MODULE No. 16: Conformational Analysis of Cycloalkanes

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

Module Tag CHE_P1_M16

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

TABLE OF CONTENTS

1. Learning Outcomes 2. Introduction

3. Baeyer strain Theory

4. Conformational Analysis of Cycloalkanes 4.1. Cyclopropane

4.2. Cyclobutane 4.3. Cyclopentane 4.4. Cyclohexane

4.5. Monosubstituted cyclohexane

4.6. Disubstituted cyclohexanes

5. Summary

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

 Understand Baeyer strain theory for predicting stability of ring compounds and its incorrectness.

 Identify different types of strains in conformations of Cycloalkanes.

 Draw energy profile diagrams for various conformations of cyclohexane.

 Preferred configuration of substituted cyclohexanes.

2. Introduction

Three Dimensional Shapes of Organic Molecules

We live in a three dimensional world and the same is true for molecules! Molecules are three dimensional entities with well-defined shapes and structures. Though most of the time we see their 2D drawings in books, it is always a challenge to visualize their 3D shapes without the help of models. The study of stereochemistry of organic molecules allows us to visualize and draw these molecules in a better way and also to analyze and predict their behavior in 3-D space. The shapes of organic molecules depends on the type of bonds – single, double or triple. While the single bonds imparts flexibility, the double and triple bonds imparts rigidity in the molecules.

The free rotation around C-C single bond gives rise to conformations that are interconvertible without breaking any bond. And the restricted rotation around a double bond gives rise to configurations or geometrical isomers which are not interconvertible unless a bond is broken. The free rotation around all single bonds within a same molecule can give rise to various different shapes of the molecule. For example, figure 1 shows several views of the same molecule ( it is the structure of pea moth pheromone used by female moths to attract the male moths). It can be seen that without changing the bonded structure of the molecule, we can get different shapes simply by rotating the single bonds at specific sites within the molecule. Note that the arrangement around the double bond is never disturbed as their rotation is restricted!

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

Figure 1. Conformations of a pea moth pheromone

The different shapes that a molecule can adopt due to rotation about single bonds are called conformations. Since the single bonds can be rotated to any fractional amount of a degree, giving rise to a new conformation minutely different from the other, conformations are infinite in number and hence are called conformers instead of stereo-isomers, The term rotational isomers is also used often. The study of molecular conformations and their relative energies is called Conformational Analysis. Conformational analysis allows us to relate the shapes of molecules with their chemical reactivity and physical properties.

3. Baeyer Strain Theory

The theory proposed by Adolf von Bayer in 1885, popularly known as Bayer Strain theory, suggested that the angle strain in cycloalkanes increases proportionally as the deviation from regular tetrahedron geometry increases. Hence, a cyclopentane ring with an internal angle 108°

would be most stable (as it has minimum deviation from a regular tetrahedral angle of 109.5°) and angle strain would increase on either increasing or decreasing the ring size (Fig. 2).

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

Figure 2. Internal bond angles in cycloalkane rings assuming a planar structure

However, it was soon realized that cycloalkanes (except cyclopropane) are not planar compounds and the theory was not correct except for very small rings. Cycloalkanes can bend and twist about their C-C single bonds to acquire stability. Infact, a puckered structure of cyclohexane has a zero angle strain! (Fig. 3)

Figure 3. Puckered structures of cyclohexane having no or very less angle strain

One can compare the stabilities of cycloalkanes by using their heats of combustion data. Minimum value of heats of combustion suggests maximum stability. According to this data, cyclo propane has a maximum strain and is least stable while cyclohexane has the least strain and is most stable.

Figure 4. Molar heats of combustion data for cycloalkanes

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

4. Conformations of Cycloalkanes

Molecules show strain arising out of non-ideal geometry. The internal energy of the molecule is dependent on several factors. These are

Total strain energy = 1 + 2 + 3 + 4

1 = stretching and compression of bonds (bond strain) 2 = Bond angle distortion (Baeyer strain, classical strain) 3 = Tortional strain (eclipsing strain)

4 = steric strain (vander waals strain)

A molecule will adopt the geometry, that minimises its total strain energy. The method of calculation of total strain energy is spoken as molecular mechanics.

Steric strain: Any type of repulsion between two closely spaced non-bonded atoms or group of atoms is termed as steric strain. The repulsions between electrons of these closely spaced atoms imparts a destabilising effect and is the major cause of the overall strain in a molecule. It can be classified into various types of strains as described below.

Angle strain: If the angle between a pair of adjacent bonds on a carbon atom is less than the tetrahedral angle (i.e., 109.5^o) then there is a destabilisation due to the bond pair - bond pair repulsion.

Figure 5. Angle strain

Van der Waals strain: This type of strain arises when the electron clouds of a pair of bulky groups are too close to each other. It leads to an increase in energy of the system due to the electrostatic repulsion of the electron clouds.

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

Figure 6. Van der Waals Repulsion

Torsional strain: When a molecule is able to rotate around a sigma bond, the other three bonds on each carbon holding the single bond move relative to each other resulting in different levels of torsional strain. The relative movement of these bonds can be better understood in terms of dihedral angle. A dihedral angle (θ) is the angle between the two intersecting planes formed by the bonds on adjacent carbon atoms (figure 7). The maximum strain is observed when these bonds are closest to each other, i.e. in an eclipsing position (θ = 0°). Hence this strain is also known as eclipsing strain. With the rotation around the sigma bond, the dihedral angle changes and consequently the repulsion between the bonded pair of electrons (torsional strain) also changes. The strain is minimum at θ = 60° (staggered conformation).

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

Figure 7. Torsional strain and torsional angle

Ring strain: Generally, a ring or cyclic structure is less stable than an equivalent acyclic structure, primarily due to angle and torsional strain. The extra energy is released when the ring is opened is known as ring strain.

Let us now look at the conformations of specific cycloalkanes and their respective stabilities in detail.

Conformations of small rings Cyclopropane

The three carbons in cyclopropane should lie in a plane as any three points describe a plane. All the C-C bond lengths in propane are same which suggests that all the three carbons must lie at the corners of an equilateral triangle. In this geometry, the deviation from the regular tetrahedral angle is the maximum (from normal tetrahedral angle of 109.5° to 60°) and hence there is extensive strain in the cyclopropane ring. This is evident from the large heat of combustion value per methyl group.

Infact the C-C bonds in cyclopropane are bent in order to form an equilateral triangle. Further strain is imparted by eclipsing interactions as all the C-H bonds in cyclopropane are eclipsed. And C-C bond rotation to relieve this strain is not possible due to the rigidity of the ring. Hence cyclopropane is considerably strained molecule and readily undergoes reactions involving ring opening.

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

Figure 8. Planar conformation of cyclopropane: All the bonds are eclipsed

Figure 9. Orbital overlap in cyclohexane showing bent bonds Cyclobutane

In cyclobutane, the ring adopts a puckered or wing-shaped conformation. Though the distortion from the planar structure reduces the torsional strain (eclipsed bonds move slightly away), it increases the angle strain (angle decreases as the ring puckers). A balance between the two is struck when the ring puckers to about 34° (i.e. when one methylene moves 34° up or below the rest of the three carbon forming a plane). The planar form of cyclobutane (where all the bonds are eclipsed) is just 1.4 kcal/mol more in energy than the puckered conformation.

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

Figure 10. Puckered conformation of cyclobutane Cyclopentane

Unlike what was predicted by Baeyer, cyclopentane is not entirely strain free even though in a planar conformation the C-C-C bond angles are close to 109.5°. The eclipsed bonds in the planar cyclobutane impart considerable torsional strain forcing it to attain a more stable puckered conformation. The heat of combustion data indicates the total strain in the ring. On distorting the planarity, cyclopentane partly relieves the torsional strain but increases the angle strain (similar to cyclobutane). The minimum energy conformation is thus adopted by balancing the two opposing effects. There are two conformations of comparable energy, the ‘open envelope’ (with four carbon atoms in a plane and one above or below it) and the ‘twist form’ (with three carbon atoms in a plane and two above or below it). The atoms in the ring rapidly take turns not to be in the plane and cyclopentanes have much less well defined conformational properties than cyclohexanes.

Figure 11. Open envelope conformation of cyclopentane Conformational Analysis of Cyclohexane

As predicted by heats of combustion, cyclohexane is strain free ring. It has neither angle strain nor torsional strain in its chair conformation. This is because it can pucker in such a way that all of the bonds are perfectly staggered, and in this conformation all of the bonds are 109°. In the chair conformation, four carbons lie in a plane while two lie above and below this plane. There are two

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

Figure 12. Chair conformation of cyclohexane; axial and equatorial bonds in chair conformation All six axial C-H bonds are anti to each other and skew or gauche to equatorial C-H bonds and also to ring skeletal bonds as shown in the Newman projection of chair conformation of cyclohexane figure 13.

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

Figure 13. Newman projection of chair conformation of cyclohexane showing gauche interaction; cis and trans relationship of axial and equatorial bonds

Note that any pair of axial and equatorial bonds on adjacent carbon atoms are cis to each other (i.e.

they point in the same direction, either up or down) and any pair of axial-axial or equatorial- equatorial bonds on adjacent carbon atoms are trans (or anti) to each other.

Cyclohexane theoretically can exist in two different chair conformations as shown in figure and the two forms can interconvert easily through ring flipping as shown in the figure 14. Ring flipping is nothing but a rotation of single bonds in the molecule. An interesting point to note in this interconversion is that all the axial bonds in ring 1 (chair) become equatorial bonds in ring 2 (inverted chair) and vice versa.

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

Figure 14. Ring flip in cyclohexane: interconversion of chair and inverted chair conformations There are other infinite conformations of cyclohexane of varying energies besides chair conformation due to the rotation around single bonds. Some of them with special names are boat, twist boat and half chair conformations (ones representing the peaks and valleys in the energy diagram of cyclohexane conformations) as shown in figure 15.

Figure 15. Energy Diagram of various conformations of cyclohexane

From the figure we can see that chair conformation has the minimum energy out of all the possible conformations and is therefore called the ground state conformation of cyclohexane. The boat conformation is 6.9 kcal/mol higher in energy than the chair conformation. This may largely be attributed to torsional strain among the four pairs of hydrogens and to some extent to the flagpole interactions between the hydrogens on the diagonally opposite carbons (figure 16). In twist boat conformation, the planarity of the four carbons (as in boat) is distorted or twisted and hence the

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

name ‘twist boat’. By twisting the planar carbons, the strain due to eclipsed bonds (in boat) is somewhat relieved. The twist boat conformation is only 0.4 kcal/mol more stable than the boat conformation. In fact, boat conformation is the transition state in moving from one twist boat to another. Likewise the two half chair conformations (represented by the highest energy peaks) are the transition states in the interconversion of one chair form to another. Table 1 summarizes the amount and types of strain in various conformations of cyclohexane.

Figure 16. Boat, twist boat and half chair conformations of cyclohexane Table 1. Types of strain in various conformations of cyclohexane

Conformation Angle strain Torsional strain Van der Waals strain

Flagpole strain

Chair × × × ×

Boat × √ √ √

Twist boat √ (slight) √(slight) √(slight) ×

Half chair √ √ √ ×

These relative energies of conformations are only for unsubstituted cyclohexane, the presence of substituents can change their relative energies.

Let us see how the presence of one or two substituents on the cyclohexane ring effect the energies of various conformations.

Monosubstituted cyclohexane : Methyl cyclohexane

Though all the six carbons in cyclohexane are equivalent, there are two types of bonds on each carbon - namely axial and equatorial where the substituent can be placed. Let us take methyl group as the substituent for conformational analysis of monosubstituted cyclohexane. The two

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

Figure 17. Chair conformations of methylcyclohexane showing axial and equatorial methyl group Which of the two is more stable? If we draw Newman projection for methylcyclohexane, we will see that the axial methylcyclohexane experiences gauche interactions between the methyl group and ring methylene (figure 18) while equatorial methylcyclohexane has no such interactions and hence has somewhat lesser energy than the axial methylcyclohexane. Besides gauch interactions, axial methyl group experience steric repulsions from the nearby axial hydrogens which further increases the energy of axial methylcyclohexane. These steric interactions between the substituent in axial position at C-1 and the axial hydrogens at C-3 are called 1,3-diaxial interactions (figure 17). When the methyl group is at equatorial position, there are no significant gauche interactions as methyl group is anti to ring C-C bond. There are no diaxial interactions as well and hence equatorial conformation becomes more stable than the axial. The equatorial conformation is favored in the equilibrium because the axial isomer has about 1.8 kcal/mol of steric strain. This observation can be generalized to all the substituents, if present at the equatorial position will always be more stable than at the axial position.

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

Figure 18. Newman projection of chair conformations of methylcyclohexane showing axial and equatorial methyl group

Disubstituted cyclohexane: 1,2-disubtitution

Because of the restricted rotation around the ring carbons, 1,2-dimethylcyclohexane can exist as geometrical isomers (i.e. either cis or trans isomer). Recall that cis and trans isomers are geometrical isomers (or diastereoisomers) and cannot be readily interconverted by a simple rotational process (a bond must be broken). They are not different conformations of the same isomer. As discussed above, the cis isomer is the one where one of the methyl substituent occupies axial position and the other occupies equatorial position (a,e conformer, both the bonds pointing upwards) or vice versa (e,a conformer, both the bonds pointing downwards) as shown in figure 19.

Figure 19. Chair conformations of cis-1,2-dimethylcyclohexane showing axial and equatorial methyl groups

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

Figure 20. Chair conformations of trans-1,2-dimethylcyclohexane showing axial and equatorial methyl groups

Out of the cis and trans configurations, trans isomer would be more stable in its e,e conformation as both the methyls are placed at less hindered equatorial positions. However, there is a slight destabilizing gauche interaction between the two methyl groups in this conformation amounting to 0.9 kcal/mol of energy. On the other hand, the a,a conformation is highly unstable due to strong gauche and 1, 3-diaxial interactions raising the energy to 3.6 kcal/mol (1.8 kcal/mol for each axial substituent).

The cis conformers, a,e and e,a, are both equal in energy, i.e. 1.8 kcal/mol (equivalent to one axial substituent) and can interconvert through ring flipping. The Newman projections of Chair conformations of cis and trans-1,2-dimethylcyclohexane are shown in figure 21.

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

Figure 21. Newman projection of Chair conformations of cis and trans-1,2-dimethylcyclohexane 1,3-disubtitution

In 1,3-disubtituted cyclohexane the two geometrical isomers, cis and trans are shown in figure by using Newman projection formula. The cis isomer has either both methyls on axial positions (a,a) or both on equatorial positions (e,e). While the trans isomer has one of the methyls on axial and other on equatorial position in both the conformers (a,e and e,a).

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

Figure 22: Newman Projection

The diaxial (a,a) and diequatorial (e,e) conformers of cis isomer has a considerable energy difference. The diaxial conformer is much less stable not only due to destabilising gauch interactions but also due to the severe 1,3-diaxial interactions. As both the methyl groups lie on the same side if the ring and at 1,3-positions they suffer strong strain due to axial methyl-axial methyl interactions (1,3-diaxial interaction) (figure) as compared to axial methyl-axial hydrogen interaction in monosubstituted methylcyclohexane. These destabilizing interactions (gauch and 1,3-diaxial) raises the energy of diaxial cis isomer resulting in very insignificant amount of ring flipping giving rise to this isomer. On the contrary, the diequatorial (e,e) conformer is absolutely strain free and thus the ring prefers to remain in this conformation.

Figure 24: 1,3-diaxial conformation

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

The trans isomer has both the conformers equivalent in energy (a,e or e,a) and thus ring flipping occurs without any preference.

Figure 25

Out of the cis and trans isomers of 1,3-dimethylcyclohexane, the cis isomer is the most stable where both the substituents occupy equatorial positions. Note that both the conformers of trans isomer are less stable than the diequatorial cis-isomer, mainly due to gauch interactions, but are more stable than the diaxial cis-isomer.

1,4-disubtitution

Figure 26: The cis and trans isomers of 1,4-dimethylcyclohexane

Note that in the cis isomer, one of the methyl groups occupies axial position while the other occupies equatorial position (a,e conformer). The ring flip reverses this arrangement and we get e,a conformer having identical amount of strain. Hence the two conforms, a,e and e,a are equal in energies and are easily interconvertible.

On the contrary, the trans isomers differ significantly in energies between a,a and e,e conformers.

The diequatorial (e,e) conformer is has no strain at all as both the methyl groups lie on the less hindered equatorials positions. The ring flip gives the diaxial (a,a) conformer which has considerable strain due to gauche interactions between the methyl groups and ring methylene. Each

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

Table 2. Summary of Conformational analysis of disubstituted cycloalkanes Position of the

substituents

cis-isomer trans-isomer Most stable

1,2 a,e or e,a a,a or e,e trans (e,e)

1,3 a,a or e,e a,e or e,a cis (e,e)

1,4 a,e or e,a a,a or e,e trans (e,e)

It can be concluded from the above table that placing the substituent on the equatorial position always leads to stabilisation!

Both trans-1,4-dimethylcyclohexane and cis-1,3-dimethylcyclohexane have essentially the same energy, since neither one of them has any strain at all.

CHEMISTRY PAPER No. 1: Organic Chemistry-I (Nature of bonding and Stereochemistry)

MODULE No. 16: Conformational Analysis of Cycloalkanes

5. Summary

 Stereochemistry is the study of 3D structures and shapes of organic molecules. It allows us to visualize, draw and understand these molecules in a better way and also to analyze and predict their behavior in 3-D space.

 The different shapes that a molecule can assume due to rotation about single bonds are called conformations. The study of molecular conformations and their relative energies is called Conformational Analysis.

 The stabilities of cycloalkanes can be compared by using their heats of combustion data.

Minimum value of heats of combustion suggests maximum stability. A puckered structure of cyclohexane has a zero angle strain!

 Various types of strain that we need to be familiar with while working with cycloalkanes are: angle strain, torsional strain, and van der Waals strain.

 Cyclopropane is considerably strained molecule with all the atoms in a plane and all C-H bonds completely eclipsed with no possibility of rotation around C-C single bonds.

 Cyclobutane, the ring adopts a puckered or wing-shaped conformation to relieve torsional strain but in doing so acquires angle strain.

 Cyclopentane adopts either an open envelope or a twist conformation and keep changing the envelope flap around the ring generating five possible puckered conformers and thus have less well defined conformational properties.

 Cyclohexane, in chair conformation is strain free as all the C-H bonds are anti to each other and there is no angle strain. It can have two chair conformations (chair and inverted chair) which can interconvert by ring flipping. Ring flipping changes all the equatorial bonds to axial and axial bonds to equatorial.

 Other significant conformations of cyclohexane boat, twist boat and half chair conformations. The relative energies of these conformations are : Chair < twist boat < boat

< half chair.

 The boat conformation possess torsional strain due eclipsing of four C-H bonds and flagpole interactions. It is 6.9 kcal/mol more than the chair conformation.

 Twist boat and half chair are more in energy than the chair conformation by 5.5 kcal/mol and 10 kcal/mol respectively.

 Monosubtitution in cyclohexane prefers equatorial position which is free from gauch or steric strain as compared to axial position which is energetically destabilized due to gauch and 1,3-diaxial interactions. One axial substitution roughly costs 1.8 kcal/mol of energy.

 Same is true for di-substituted cyclohexanes, where the preferred position of the substituents are equatorial over axial.