Cyclohexanes

Sugars, steroids, alkaloids and many drugs are built on rings of six atoms, and six-membered rings turn up far more often than rings of any other size. The reason is geometric. Six carbons can close into a ring that carries almost no strain, and no smaller ring can.

Ring strain is the extra energy a ring holds because closing the loop forces its bonds into worse positions than they would take in an open chain. It comes in three kinds.

Three kinds of ring strain

Start with cyclopropane, C₃H₆, three carbons joined in a triangle. Each carbon is sp³, so its bonds would like to sit 109.5° apart, the tetrahedral angle from Molecular geometry. The triangle holds every C–C–C angle at 60° instead. Squeezing an angle that far costs energy, and that cost is angle strain. The orbitals that make each C–C bond can no longer point straight at each other, so they overlap poorly and the bond is weaker.

Now sight down one of cyclopropane’s C–C bonds, as in a Newman projection. Each hydrogen on the front carbon sits directly in front of a hydrogen on the back carbon. In an open chain the bond would simply turn to a staggered view, but the ring locks it in place. The cost of the eclipsed bonds is torsional strain, the same eclipsing cost as in ethane. Every flat ring pays it, because in a flat ring the bonds on every pair of neighboring carbons are eclipsed.

The third kind is easiest to see in gauche butane. Its two methyl groups sit 60° apart, so nothing is eclipsed, yet this conformation is 0.9 kcal/mol higher in energy than anti, because the methyls bump into each other. That is steric strain: the cost of two atoms that are not bonded to each other being pushed too close together in space.

The repulsion behind steric strain is called van der Waals repulsion. Every atom is wrapped in a cloud of electrons. Push two clouds into the same space and their electrons repel each other, long before the nuclei come anywhere near touching. Groups attached to a cyclohexane ring can clash in the same way. The next section, Axial/equatorial, shows where it happens and calls it a 1,3-diaxial interaction.

The three kinds are separate, and a ring can trade one for another. It settles into the shape where their sum is lowest, and whatever strain is left in that shape is its total ring strain.

Where the strain numbers come from

Ring strain is measured, not estimated from a drawing. The measurement is the heat of combustion: the energy released when a compound burns completely to CO₂ and water. Burn a long straight-chain alkane, which has no strain, and each CH₂ group in it releases 157.4 kcal/mol.

The same subtraction works for any cycloalkane, because every one is built only from CH₂ groups. Multiply 157.4 by the number of carbons, and whatever the ring releases beyond that is its ring strain.

Raw heats of combustion can be compared directly only between isomers, compounds with the same formula. A bigger molecule releases more heat simply because it has more bonds to burn. Between two isomers, though, the more strained one starts higher in energy, so it releases more.

Ring strain does not have that limit. The subtraction has already removed the heat that comes from size, so the strain of a three-carbon ring can be set directly against that of a six-carbon ring.

Later sections compare chair shapes that differ by only a kcal/mol or two. Differences that small are still real, and they can be measured.

Small rings pay these costs differently

The table gives each ring’s total strain in kcal/mol, worked out by that subtraction from measured heats of combustion.

Cyclopropane has to be flat, because any three points lie in one plane. It is stuck with its 60° angles and with every C–H bond eclipsing its neighbor. Its bonds are so distorted that chemists often call them bent bonds, or banana bonds: the electron density between two carbons bulges outside the straight line that joins them. Strain this large is why cyclopropane rings break open in reactions that ordinary alkanes never undergo.

Cyclobutane could stay flat, with 90° angles, which would already mean less angle strain than cyclopropane has. Instead it puckers: it folds slightly out of the flat shape. The fold closes its angles to about 88°, which is worse, but it staggers the hydrogens a little and relieves some of the eclipsing. A ring that accepts worse angles to reduce eclipsing shows that torsional strain is no small effect.

A flat cyclopentane would have 108° angles, almost exactly ideal, so its problem is eclipsing, not angles. It relieves most of the eclipsing by folding into an envelope: four carbons stay in one plane and the fifth lifts out of it, like the flap of an envelope. The fold narrows the angles to about 104°. That costs a little angle strain but saves much more torsional strain, and 6.5 kcal/mol of strain remains.

Past six carbons, strain comes back from a new source. In larger rings some hydrogens on opposite sides of the ring point into the middle and crowd each other. This is transannular strain; the word means “across the ring”. A small ring is too tight for its hydrogens to point inward, and a large ring has room to keep them apart.

Cycloheptane pays about 6.4 kcal/mol and cyclooctane about 10. Rings of roughly eight to eleven carbons, called medium rings, are the most strained sizes after the small rings. From about fourteen carbons up, a ring is floppy enough to find a shape with no eclipsing and no crowding across the ring, and its strain falls back to near zero.

Why the chair works

Now try six carbons. Forced flat, cyclohexane would be a regular hexagon with 120° angles, 10.5° wider than ideal. All six ring bonds would also be eclipsed. At each one, two pairs of hydrogens line up, so a flat ring would carry twelve eclipsed pairs.

The real molecule avoids both problems by puckering into a chair, named for its shape. One end of the ring tips up like a headrest, the other tips down like a footrest, and the four carbons between them lie in one plane. Two things go right in this shape at once.

Angles. Every C–C–C angle in a chair is about 111°, within two degrees of the ideal 109.5°, so there is almost no angle strain.

Torsion. Sight down any ring bond of a chair and you see a perfectly staggered Newman projection. Each group on the front carbon sits between two groups on the back carbon, 60° from each, and nothing in the ring is eclipsed, so there is almost no torsional strain either.

Meeting either condition alone is easy; meeting both at once takes six carbons and a pucker. Five carbons are too few, because cyclopentane cannot stagger every bond. At seven, hydrogens start to crowd across the ring. So cyclohexane’s total ring strain is essentially zero (0.1 kcal/mol in the table), as low as an open chain’s.

Drawing a chair that works

A good chair drawing is worth ten minutes of deliberate practice. The sections after this one read the direction of every bond on the ring straight off your drawing, and a badly drawn chair gives wrong answers.

Draw two parallel lines, offset from each other. Join their ends with a second pair of parallel lines, then close the ring with a third pair. A chair is made of exactly three pairs of parallel lines. If your drawing does not break down into three such pairs, it is not a chair.

Then check the ends: one must point up and the other down. A minute spent turning a model in your hands, or cyclohexane in the 3D Molecule Viewer, teaches this faster than reading does.

The other conformations

The chair is cyclohexane’s lowest-energy shape, but not its only one. Push the chair’s down end up, so that both ends point the same way, and you get the boat. The boat sits about 6.5 kcal/mol above the chair, for two reasons. On each raised end, one hydrogen points in toward the other end. These two are the flagpole hydrogens, and they crowd each other. And the two long sides of the boat are eclipsed.

Twist the boat slightly and you get the twist-boat, about 5.5 kcal/mol above the chair. The twist moves the flagpole hydrogens apart and partly staggers the eclipsed bonds, so the twist-boat is lower in energy than the boat.

These shapes are not all the same kind of thing. Some are energy minima, or dips: any small change of shape from a minimum raises the energy, so a molecule can rest there briefly, long enough in principle to be detected. Others are transition states: the highest point on the path from one shape to another. A molecule passes over a transition state within a single vibration and is never found sitting in one.

The chair is the deepest minimum. The twist-boat is a minimum too, although a shallow one. The boat is a transition state, the peak between two twist-boats. The highest peak of all is the half-chair, about 10.8 kcal/mol above the chair. In it, four carbons joined in a chain lie in one plane (the chair’s four level carbons are two separate pairs), which opens their angles and eclipses the bond in the middle of the chain. The half-chair is the transition state between a chair and a twist-boat, so every molecule that leaves a chair has to pass over it.

In unsubstituted cyclohexane, more than 99% of molecules are in a chair at any moment. The other shapes matter mainly as stops on the way from one chair to another, a path that the Ring flips section follows step by step.

What carries forward

The chair is the setting for the rest of this chapter. The next section names the two directions a bond on a chair can point, and those directions decide how every substituted six-membered ring behaves.

Two later chapters build on this page. In Substitution & Elimination you will meet E2 eliminations, which remove two groups from neighboring carbons to form a C=C bond; the chair decides which of them can happen at all. In Alcohols, Ethers & Related Chemistry, ring strain explains why epoxides, three-membered rings that contain an oxygen, react far more readily than ordinary ethers. The same strain arithmetic applies.