Modern Structural Chemistry

A Chemist Who Arrived Just in Time

Linus Pauling was born in Portland, Oregon, in 1901, the son of a pharmacist. He was largely self-taught as a young scientist, working through problems in mathematics and chemistry with ferocious independence. He arrived at Caltech in the early 1920s as a graduate student and stayed for most of his career, eventually becoming one of its most famous ornaments. In 1926, on a Guggenheim Fellowship, he went to Europe and spent time with the physicists — Bohr, Heisenberg, Schrödinger, Pauli — who were in the middle of inventing quantum mechanics. He came home having absorbed the new theory, and spent the next three decades asking what it meant for chemistry.

When he stood in Stockholm in December 1954, the timing was charged with significance that he did not mention at the podium. His passport had been revoked by the US State Department in 1952 — at the height of McCarthyite suspicion — because of his outspoken opposition to nuclear weapons testing. It was only restored, under pressure, shortly before the Nobel ceremony. He delivered his Chemistry lecture on December 11th; nine years later, almost to the day, he would return to Stockholm to collect the Nobel Peace Prize for his anti-nuclear activism. He remains the only person ever awarded two unshared Nobel Prizes.

None of this is in the lecture. What is there is thirty years of concentrated scientific work, narrated with the confidence of a man who knows he built the field he is describing. The lecture opens with a history that begins in 1852 — with Frankland's concept of valence — and moves briskly through a century of structural chemistry to arrive, at its close, at the edge of molecular biology. Pauling begins the lecture by saying that the structure theory of organic chemistry was developed "a century ago." He ends it by pointing toward the structure of proteins, nucleic acids, and polysaccharides — and the new chemistry that will be needed to understand them.

What Quantum Mechanics Promised, and What It Could Not Deliver

The central problem that Pauling inherited from the nineteenth century was deceptively simple: why do atoms bond the way they do? Chemists had learned, through decades of experiment, that carbon forms four bonds, that they point to the corners of a tetrahedron, that some molecules are magnetic and others aren't, that certain compounds are more stable than their structural formulas suggest. They had rules. But they had no understanding of where the rules came from.

The electron, discovered in 1897, began to change this. In 1916, Gilbert Newton Lewis proposed what now seems obvious but was then a genuine leap: that a chemical bond between two atoms consists of a pair of electrons held jointly by both. The shared electron pair. Lewis also noticed that atoms tend to surround themselves with eight outer electrons — a noble-gas configuration — and that these eight electrons arrange themselves in four pairs, pointing to the corners of a tetrahedron. This was the first structural explanation of carbon's geometry, without any quantum mechanics at all.

Then, in 1925, quantum mechanics arrived. The Schrödinger wave equation, in principle, contained all of chemistry. In practice — as Pauling notes with characteristic directness in the lecture — "these equations cannot be solved rigorously for any but the simplest molecules." The hydrogen atom, yes. The hydrogen molecule, approximately. Anything larger: intractable. The great challenge of the next three decades was to find conceptual tools that were grounded in quantum mechanics but workable by chemists — ideas that could make predictions, correlate observations, and illuminate structure without requiring the full machinery of the wave equation to be solved from scratch for every molecule.

This is what Pauling spent his career building. The lecture is his account of what those tools are, where they came from, and what they revealed.

Hybridisation: Why Carbon Is a Tetrahedron

The carbon atom, in its ground state, has one electron in a spherical s orbital and two electrons in two of its three dumbbell-shaped p orbitals. These orbitals are not equivalent — they have different shapes, different energies, and different spatial orientations. And yet every chemist knows that carbon forms four bonds that are completely equivalent to one another, pointing to the corners of a perfect tetrahedron. How?

The answer Pauling developed — and the lecture describes as his first major contribution — is hybridisation. The quantum mechanical phenomenon of resonance (which we will meet again in the next section in a different guise) allows the s orbital and the three p orbitals to mix together into four new, equivalent hybrid orbitals, each pointing toward a corner of a tetrahedron. These are called sp³ hybrid orbitals, and they are neither s nor p in character — they are something new that the atom creates by blending its available orbitals in the right proportions.

This was not just an explanation of carbon's geometry. It was a general principle. Different mixtures of s, p, and d orbitals produce different hybrid shapes — square planar, octahedral, linear — and these correspond exactly to the geometries of complex molecules that had been discovered empirically by Werner half a century earlier and confirmed by X-ray crystallography. Pauling points out with some satisfaction in the lecture that his theory of dsp² hybrid orbitals predicted that certain nickel complexes must be diamagnetic (non-magnetic) — a prediction that had not previously been made, and which was then confirmed. The geometry of molecules was no longer a catalogue of observations. It had an explanation.

Electronegativity and Resonance: Putting Numbers on Chemistry

Hybridisation explained the geometry of bonds. But it said nothing about their energy — why some bonds are stronger than others, why the bond between hydrogen and fluorine releases far more energy than the bond between hydrogen and carbon. For this, Pauling developed the concept of electronegativity: a single number assigned to each element, expressing how strongly it pulls electrons toward itself when bonded to another atom.

The idea arose from a close look at bond energies. Pauling observed that the energy of a bond between two different atoms — say, hydrogen and chlorine — is always somewhat greater than the average of the energies of the two corresponding identical bonds (H–H and Cl–Cl). The extra stabilisation, he argued, comes from the partial ionic character of the bond: because chlorine pulls electrons more strongly than hydrogen, the electrons are not perfectly shared but slightly displaced toward the chlorine. This displacement lowers the energy. From the magnitude of the extra stabilisation across many different bonds, Pauling could assign consistent electronegativity values to every element — a scale that chemists still use today, essentially unchanged, more than ninety years later.

Resonance is the third tool, and in some ways the most radical. Pauling introduces it in the lecture with a defence as well as a description, because by 1954 it had attracted criticism — including, notably, from Soviet chemists who objected to its allegedly idealist character. His response is instructive.

The problem resonance addresses is this: some molecules simply cannot be described by a single arrangement of bonds. The most famous example is benzene — a ring of six carbon atoms. Organic chemistry in the nineteenth century had proposed two possible arrangements, both due to Kekulé, in which single and double bonds alternate around the ring. But benzene doesn't behave like either Kekulé structure. Its bonds are all the same length, intermediate between a single and a double bond. It is more stable than either structure would predict. And it doesn't undergo the addition reactions characteristic of double bonds.

Pauling's argument in the lecture is that this "element of arbitrariness" — the fact that the contributing structures are hypothetical, that no one can isolate a pure Kekulé benzene — is no worse than the arbitrariness already present in the simple structure theory that everyone accepts. The concept of a carbon–carbon single bond is itself an idealisation. The propane molecule has its own structure; you cannot extract a portion of it and say "this is the C–C single bond, identical with a piece of ethane." All structural concepts in chemistry are idealisations. Resonance is no different in kind, only in degree.

What makes resonance more than a bookkeeping device is that it makes quantitative predictions. Pauling shows in the lecture how the contributing structures can be assigned fractional weights — the relative proportions in which they contribute to the actual molecular state — and these weights predict measurable properties: bond lengths, bond energies, the planarity of groups of atoms. It is this last consequence that will prove most consequential of all.

From the Amide Bond to the Alpha Helix

The most important application of resonance in the lecture is not benzene but the amide group — the structural unit that links amino acids together in proteins. An amide group contains a carbon atom bonded to both an oxygen atom and a nitrogen atom. In classical structural theory, the C–O bond is a double bond and the C–N bond is a single bond. But Pauling shows that this picture is incomplete.

The amide group can be described as resonating between two valence-bond structures. In the first, the double bond is between carbon and oxygen — the classical picture. In the second, the double bond has shifted to sit between carbon and nitrogen, leaving oxygen with a negative charge and nitrogen with a positive one. Pauling estimates, from the relative stability of the two structures, that they contribute roughly 60% and 40% respectively to the actual state of the amide group. The exact numbers matter less than the consequence of the 40% contribution from the second structure: it means the C–N bond has approximately 40% double-bond character.

A double bond cannot rotate freely. Two atoms joined by a double bond, and all the atoms directly bonded to them, are locked into a plane. If the C–N bond in a peptide group has 40% double-bond character, then the entire group of six atoms — the carbon, the oxygen, the nitrogen, the hydrogen on the nitrogen, and the two carbon atoms flanking them — must be essentially planar. The resistance to deformation from this planar configuration, Pauling calculates, is 40% as great as for a molecule with a pure double bond. Rotating one end of the group by just 3° relative to the other introduces a strain energy of 100 calories per mole. The amide group is, in practice, rigidly flat.

This single constraint — planarity of the amide bond — is the key that unlocks protein structure. A protein is a long chain of amino acids linked by amide bonds. If those bonds were free to rotate, the chain could adopt an essentially unlimited number of configurations. But they are not free: the amide bond is rigid and flat. The chain has only two remaining degrees of rotational freedom per residue, at the bonds flanking each amide group. And those rotations are themselves constrained: atoms in different parts of the chain must not approach each other too closely (steric repulsion), and the N–H and oxygen atoms of different amide groups should be positioned to form hydrogen bonds at a precise geometry.

Working from these requirements — planarity, steric constraints, hydrogen bond geometry — Pauling and his collaborator Robert Corey built physical molecular models with great precision (scale: 2.5 cm per ångström, accurate to better than 0.01 cm) and searched for configurations of the polypeptide chain that satisfied all the constraints simultaneously. They found two: the alpha helix, in which the chain spirals with hydrogen bonds running along the axis of the helix; and the beta sheet, in which extended chains lie side by side with hydrogen bonds running between them. Published in 1951, these two structures are the fundamental architectural elements of nearly every protein in every living thing.

The closing passage of the lecture looks forward from here. Pauling writes that the chemist of the future will apply a new structural chemistry — one involving "precise geometrical relationships among the atoms in the molecules and the rigorous application of the new structural principles" — to the problems of biology and medicine. He lists proteins, nucleic acids, and polysaccharides as the territory ahead. He published this in December 1954. Watson and Crick had published the structure of DNA in April 1953. The territory he was pointing toward was already being explored.

What a Theory of Bonding Made Possible

The lecture is short enough that a reader who has followed this far should read it whole — the original PDF is eight pages, and Pauling's own prose is exceptionally clear. What this note has tried to do is lay out the conceptual sequence: the problem quantum mechanics posed, the three tools Pauling built to meet it, and the culminating application to proteins that the lecture is really building toward.

The deeper significance of the work is perhaps best seen in what it did to the boundary between chemistry and biology. Before Pauling, molecular biology did not exist as a discipline. Biology worked with organisms, tissues, cells; chemistry worked with small molecules and their reactions. Pauling showed, through the alpha helix and beta sheet, that the architecture of large biological molecules could be deduced from the precise application of chemical principles — bond lengths known to 0.02 ångströms, bond angles known to within 2 degrees, planarity enforced by resonance theory. Life, at the molecular level, was chemistry. And chemistry, at its foundations, was quantum mechanics made workable.

There is also something worth holding onto in Pauling's defence of resonance against its critics. His argument — that all structural concepts in chemistry are idealisations, that the question is whether an idealisation is useful and predictively powerful, not whether it corresponds to some isolable physical reality — is a more general epistemological point. Models that work are not made less legitimate by the fact that their elements are abstractions. The tetrahedron, the single bond, the Kekulé structure, the resonance hybrid: these are not things you can hold in your hand. They are the tools a mind uses to think about things too small to hold. Pauling understood this with unusual clarity, and said so plainly, at the Nobel podium, in 1954.