Conformational Isomerism and Newman Projections

Conformations are the different spatial arrangements of a molecule that arise from rotation about single bonds, and a Newman projection is a way of drawing them by looking down a C–C bond; the staggered conformation of ethane is about 12 kJ/mol more stable than the eclipsed one. In brief: in butane the anti conformation is the most stable, the gauche conformation is 3.8 kJ/mol higher in energy, and at 25 °C about 70 % of butane molecules are anti and 30 % gauche.

Single bonds are not rigid: groups can rotate around them, and the molecule is constantly changing between conformations. Conformational analysis explains the shapes of molecules, the stability of rings and the reactivity of many compounds. This article explains how to draw and read Newman projections, analyzes ethane, butane and cyclohexane, with energy data tables and calculations of populations, and shows why the chair form of cyclohexane is so important.

What is a Newman projection?

A Newman projection shows a molecule viewed along one C–C bond. The front carbon is represented by a point (the center of a circle) from which three bonds radiate, and the back carbon by the circle itself, with three bonds emerging from its edge. The angle between a bond on the front carbon and a bond on the back carbon, measured in the projection, is the dihedral (torsion) angle. In the staggered conformation the dihedral angles are 60°, and the bonds of the front and back carbons are as far apart as possible. In the eclipsed conformation they are 0°, and each bond on the front carbon hides one on the back. Another notation is the sawhorse projection, which shows the molecule from an oblique angle.

What are the conformations of ethane?

As one methyl group rotates relative to the other by 360°, the energy goes through three maxima (eclipsed) and three minima (staggered). The eclipsed form is about 12 kJ/mol (2.9 kcal/mol) higher in energy than the staggered form. The difference is called the torsional strain, and is caused mainly by the repulsion between the electrons in the eclipsed C–H bonds, and partly by the stabilizing effect of hyperconjugation in the staggered form. The barrier of 12 kJ/mol is small compared with the thermal energy at room temperature (RT = 2.48 kJ/mol), so the rotation is very fast: rate ≈ (k_BT/h) e^−12/2.48 = 6.2 × 10¹² × 0.0079 = 4.9 × 10¹⁰ s⁻¹. The conformers of ethane cannot be separated.

What are the conformations of butane?

Looking down the C2–C3 bond of butane, each carbon has a methyl group and two hydrogens. Four conformations of special interest are found as the dihedral angle between the two methyl groups changes:

• Anti (180°): staggered, with the methyl groups as far apart as possible. This is the most stable conformation.
• Gauche (60° and 300°): staggered, with the methyl groups close to each other. The steric repulsion (van der Waals strain) between the methyl groups raises the energy by about 3.8 kJ/mol. There are two gauche conformers (mirror images of each other).
• Eclipsed (120° and 240°): a methyl group eclipses a hydrogen. About 16 kJ/mol above anti.
• Totally eclipsed (0°): the two methyl groups eclipse. The highest energy, about 19 kJ/mol above anti, from the combined torsional and steric strain.

Energies of the butane conformations

What are the conformations of cyclohexane?

Cyclohexane is not flat. If it were a regular planar hexagon, the C–C–C angles would be 120°, much larger than the ideal 109.5°, and all the hydrogens would eclipse. By puckering, the molecule achieves the chair conformation, in which all the bond angles are close to 109.5° (about 111°) and all C–H bonds on adjacent carbons are staggered. The chair is free of strain, and is the most stable conformation. Other conformations are the boat (about 30 kJ/mol less stable, because of eclipsing and the interaction of the two “flagpole” hydrogens), the twist-boat (about 23 kJ/mol) and the half-chair transition state (about 45 kJ/mol).

In the chair, the twelve hydrogens are of two kinds: six axial (parallel to the ring axis, pointing alternately up and down) and six equatorial (pointing outward around the ring’s “equator”). The ring flips between two chair forms with a barrier of about 45 kJ/mol, at about 10⁵ times a second at room temperature, and axial and equatorial positions exchange. In a substituted cyclohexane, the two chairs are different in energy: a substituent in an axial position has steric repulsion with the two other axial atoms on the same side of the ring (1,3-diaxial interactions), so large groups prefer the equatorial position.

Axial and equatorial preferences

A tert-butyl group is so large that the ring is essentially locked in the chair with this group in the equatorial position.

Worked examples

Example 1: the populations of butane conformers

At 298 K, RT = 2.479 kJ/mol. The ratio of one gauche conformer to the anti is e^−3.8/2.479 = e^−1.533 = 0.216. There are two gauche conformers, so the gauche : anti ratio is 2 × 0.216 = 0.432. The fraction anti is 1 / (1 + 0.432) = 0.70 (70 %), and gauche 30 %. The totally eclipsed form is so high in energy (e^−19/2.479 = 4.7 × 10⁻⁴) that it is only a transition state.

Example 2: methylcyclohexane

The equatorial conformer is 7.3 kJ/mol lower in energy than the axial. K = e^7.3/2.479 = e^2.945 = 19. The equatorial conformer fraction is 19 / 20 = 0.95 (95 %), and the axial is 5 %.

Example 3: cis- and trans-1,4-dimethylcyclohexane

In the trans isomer, both methyl groups can be equatorial (diequatorial), which is the favored chair with no 1,3-diaxial strain, and the other chair has both axial. In the cis isomer, one methyl is axial and the other equatorial in either chair, so the molecule always has one axial methyl, about 7.3 kJ/mol of strain. The trans isomer is therefore about 7 kJ/mol more stable than the cis.

Example 4: how to draw a Newman projection of butane

Look from C2 toward C3. The front carbon (C2) has the methyl group at the top, and two H atoms at the lower left and lower right. The back carbon (C3) has a methyl at the bottom (anti conformation), and two hydrogens at the upper left and upper right. The methyl groups are at 180° from each other. Rotate the back carbon by 120° and the methyl groups are at 60°: gauche.

Example 5: energy of a rotation

In 1 mole of ethane at 25 °C, what fraction of the molecules is in the eclipsed conformation at a given moment? Taking the barrier of 12 kJ/mol, the ratio of eclipsed to staggered is e^−12/2.479 = 0.0079, so about 0.8 % of the time is spent near the eclipsed state, but because the eclipsed form is a maximum, it is not a stable conformation.

Who developed conformational analysis?

Kemp and Pitzer showed in 1936 that rotation about the C–C bond in ethane is not entirely free, but has a barrier of about 12 kJ/mol. Hermann Sachse proposed in 1890 that cyclohexane exists in non-planar strain-free forms, which was ignored for decades. Odd Hassel in Norway used electron diffraction in the 1930s to show that cyclohexane exists in a chair form with axial and equatorial bonds, and Derek Barton introduced conformational analysis into organic chemistry in 1950, showing that the reactivity of molecules depends on the conformation. Hassel and Barton shared the Nobel Prize in Chemistry in 1969. Melvin Newman introduced the projection that bears his name in the 1950s.

Which mistakes are common?

• Calling conformers different compounds: they interconvert quickly by rotation.
• Drawing cyclohexane as flat: the chair is the realistic shape.
• Confusing staggered with anti: anti is a special staggered arrangement with the largest groups at 180°.
• Putting large substituents axial: they prefer the equatorial position.
• Mixing up the dihedral angle with the bond angle: they are different quantities.