The ring that is not alternating

All six carbon–carbon bonds are the same length, and the molecule is 150 kJ/mol more stable than it has any right to be. Two independent measurements, neither of which needs a theory of aromaticity in order to be stated.

1825 – 193616 min

By the end you should be able to

State the two measurements that settle benzene’s structure, and why each one alone is not enough
Do the hydrogenation arithmetic and get the resonance energy out of it
Give Lonsdale’s 1929 result and say why hexamethylbenzene rather than benzene
Explain why resonance is not oscillation, and what Kekulé actually proposed

Benzene arrives from the gasworks. In 1825 Michael Faraday was handed the oily residue that collected in cylinders of compressed illuminating gas — the gas that lit London — and pulled a new liquid out of it, which he named bicarburet of hydrogen. Nine years later Eilhard Mitscherlich made the same substance from benzoic acid and lime, and got the formula: C₆H₆. That formula is a scandal. Six carbons in an open chain, fully saturated, is hexane, C₆H₁₄. Benzene is missing eight hydrogens. Every other compound that far short of hydrogen was a violently reactive thing that would add bromine on contact, polymerise if you looked at it, and generally not sit in a bottle.

And benzene sits in a bottle. It does not decolourise bromine water. An alkene does that instantly; it is the standard test. Benzene needs a catalyst before it will react with bromine at all. It substitutes rather than adds. Push it hard enough and a hydrogen comes off and a bromine goes on, and the ring survives. An alkene would have taken the whole Br₂ across the double bond and stopped being an alkene. It is thermally stable, unusually so, in a way that a molecule with three double bonds has no business being. So there are two puzzles, not one. What is the structure — and why does a molecule that unsaturated behave like a saturated one? For seventy years the second question had no answer at all, and the first had an answer with a hole in it.

August Kekulé’s answer, published in Paris in 1865, is the ring. Six carbons in a closed loop, one hydrogen on each, and the bonds alternating — single, double, single, double, single, double. Every carbon gets its four bonds. The formula comes out exactly right. And it does something a formula alone cannot: it predicts a count. One monosubstituted benzene. Replace any hydrogen on a ring and you can rotate the ring to superimpose it on any other choice. However you make C₆H₅Br, you get the same substance — and however anyone made it, they did. Three disubstituted benzenes. Put the second substituent one, two or three positions round: ortho, meta, para. Three, and no more. Chemists had found three and no more. That is a real prediction, checked against real bottles, and it is why organic chemistry became a subject about arrangements in space rather than a catalogue of reactions. It deserves the reputation it has.

The hole in it, and the repair

Kekulé saw the problem himself, and it is the ortho compounds. If the bonds alternate, then two adjacent positions on the ring are not equivalent. One neighbouring pair has a double bond between them; the next pair along has a single bond. Substituting on either side of a double bond and either side of a single bond gives two different molecules. So the alternating ring predicts four disubstituted benzenes, not three. And only three exist. His repair, in 1872, was the oscillation hypothesis: the double bonds swap places continually, faster than any experiment can follow, so that on any timescale a chemist can reach, all six bonds and all six adjacent pairs are equivalent. It is worth being clear about what kind of move that is. It is a patch — a mechanism invented specifically to absorb a fact the theory predicted wrongly — of exactly the sort phlogiston’s defenders used when the calx came out heavier. And, like theirs, it is not stupid. Molecules do move; nothing in 1872 said they could not move that way; and no instrument then or for fifty years afterwards could look inside a molecule to check. What finishes a patch is not an argument. It is a measurement it cannot survive, and there turn out to be two.

Start on the alternating ring, drawn with its bonds to scale, and drag it round to see it is flat. Then press "What was measured" and compare the six numbers.

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A carbon–carbon double bond is 1.339 Å and a single bond is 1.535 Å — a difference of 0.196 Å, which by 1930 was twenty times anyone’s error bar. An alternating ring is therefore a visibly lumpy hexagon. The measured ring is not: all six bonds are 1.397 Å, which is neither of the two values and is also shorter than their average of 1.437 Å.

The experiment

The structure of the benzene ring in hexamethylbenzene

Kathleen Lonsdale, in W. H. Bragg’s laboratory at the Royal Institution · 1929 · London

The question: Is the six-membered ring flat, and are its six carbon–carbon bonds the same length or two alternating lengths?
The apparatus: X-ray diffraction photographs of crystalline hexamethylbenzene — benzene with a methyl group in place of every hydrogen. The choice of compound is the whole design: hexamethylbenzene is triclinic with ONE molecule in the unit cell, which forces the molecule onto a centre of symmetry and leaves nothing to disentangle. Benzene itself is a liquid at room temperature and an awkward crystal below it.

Theory predicted

On the alternating structure, three short bonds around 1.34 Å and three long ones around 1.54 Å. On the oscillation hypothesis, a time average — which for a diffraction measurement means an apparent length near 1.44 Å, midway between them.

They measured

A planar, regular hexagon. All six ring bonds equal at about 1.42 Å within her uncertainty, and the six methyl carbons attached at 1.53 Å — an entirely ordinary single-bond length, which is the internal control that says the method could have seen a long bond if there had been one.

How sure could they be? Solved by hand. Structure factors were computed with logarithms and a slide rule, Fourier syntheses summed by arithmetic, and the trial structure adjusted until the calculated intensities matched the photographs. There were no machines of any kind involved, and it took months.

Why it mattered

The ring is flat and regular. That kills the static alternating structure outright — three long bonds and three short ones is not what a regular hexagon looks like — and it puts the oscillation hypothesis under pressure, because later, better measurements on benzene itself gave 1.397 Å, well short of the 1.437 Å that alternating bonds would average to. What it cannot do on its own is kill oscillation completely, since diffraction averages over time. That takes a heat.

A photographic portrait of Kathleen Lonsdale in middle age, seated, in a dark jacket, looking towards the camera. — She solved the structure by hand, from photographic plates, with logarithms and a slide rule. The choice of hexamethylbenzene rather than benzene is the part of the work that does not show up in the answer — picking a crystal whose symmetry does the reasoning for you is the whole craft of early crystallography.

Lonsdale is usually a footnote in this story, and she should not be. She was born Kathleen Yardley in Newbridge, County Kildare, the tenth child of a postmaster, and joined W. H. Bragg’s group at the Royal Institution in 1922 at the age of nineteen. The hexamethylbenzene structure was hers, and so was the choice of compound that made it tractable at all. She went on to compile the International Tables for X-ray Crystallography, which is the book every structural chemist on earth then worked from, and to establish the C–C distances in diamond and graphite by the same methods. In 1945 she and the microbiologist Marjory Stephenson became the first two women elected Fellows of the Royal Society. She was the first woman to hold a professorship at University College London, the first to preside over the International Union of Crystallography, and the first to preside over the British Association. In 1943 she spent a month in Holloway prison. A Quaker and a pacifist, she had refused to register for civil defence duties, and then refused to pay the fine.

One length, and it is the wrong one

Later work on benzene itself — solid-state X-ray work by Cox from 1932, then gas-phase electron diffraction, then neutron diffraction and microwave spectroscopy — converged on the number now in every table. Every carbon–carbon bond in benzene is 1.397 Å. Hold that against the two lengths it is supposed to be made of: A double bond, in ethene, is 1.339 Å. A single bond, in ethane, is 1.535 Å. The first thing to notice is that 1.397 is neither. The second, and more useful, is that it is not their average either: the average is 1.437 Å, and the measured bond is four hundredths of an ångström shorter than that. That second point is what makes the measurement decisive rather than merely suggestive. A ring whose bonds genuinely alternated but swapped places quickly would show up in a diffraction experiment as an average, because diffraction integrates over time. It would show up at 1.44 Å. It shows up at 1.40 Å. So the six bonds are not two kinds of bond taking turns. They are one kind of bond, and it is a kind that did not previously exist in anyone’s list.

The experiment

Heats of hydrogenation of cyclohexene, cyclohexadiene and benzene

George Kistiakowsky, with J. R. Ruhoff, H. A. Smith and W. E. Vaughan · 1936 · Harvard

The question: Structure aside — how much energy does benzene actually hold, compared with a molecule made of three ordinary double bonds?
The apparatus: A gas-phase calorimeter at 82 °C with a nickel catalyst. Hydrogen is added to each unsaturated ring in turn and the heat released is measured. The design point is that all three rings end up as the same substance, cyclohexane, so the heats are directly comparable without any assumption whatever about what the starting materials are made of.

Theory predicted

If a double bond in a ring releases about the same heat wherever it sits, then two double bonds should release twice as much as one, and three should release three times as much. Cyclohexene gives 119.6 kJ/mol, so a ring with three isolated double bonds should give about 359 kJ/mol.

They measured

1,3-cyclohexadiene gives 231.7 kJ/mol, against the 239.2 that two isolated double bonds predict — short by 7.5, which is what conjugating a pair of double bonds is worth. Benzene gives 208.3 kJ/mol, against 359. Short by 150.

How sure could they be? The measurements are calorimetry on gases with a catalyst, reproducible to about a kilojoule per mole. A 150 kJ/mol discrepancy is a hundred times that, and the diene, measured on the same apparatus by the same people, is the control that shows a small effect looks small.

Why it mattered

This is the measurement the oscillation hypothesis cannot survive. A molecule that is a cyclohexatriene at every instant — whichever of the two it happens to be at that instant — still contains three double bonds at every instant, and still owes their hydrogenation energy. It does not pay. Benzene simply starts 150 kJ/mol lower than any structure anyone could draw for it, and the shortfall is a measurement rather than an interpretation.

Read the ladder from the bottom. Cyclohexane is the floor because everything ends there. The dashed rung is the only level that was never measured — it is three times cyclohexene, and benzene sits far below it.

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Four levels, three of them measured directly and one extrapolated. The gap between the dashed rung and benzene is the resonance energy: energy the molecule turns out never to have had, inferred entirely from heat that failed to appear. Note also how small the diene’s shortfall is beside it — conjugation is real, and it is not remotely enough to account for the ring.

Problem

How much is the ring worth?

Cyclohexene, with one double bond, releases 119.6 kJ/mol when hydrogenated to cyclohexane. A hypothetical "cyclohexatriene" — a ring of three isolated double bonds — should release three times as much. Benzene actually releases 208.3 kJ/mol. By how much does benzene fall short of the prediction?

Cyclohexene → cyclohexane: -119.6 kJ/mol
1,3-cyclohexadiene → cyclohexane: -231.7 kJ/mol
Benzene → cyclohexane: -208.3 kJ/mol
All three give the same product: cyclohexane, C₆H₁₂

You might think

Benzene flickers rapidly between the two Kekulé structures, and that is what resonance means.

Actually

It does not flicker, and resonance is not a rate. There is no interval, no frequency, and no moment at which the molecule is one structure rather than the other; benzene has a single, unchanging electronic state with sixfold symmetry, and the vibrational spectrum shows that symmetry directly. The two Kekulé drawings are basis functions in a mathematical expansion of that one state — the way a musical note is not taking turns between its harmonics, but is made of them at once. The double-headed arrow between the two rings means "these are two terms in one description", and it is drawn differently from an equilibrium arrow for exactly this reason. It is worth being precise about this, because the flickering picture IS Kekulé’s 1872 oscillation hypothesis, which was a claim about time and which the hydrogenation heat refutes: a molecule that really was a cyclohexatriene at every instant would owe three double bonds’ worth of energy at every instant, and benzene does not pay it.

The part the story usually rounds off

You will see 150 kJ/mol quoted as though it were a measured constant of benzene, like a bond length. It is not, quite. The trouble is the thing it is measured against. "Cyclohexatriene" does not exist and never has, so the 359 kJ/mol is an extrapolation from cyclohexene — and a slightly unfair one, because a real molecule with three alternating bonds would have different bond lengths, different ring strain and different hybridisation from benzene. Correct for those and the number moves. Use 1,3-cyclohexadiene as the yardstick instead and you get a smaller answer, because the diene already contains some conjugation of its own. Published "empirical resonance energies" for benzene run from about 120 to 155 kJ/mol depending on the reference chosen. What no choice of reference touches is the sign and the order of magnitude. Benzene is many tens of kilojoules per mole below anything anyone can draw with three ordinary double bonds, and that is not a rounding error in an extrapolation. And there is a stranger footnote, which has been argued about since the 1980s and is not settled. Separate the calculated energy of benzene into its σ framework and its π system, and it is the π system that turns out to prefer a distorted, bond-alternating ring — while the σ framework, which resists stretching and compressing, is what holds the hexagon regular. If that analysis is right, the familiar sentence "the π electrons delocalise and make the ring symmetric" has the responsibility the wrong way round. The measurements in this lesson are untouched either way. It is the story told over them that turns out to be less settled than it sounds.

Let us learn to dream, gentlemen, and then perhaps we shall learn the truth. But let us beware of publishing our dreams before they have been put to the proof by the waking understanding.
August KekuléSpeech at the Benzolfest, Berlin, March 1890 — the celebration of the twenty-fifth anniversary of the ring. This is the occasion on which he first told the story of dozing before the fire and seeing a snake seize its own tail. It is the only source for it, it was told a quarter of a century after the fact, and historians of chemistry have argued ever since about how much of it is reconstruction. Note that the sentence he actually built the story towards is a warning about proof.

1825Faraday isolates benzene from compressed illuminating gas and calls it bicarburet of hydrogen.
1834Mitscherlich makes it from benzoic acid and gets the formula C₆H₆.
1865Kekulé proposes the ring with alternating bonds. It predicts one monosubstituted and three disubstituted benzenes.
1867 – 1869Rival structures: Dewar benzene, Ladenburg’s prism, Claus’s diagonal formula. All are serious proposals; all are wrong.
1872Kekulé patches the ortho problem with the oscillation hypothesis: the double bonds swap places too fast to catch.
1890At the Benzolfest, twenty-five years on, Kekulé tells the story of the snake seizing its tail.
1929Lonsdale solves hexamethylbenzene by hand: the ring is flat, and its six bonds are equal.
1931Hückel’s molecular-orbital treatment of the ring, largely ignored by chemists for a decade.
1933Pauling and Wheland give the valence-bond account and the phrase "resonance energy".
1936Kistiakowsky measures the heats of hydrogenation. Benzene is 150 kJ/mol short.

Where this leaves us

The ring is flat, its six bonds are one length — 1.397 Å, shorter than the average of a single and a double bond — and it sits about 150 kJ/mol below any structure anyone can draw for it. Two measurements, seven years apart, on different instruments, by people working on different problems. Neither one needs a theory of aromaticity in order to be stated, and that is precisely why they are evidence for one. Lonsdale measured a length by hand from photographic plates. Kistiakowsky measured a heat in a calorimeter. Between them they force a kind of bond that was not on anyone’s list, and the accounts that arrived afterwards — Hückel’s orbitals, Pauling’s resonance — are attempts to say what that bond is. But look again at how the second argument worked, because the move is bigger than benzene. Three different substances. One common product. A comparison of heats — and no route between the starting materials was needed anywhere. Kistiakowsky never turned benzene into cyclohexatriene, and could not have; he did not need to. That is a very powerful trick, and it has a name and a date. It means you can measure the heat of a reaction that has never been made to happen, by adding up the heats of ones that have. A 0.20 Å difference in bond length is a fact about structure. Heats that add up regardless of route is a fact about energy, and it is where chemistry goes next.