituent groups prefer to be equatorial and that chair conformer predominates in the equilibrium.
We noted earlier that cycloalkanes having two or more substituents on different ring carbon atoms exist as a pair (sometimes more) of configurational stereoisomers. Now we must examine the way in which favorable ring conformations influence the properties of the configurational isomers. Remember, configurational stereoisomers are stable and do not easily interconvert, whereas, conformational isomers normally interconvert rapidly. In examining possible structures for substituted cyclohexanes, it is useful to follow two principles.

Chair conformations are generally more stable than other possibilities.
Substituents on chair conformers prefer to occupy equatorial positions due to the increased steric hindrance of axial locations.

The following equations and formulas illustrate how the presence of two or more substituents on a cyclohexane ring perturbs the interconversion of the two chair conformers in ways that can be predicted.

Conformational Structures of Disubstituted Cyclohexanes

1,1-dimethylcyclohexane
1-t-butyl-1-methylcyclohexane
cis-1,2-dimethylcyclohexane
trans-1,2-dimethylcyclohexane
cis-1,3-dimethylcyclohexane
trans-1,3-dimethylcyclohexane
cis-1,4-dimethylcyclohexane
trans-1,4-dimethylcyclohexane

In the case of 1,1-disubstituted cyclohexanes, one of the substituents must necessarily be axial, and the other equatorial, regardless of which chair conformer is considered. Since the substituents are the same in 1,1-dimethylcyclohexane, the two conformers are identical and present in equal concentration. In 1-t-butyl-1-methylcyclohexane the t-butyl group is much larger than the methyl, and that chair conformer in which the larger group is equatorial will be favored in the equilibrium( > 99%). Consequently, the methyl group in this compound is almost exclusively axial in its orientation.
In the cases of 1,2-, 1,3- and 1,4-disubstituted compounds the analysis is a bit more complex. It is always possible to have both groups equatorial, but whether this requires a cis-relationship or a trans-relationship depends on the relative location of the substituents. As we count around the ring from carbon #1 to #6, the uppermost bond on each carbon changes its orientation from equatorial (or axial) to axial (or equatorial) and back. It is important to remember that the bonds on a given side of a chair ring-conformation always alternate in this fashion. Therefore, it should be clear that for cis-1,2-disubstitution, one of the substituents must be equatorial and the other axial; in the trans-isomer both may be equatorial. Because of the alternating nature of equatorial and axial bonds, the opposite relationship is true for 1,3-disubstitution (cis is all equatorial, trans is equatorial/axial). Finally, 1,4-disubstitution reverts to the 1,2-pattern.