Beautiful arguments: Linus Pauling's triumphal calculation of the chemical bond

27 May 2010 // science

Arguably the second greatest scientist of the Twentieth Century was Linus Pauling. He single-handedly created modern chemistry by figuring out how to mathematically model the chemical bond.

After studying at Oregon State College and getting his phd at Caltech, Pauling travelled to Germany in the 30's to learn the shit-hot theory of quantum mechanics. When he arrived in Europe, quantum mechanics had been successfully used to calculate, in astonishing precision, the atomic spectra of hydrogen and other such simple atoms.

It seems obvious with 90 years of hindsight, but quantum mechanics is the quantitative theory of molecules and, by extension, all of modern chemistry. But the early physicists who invented quantum mechanics couldn't see that (although Dirac famously quipped after discovering the relativistic version of the Schrödinger equation, 'the rest is chemistry') because, well, the early physicists just didn't know enough chemistry.

This is where Pauling came in. He arrived in Europe with the latest ideas about chemical bonds from the US such as Lewis electron pairs and the hydrogen bond. Combined with his unparalleled breadth of knowledge of chemistry and superb mathematical ability, Pauling realized that the electron orbitals of atomic structure could be bent into the first ever mathematical description of the chemical bond.

In a series of papers in JACS in 1931 and 1932, titled under the rubric "The Nature of the Chemical Bond", Linus Pauling made the first ever attempt to mathematically model the chemical bond in terms of linear combinations of atomic electron orbitals. Compared to today's macho quantum chemists and their chtonic cpu-hungry calculations, these approximations might seem like child's play, but you have to remember just how much insight Pauling squeezed out of his remarkably simple calculations of hybrid orbitals.

I believe that Pauling's 1931 paper, The Nature of the Chemical Bond. Application of Results obtained from the Quantum Mechanics and from a Theory of Paramagnetic Susceptibility to the Structure of Molecules, the first of the lot, is one of the great papers of science. It ranks up there with Einstein's paper of special relativity and Watson & Cricks DNA paper.

The argument is so clean that even 2nd year physicists should be able to follow. In that paper, Pauling showed that the lowest energy hybrid orbital of the 1s and 3p orbitals gives you the so-called 4sp hybrid-orbitals that are symmetric and tetrahedral. This immediately explains the tetrahedral bonding nature of carbon, and thus the chemical basis of organic chemistry.

I first came across this beautiful calculation in Pauling's 1960 book, but it is much more exciting to read the argument in the 1931 paper. That paper is easy to find at the Linus Pauling archive at the Oregon State archive but is unfortunately stored in a stupid TIFF format. Here, I've taken the liberty of stitching it together as a PDF file for your reading pleasure. Enjoy.