Walter Heitler

The man who taught hydrogen to bond

Walter Heinrich Heitler was born on the second of January 1904 in Karlsruhe, the same Baden city that had produced Friedrich Hund eight years before and that, a generation earlier, had hosted Heinrich Hertz’s first detection of radio waves. His father Adolf was a professor of engineering, his mother Ottilie came from a cultivated Jewish family in the Rhineland. The household read Goethe at the dinner table and argued about Wagner in the evenings. Walter was the second of three children and the only one who would inherit the family’s restless habit of asking what holds the world together.

He studied first at the Technische Hochschule in his home city, then moved south to Berlin for a year, and finally settled in Munich, drawn by the reputation of the Sommerfeld seminar. Arnold Sommerfeld ran what was already the most productive doctoral school in theoretical physics in Europe. Heisenberg, Pauli, Hans Bethe, and Linus Pauling all passed through it. Sommerfeld taught his students the calculus of old quantum theory with the patience of a man who suspected, correctly, that the whole edifice was about to be replaced. Heitler took his doctorate in 1926 with a thesis on solutions in electrolytes, a respectable but unremarkable problem. The remarkable work came next.

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The H₂ paper

In the spring of 1927, Heitler was at the University of Zurich on a Rockefeller fellowship, sharing a small office with Fritz London, a fellow Sommerfeld graduate of almost exactly his own age. The two men had become friends in Munich and were now working in adjacent corners of the same room. One Sunday afternoon, while resting after a long hike in the Alps above Zurich, Heitler had what he later described as a sudden image of two hydrogen atoms approaching one another. He saw the two electron clouds, one bound to each proton, and he saw what would happen if you wrote the joint wavefunction as a symmetric combination of the two single-atom states.

He woke London from a nap and dragged him to the blackboard. By evening they had it. The trick was to take the antisymmetry the electrons require under the new Pauli rule (recently formalised by Heisenberg and Dirac) and combine it with a spatial wavefunction in which the two electrons could each be on either atom. The symmetric combination of spatial parts paired with the antisymmetric spin combination produced a bound state with an energy four electron-volts below the separated atoms. The antisymmetric spatial combination, by contrast, produced no binding at all. The energy gap, the bond length, and the vibrational frequency they computed matched the experimental H₂ molecule to within a few percent. They had derived a chemical bond from the Schrödinger equation. The paper appeared in Zeitschrift für Physik in June 1927 under the title Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik. It was thirty pages long. It founded quantum chemistry.

What made the result extraordinary was not the numerical agreement, striking as it was, but the conceptual content. Before 1927, a covalent bond was a phenomenological notion. Chemists drew lines between atoms and labelled them with letters. The lines worked but nobody could say what they were. Heitler and London showed that the line was a manifestation of an exchange integral, a purely quantum-mechanical term with no classical analogue. The bond existed because the two electrons were indistinguishable. Take away indistinguishability and the binding energy vanished. Chemistry, in this sense, was a consequence of the antisymmetry of fermions. The whole periodic table of compounds, from water to insulin, ran on the exchange interaction Heitler and London had isolated in the simplest possible molecule.

Exile, Bristol, Dublin

Heitler stayed in Zurich another two years before taking a Privatdozent position at Göttingen in 1929. He published a textbook on the quantum theory of radiation that became the standard reference for a generation and that John Wheeler later credited with teaching him electrodynamics. Then 1933 arrived. The Nazi Gesetz zur Wiederherstellung des Berufsbeamtentums forced Jewish academics out of their posts. Heitler’s mother was Jewish, which made him a Mischling under the new race laws and ineligible for state employment. He left Germany within months. Max Born, similarly displaced, had landed at Bristol. He arranged for Heitler to join him as a research fellow at the H. H. Wills Laboratory. Heitler spent eight years at Bristol, working on cosmic-ray showers and on the quantum theory of the meson that Yukawa had predicted from Osaka and that Powell would later photograph from the same Bristol building.

In 1941 Erwin Schrödinger, by then directing the new Dublin Institute for Advanced Studies under the personal patronage of the Irish Taoiseach Éamon de Valera, invited Heitler to head the institute’s School of Theoretical Physics. Heitler accepted. The arrangement at Dublin was unusual. De Valera, a former mathematics teacher who had imagined the institute as an Irish answer to Princeton, gave its fellows complete freedom from teaching duties. Heitler used the freedom to write a second textbook (Elementary Wave Mechanics, 1945) and to develop a damping theory of meson scattering that brought him the Max Planck Medal in 1968. When Schrödinger retired in 1949 and returned to Vienna, Heitler succeeded him as the institute’s senior theoretical physicist. He left Dublin in 1949 to take the chair of theoretical physics at the University of Zurich, the city where the H₂ paper had been written twenty-two years earlier. He held the chair for twenty-five years until his retirement in 1974.

A devout man in a secular field

Heitler was unusual among the founders of quantum mechanics for being openly religious. He had been raised in a partly Jewish, partly Lutheran household, and in middle age he converted to Catholicism. He wrote essays on the relationship between physics and the philosophy of nature that drew on Aquinas and that argued, against the prevailing positivism, that the success of quantum mechanics did not eliminate the metaphysical questions it had inherited from classical physics. The essays were polite, learned, and unfashionable. Few of his colleagues read them. He continued to publish them into his seventies.

He married Kathleen Winifred Nicholson, an Irishwoman he had met in Dublin, in 1942. They had two sons. The family kept houses in Zurich and County Wicklow and divided their summers between the Alps and the Irish coast. Heitler corresponded for decades with Pauli, who had taken the Zurich chair in physics next door, and the two men argued about the philosophy of measurement until Pauli’s death in 1958. Heitler died on the fifteenth of November 1981 in Zurich, aged seventy-seven. He had outlived London by twenty-seven years, Born by eleven, and Heisenberg by five.

Why he matters

The Heitler-London paper is the moment chemistry became a branch of physics. Every modern computational-chemistry package, from Gaussian to ORCA, ultimately solves the same many-electron Schrödinger equation they first attacked on a Zurich blackboard in 1927. The two competing schools of quantum chemistry that grew from it (the valence-bond school of Pauling and the molecular-orbital school of Hund and Mulliken) both took Heitler and London as their common starting point. When a chemist today draws two dots between two atomic symbols to represent a shared pair of electrons, the picture they are drawing is the one Heitler saw on his hike above Zurich. The bond is exchange, and exchange is the antisymmetry of fermions made visible. Walter Heitler was the first person to know that.