CHAPTER OUTLINE
4.2 Newman Projections and Dihedral Angles
4.3 Conformations and Energies of Ethane—Torsional Strain
4.4 Conformations and Energies of Larger Acyclic Molecules—Steric Strain
4.5 Conformations of Small Rings
Box 4.1—The three major types of strain in organic molecules
4.6 Conformations of Cyclohexane and Related Six-Membered Rings
Box 4.2—Drawing chair conformations
4.7 Estimating the Conformational Preferences of Substituted Cyclohexanes
4.8 Conformationally Constrained Ring Systems
Box 4.3—Conformational constraint in opiate analgesics
4.10 Case Study—Neuraminidase Inhibitors and the Influenza Virus
4.1 Introduction
In this chapter we will consider the conformations, or three-dimensional shapes, that organic molecules can adopt via rotations about single bonds in their structures. These rotations occur rapidly at physiological temperatures and so most molecules can readily adopt several distinct conformations that are in equilibrium with each other. These various conformations will have different free energies, which will determine the relative abundance of the different conformations. Two energetic extremes in the conformations of ethane are shown below, with the staggered conformation being lowest in energy (most favored) and the eclipsed conformation highest in energy (Figure 4.1). When a drug molecule interacts with its biological target, it must adopt a conformation (shape) that is compatible with binding to the target. The conformation of organic molecules is therefore a topic of great relevance to the action of drug molecules.
Figure 4.1 Staggered and eclipsed conformations of ethane represented as stick (left) and space-filling models (right). (Reproduced, with permission, from Carey FA, Giuliano RM. Organic Chemistry. 9th ed. New York: McGraw-Hill Education; 2014.)
It is important at this stage to clarify the distinction between the terms configuration and conformation. As we learned in Chapter 3, configuration relates to the connectivity of atoms. A molecule might exist with either the S or R configuration at a chirality center but these two possibilities represent different molecules—they cannot interconvert without breaking and reforming chemical bonds. In contrast, two different conformations (or conformers) of a given molecule may have different shapes but they are still the same molecule—their interconversion requires only rotations about certain bonds. These rotations usually occur rapidly on the human timescale and so many different conformers are in equilibrium. To study the conformations of organic molecules then, we must imagine freezing time so that the different conformers can be compared and analyzed. This is what we will learn to do in this chapter.
4.2 Newman Projections and Dihedral Angles
To study the conformations of a simple organic molecule like ethane it is helpful to visualize rotations about single C–C bonds. Traditional structural drawings are less than ideal in this regard because they depict bonds from the side. An end-on view down the axis of a bond as it rotates provides a much better picture of what is happening. Consider the three different drawings of ethane below (Figure 4.2). All three drawings illustrate a “staggered” conformation but the Newman projection provides the clearest view of how the C–H bonds on the respective carbon atoms are staggered. A Newman projection represents a view looking exactly down the C–C bond axis. The carbon “in front” from this perspective appears with three C–H bonds separated by 120° (i.e., at 2, 6, and 10 o’clock). The carbon “behind” is shown as a circle with C–H bonds emanating from it and separated by 120° from one another. The angle of rotation between two specific bonds on the neighboring atoms is referred to as a dihedral angle. We can measure dihedral angles of 60° and 180° in the staggered conformation of ethane, depending on which specific C–H bonds are being compared.
Figure 4.2 Three representations of the staggered conformation of ethane. The Newman projection (c) provides the clearest indication of dihedral angles between neighboring C–H bonds. (Reproduced, with permission, from Carey FA, Giuliano RM. Organic Chemistry. 9th ed. New York: McGraw-Hill Education; 2014.)
It is important to note that the staggered conformation of ethane is only one of many possible conformations. These conformations may have similar or quite different energies depending on various factors, as we will see. A useful way of visualizing the relative energies of different conformers is to plot the dihedral angle between two bonds against the corresponding potential energy. Such a plot is referred to as a potential energy diagram and typically takes the form of a series of peaks and valleys of varying complexity depending on the complexity of the molecule being studied. In the next two sections we will employ Newman projections and potential energy diagrams to understand the relative energies of the major conformers of ethane and butane.
4.3 Conformations and Energies of Ethane—Torsional Strain
The staggered conformation of ethane is the most stable and thus the most populated conformation. If you were able to take a snapshot of a collection of ethane molecules, the vast majority would be observed in staggered or nearly staggered conformations. In the staggered conformation of ethane, each C–H bond possesses a dihedral angle of 60° with respect to the nearest two C–H bonds on the neighboring carbon. On the opposite extreme one can imagine a conformation in which all dihedral angles between nearest C–H bonds is 0°. Viewed in a Newman projection down the C–C bond axis, each C–H bond would block, or eclipse, a C–H bond on the carbon atom immediately behind it. Accordingly this conformation is referred to as the “eclipsed” conformation, and is the least stable conformation of ethane (Figure 4.3). Our hypothetical snapshot of ethane molecules would have very few molecules in eclipsed conformations.
Figure 4.3 Three representations of the eclipsed conformation of ethane. (Reproduced, with permission, from Carey FA, Giuliano RM. Organic Chemistry. 9th ed. New York: McGraw-Hill Education; 2014.)
The staggered conformation of ethane is lower in energy than the eclipsed conformation by about 3 kcal/mole (~12 kJ/mol). The reason(s) for the special stability of staggered conformations has been surprisingly difficult to work out, with favorable orbital-orbital interactions and repulsive interactions both playing roles. Historically, chemists have used the term torsional strain to describe the preference for staggered conformations and this description is at least intuitively satisfying. Thus torsional strain can be thought of as the excess enthalpy required to adopt an eclipsed conformation starting from a staggered one.
Now let us examine a potential energy diagram describing all possible conformations of ethane. We will start with an eclipsed conformation and arbitrarily select two eclipsed C–H bonds with a dihedral angle of zero (the bonds to red hydrogen atoms in Figure 4.4). We then perform a full 360° rotation of the carbon atom in front, while holding the other carbon atom static (i.e., we examine all possible dihedral angles). Each time the ethane molecule adopts a staggered conformation we observe an energy minimum, while each time an eclipsed conformation is produced an energy maximum is observed (Figure 4.4). Note that with three C–H bonds on each carbon we have three minima and three maxima in a full rotation. Note also that because all bonds in question are the same (C–H bonds), each of the three minima and each of the three maxima are of equal energy (such states of equivalent energy are said to be degenerate). To summarize, a rotation of 360° about the C–C bond in ethane produces three eclipsed conformations, three staggered conformations, and many additional conformations that are somewhere between eclipsed and staggered, both geometrically and energetically.
Figure 4.4 Potential energy diagram for a complete rotation about the C–C bond in ethane. (Reproduced, with permission, from Carey FA, Giuliano RM. Organic Chemistry. 9th ed. New York: McGraw-Hill Education; 2014.)
4.4 Conformations and Energies of Larger Acyclic Molecules—Steric Strain
As we consider molecules more complex than ethane, additional factors begin to influence the relative energies of different conformers. To illustrate this we will next consider conformations of n-butane (C4H10), the molecule resulting from the addition of one methyl group to each carbon atom in ethane. While n-butane possesses three C–C bonds, each of which is free to rotate, we will focus our conformational analysis on the central (C2–C3) bond. As with our analysis of ethane, we imagine looking down the C2–C3 bond axis of n-butane using Newman projections (Figure 4.5). As before, a rotation of 360° will produce three eclipsed and three staggered conformers, along with many more conformers in between. The difference in the case of n-butane is that the C1 and C4 methyl groups will also interact through space, producing what is commonly referred to as steric strain. Not surprisingly, this strain will be greatest when the two methyl groups are nearest each other, which occurs when the C1–C2 and C3–C4 bonds are eclipsed (a dihedral angle of 0°). This particular conformer is denoted syn and is the highest energy conformation of n-butane because both torsional and steric strain are maximal (all bonds are eclipsed and the C1 and C4 methyl groups are nearest each other in space).
Figure 4.5 Important conformations of n-butane shown in ball-and-stick representation and as Newman projections. (Reproduced, with permission, from Carey FA, Giuliano RM. Organic Chemistry. 9th ed. New York: McGraw-Hill Education; 2014.)
Other notable conformations of n-butane include the gauche and anti conformers, which can be produced by rotations of 60° or 180°, respectively, starting from a syn conformer (Figures 4.5 and 4.6). We expect that the anti conformer should be the most preferred conformer since the C1–C2 and C3–C4 bonds are staggered and the C1 and C4 methyl groups are maximally separated in space. Two energetically equivalent gauche conformers are produced by rotations of 60° clockwise or counterclockwise starting from the syn conformer. The gauche conformers are staggered like the anti conformer, but higher in energy since the C1 and C4 methyl groups are in closer proximity in the gauche conformation. Another way of saying this is that torsional strain is similar in the gauche and anti conformations but steric strain is greater in the gauche. A final conformer worth considering is that obtained via a 120° rotation from syn. This conformer will be eclipsed like the syn conformer but will be lower in energy since the C1 and C4 methyl groups are better separated (steric strain is reduced relative to syn).
Figure 4.6 Potential energy diagram for a complete rotation about the C–C bond in n-butane. (Reproduced, with permission, from Carey FA, Giuliano RM. Organic Chemistry. 9th ed. New York: McGraw-Hill Education; 2014.)
The relative energies of n-butane conformers can be visualized with a potential energy diagram (Figure 4.6). Note that the combined effects of torsional and steric strain results in a more complex energy diagram than was the case with ethane. You may also note that the effects of steric strain become most significant at small dihedral angles (i.e., as one approaches the syn conformation). Thus, steric strain is primarily responsible for the ~3 kcal/mol potential energy difference between the syn conformation and the other eclipsed conformations. In contrast, steric strain accounts for only a ~1kcal/mol potential energy difference between the gauche and anti conformations.
The effects of steric strain will of course be more significant as the interacting groups become larger or more numerous. For example, as one, two, or three methyl groups are added to the same carbon atom in ethane, the energetic barrier to rotation increases accordingly (Table 4.1). As halogen atoms of increasing size (F, Cl, Br, I) are added to ethane, we might well expect rotational barriers to increase and this is indeed the case as one moves from H to F to Cl. However, Cl and Br analogs surprisingly have similar rotational barriers despite the larger size of a Br atom compared to Cl. The explanation for this is that the C–Br bond is longer than the C–Cl bond and so the steric effects of the larger atom are offset by a longer bond. In the case of iodine the greater bond length more than compensates for the greater size and rotational barriers actually decrease. Note as well that methylamine (CH3NH2) and methanol (CH3OH) have rotational barriers even lower than for ethane. This can be accounted for by a reduction in torsional strain due to a smaller number of interacting bonds (only two N–H bonds in methylamine and a single O–H bond in methanol). The lone pair electrons present on N and O contribute very little to the torsional strain of these molecules.
Table 4.1 Rotational Energy Barriers about the C–X Bond in CH3–X.
In summary, torsional strain and steric strain are key factors in determining the conformational preferences of small molecules. In the coming sections we will see how these same types of strain factor in the conformations of cyclic molecules and larger drug-sized molecules.
4.5 Conformations of Small Rings
Before we consider the conformations of cyclic molecules we must consider a third source of strain in small molecules. Angle strain is most common in cyclic molecules and results when a small ring size and/or the adoption of a particular conformation results in bond angles that are smaller (or larger) than the optimal value. Consider, for example, the case of cyclic hydrocarbons ranging between three and six carbon atoms (Table 4.2). Recall that for tetrahedral, sp3 hybridized carbon, the preferred bond angle is ~109.5°. It should be obvious that C–C bond angles in cyclopropane and cyclobutane must be significantly smaller than the optimal value. Indeed, we find that cyclopropane and cyclobutane rings possess significantly greater angle strain than cyclopentane or cyclohexane, where bond angles can be very close to the ideal 109.5°.
Table 4.2 Heats of Combustion (–ΔH°) and Estimated Angle Strain for Cycloalkanes.
Now let us consider the three-dimensional conformations of three, four, and five-membered ring systems. As illustrated below, the carbon framework of a cyclopropane ring is essentially flat, with all three carbon atoms lying in the same plane and rotation about the three C–C bonds effectively precluded.
(Reproduced, with permission, from Carey FA, Giuliano RM. Organic Chemistry. 9th ed. New York: McGraw-Hill Education; 2014.)
One consequence of this arrangement is that all C–H bonds in cyclopropane are eclipsed with respect to the C–H bonds on neighboring carbons. Thus cyclopropane effectively exists in a single conformation possessing severe angle strain and near-maximal torsional strain. Nevertheless, the cyclopropane ring is found in the structures of some drugs and is an example of a kinetically stable ring system that harbors significant angle and torsional strain.
The case of cyclobutane is more interesting since some degree of rotation about C–C bonds is possible in the larger four-membered ring. The flat, fully eclipsed conformation of cyclobutane represents a high-energy extreme in which angle strain and torsional strain are maximal. Lower energy conformers of cyclobutane are those in which the carbocyclic ring is “puckered” slightly, which can be accomplished via small rotations about C–C bonds in the ring (as illustrated below). The result of these rotations is that the eclipsed C–H bonds move into partially staggered arrangements that reduce torsional strain. This analysis reveals dihedral angles smaller than the 60° value of staggered ethane, but still sufficient to relieve some of the torsional strain.
(Reproduced, with permission, from Carey FA, Giuliano RM. Organic Chemistry. 9th ed. New York: McGraw-Hill Education; 2014.)
Much more significant bond rotation is possible in the cyclopentane ring and so more effective staggering of the C–C bonds is possible. These partially staggered C–H bonds can be visualized with molecular models, or even with Newman projections, which are useful for analyzing cyclic molecules as well as acyclic ones. The puckered conformation of cyclopentane resembles an unsealed envelope with the flap lifted up (Figure 4.7(b)). Of the five C–C bonds in cyclopentane, four can adopt significantly staggered conformations but one C–C bond remains mostly eclipsed. As we will see in the next section, the cyclohexane ring is able to adopt a low-energy conformation in which all six C–C bonds are perfectly staggered and torsional strain is minimized.
Figure 4.7 Representations of the (a) planar, (b) envelope, and (c) half-chair conformations of cyclopentane. (Reproduced, with permission, from Carey FA, Giuliano RM. Organic Chemistry. 9th ed. New York: McGraw-Hill Education; 2014.)
The discussion above has focused on unsubstituted rings of three to five carbon atoms and the angle strain and torsional strain present in these rings. In the case of substituted cycloalkanes, steric interactions too impact conformational preferences. The effects of ring substitution on cyclohexane conformation will be discussed in great detail in Section 4.7 but it is worthwhile remembering that the introduction of substituents will have similar effects on the conformations of smaller ring systems as well. As an exercise, you might consider which conformations of cyclopentane (Figure 4.7) would be preferred if one or more methyl groups were added at various positions in the cyclopentane ring. The three major types of strain discussed in this and the previous two sections are summarized in Box 4.1.
