Chemistry 1931

The Nature of the Chemical Bond

Linus Pauling

Mix an atom's s and p orbitals into hybrids — and the shapes of molecules follow.

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In depth · the introduction

Why is a carbon atom always tetrahedral, and why do molecules take the shapes they do? This is the paper that answered it — by letting an atom mix its own orbitals.

The idea, unpacked

Chemists had long drawn molecules with bonds at particular angles — carbon's four bonds splayed toward the corners of a tetrahedron — but nobody could say why. In 1931 Linus Pauling took the brand-new quantum mechanics and used it to explain the shapes.

His key move was hybridisation. An atom's electrons live in clouds, called orbitals, of different shapes — a round 's' cloud and dumbbell-shaped 'p' clouds. Pauling showed that an atom can blend these into a new set of identical clouds that point in specific directions. A bond then forms along each direction, wherever the clouds of two atoms overlap most — because more overlap means a stronger bond. Blend carbon's one s and three p clouds and you get four bonds aimed at the corners of a tetrahedron: exactly the shape chemists had been drawing for half a century.

Where it came from

Pauling, not yet thirty and newly arrived at Caltech, had spent time in Europe learning the quantum mechanics that Heisenberg and Schrödinger had just created. Heitler and London had used it in 1927 to explain the simplest bond, in the hydrogen molecule. Pauling saw how to carry that insight into all of chemistry, and in a 1931 paper in the Journal of the American Chemical Society — the first of a celebrated series — he laid out the rules. The same idea was reached independently that year by the physicist John Slater.

Why it mattered

For the first time the structural formulas chemists drew had a physical reason behind them. Bond angles, the rigidity of double bonds, the strength of a bond — all followed from how orbitals overlap. Pauling went on to add the ideas of electronegativity and resonance and collected everything in a 1939 book that taught a generation how to think about molecules. The work brought him the 1954 Nobel Prize in Chemistry.

An everyday analogy

Picture the atom's plain orbitals as one round flashlight beam plus a few dumbbell beams pointing along the axes — awkward for aiming at several specific spots. Hybridising is like refitting them all into identical, evenly spaced spotlights, each pointing at one corner of a room. Now every bond has a beam aimed straight at its partner, and the overlap — the grip of the bond — is as strong as it can be. Pick a hybridisation below and watch the beams snap into shape.

Where it sits

Pauling built on Lewis's 1916 picture of the bond as a shared pair of electrons and on the quantum mechanics of the 1920s. A rival and complementary view — molecular-orbital theory, developed by Mulliken and others — spread the electrons over the whole molecule instead, and the two pictures have coexisted ever since. Pauling's hybrids remain the way nearly every chemistry student first learns why molecules have shape.

The original document

Original source text

Linus Pauling · J. Am. Chem. Soc. 53(4), 1367–1400 · April 1931 · California Institute of Technology

The problem

G. N. Lewis (1916) had pictured the chemical bond as a pair of electrons shared between two atoms, but the picture could not say why a shared pair binds, why bonds adopt definite angles, or why a saturated carbon atom is tetrahedral. Heitler and London (1927) had just answered the first question for the hydrogen molecule using the new quantum mechanics. Pauling set out to carry that result into the whole of structural chemistry.

Six rules for the electron-pair bond

The paper opens by laying down six rules. The first three restate the shared-pair idea in quantum-mechanical terms: a bond forms from one unpaired electron on each of two atoms; the two electron spins pair and cancel; and the paired electrons then take no further part in bonding. The last three are new and quantitative — the bond's energy comes from the resonance (exchange) of the two electrons between the atoms; of the orbitals available, those of lowest energy form the strongest bonds; and, decisively, a bond tends to lie in the direction in which the atom's bonding orbital is most concentrated, because that direction maximises the overlap of the two orbitals and so the strength of the bond.

Hybrid bond orbitals and the tetrahedral carbon

From the maximum-overlap rule Pauling drew his most consequential result. An atom need not bond through its bare s and p orbitals; it can mix them into equivalent hybrid orbitals that are better directed and overlap more. One s orbital combined with carbon's three 2p orbitals yields four equivalent hybrids pointing to the corners of a regular tetrahedron, mutually 109.47° apart — the long-mysterious tetrahedral carbon of organic chemistry, now derived from quantum mechanics. Mixing s with two p orbitals gives three coplanar bonds at 120°; with one p orbital, two opposed bonds at 180°.

[ … ]

A magnetic criterion

The second half of the paper uses paramagnetic susceptibility — a magnetic measurement of the number of unpaired electrons — as an experimental criterion for the type of bonding in complexes of the transition metals, distinguishing essentially ionic from covalent (electron-pair) bonds. This is the origin of the 'inner-orbital' versus 'outer-orbital' distinction still used for coordination compounds.

What followed

This was the first of a celebrated series. The electronegativity scale and the concept of resonance came in the papers that followed and in the 1939 book that grew out of them. The directed-valence idea was reached independently the same year by the physicist J. C. Slater.

California Institute of Technology · 1931