Pauling’s First Paper on the Nature of the Chemical Bond

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Linus and Ava Helen Pauling in Munich, with Walter Heitler (left) and Fritz London (right), 1927.

[An examination of Linus Pauling’s first paper on the nature of the chemical bond, published in April 1931. Part 2 of 2.]

In 1928 the German physicists Walter Heitler and Fritz London published a paper that appeared to have beaten Linus Pauling to the punch in its application of quantum mechanics to the theory of chemical bonding. As with Pauling, the duo was interested in Erwin Schrödinger’s wave function, and in their paper they applied it to the simplest bond: that formed by two hydrogen atoms. In so doing, Heitler and London did indeed become the first scientists to publish an application of this type.

The German colleagues also incorporated Werner Heisenberg’s ideas on exchange energy. Heisenberg had theorized that the electrons of two given atoms would find themselves attracted to the positively charged nuclei of their atomic pairs. As such, a chemical bond, according to this theory, consisted simply of two electrons jumping back and forth between two atoms, belonging simultaneously to both and to neither.

Heitler and London extended this idea, proposing that chemical bonds sourced their lengths and strengths from the amount of repulsion extant between two positively charged nuclei. The balance between the electrons’ attraction to these nuclei, coupled with the quantifiable repulsion existing between the two nuclei, ultimately served to create the bond.


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Pauling on the precipice of greatness, 1928.

Invigorated by the promise of competition, Pauling set to work applying Heitler and London’s theory to more complex molecules. In part to motivate himself, but also to ensure that he received recognition for his research, Pauling announced in the Proceedings of the National Academy of Sciences that he believed he could solve the tetrahedral binding of carbon using the ideas put forth by quantum mechanics.

This declaration piqued significant interest throughout the scientific community, striking a nerve for chemists and physicists alike, both groups of whom had been puzzling over this specific structure in different ways. On one hand, physicists believed that carbon should have a valence of two because, of its six electrons, four were located in two different subshells. Both sets of two would then be expected to pair off with each other, leaving only two electrons logically available for bonding. On the other hand, chemists found in the laboratory that carbon typically offered four electrons for bonding in nature. In essence, both theory and experiment indicated that neither party was completely right, but so too could neither point of view be completely wrong. Pauling believed that quantum mechanics could illuminate the paradox.

In addition to his theoretical study, Pauling’s extensive graduate training in x-ray crystallography strengthened both his interest in and his flair for atomic structure. By 1928, after a busy year of research, he had established five principles for determining the structure of complex covalent and ionic crystals, later dubbed “Pauling’s Rules.” He used these rules to predict models for particular molecular structures, and then worked backward from the theoretical model to develop a more concrete picture based on x-ray data. When a colleague remarked that this technique resembled the Greek stochastic method – an approach based largely on applied guess work – Pauling offered a correction, stating that

Agreement on a limited number of points cannot be accepted as verification of the hypothesis. In order for the stochastic method to be significant, the principles used in formulating the hypothesis must be restrictive enough to make the hypothesis itself essentially unique.

In other words, Pauling was relying on his knowledge of chemical principles to develop meticulous and educated hypotheses that he could go back and prove. And as he would hasten to add, he placed very little stock in luck or guesswork.


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As work moved forward, Pauling added his rules to three others that had been established by G.N. Lewis – and then expanded and formalized by Heitler and London – concerning the electron pair bond. These rules set parameters for the circumstances in which an electron would be theoretically available to form a chemical bond.

Though equipped with a solid toolkit of his and others’ making, it ultimately took Pauling almost three years to solve the carbon tetrahedron, with his big breakthrough coming in December of 1930. Inspired by the work of MIT physicist John C. Slater, Pauling found a way to reduce the complexity of the radial wave function, a component of bond orbital theory the application of which had been giving him some trouble. With this solution in hand, the math required for solving further steps of the carbon puzzle became significantly more manageable.

Pauling’s subsequent equations led him to develop a model for the structure that consisted of four equal orbitals oriented at the angles of a tetrahedron. Using these equations, Pauling further discerned that the strength of the bonds within the structure increased in accordance with greater degrees of orbital overlap between two atoms. The overlap, Pauling found, produced more exchange energy and this in turn created a stronger bond.

Pauling sent his paper to the Journal of the American Chemical Society (JACS) in February 1931. In it, Pauling detailed three rules governing eigenfunctions that complemented G.N. Lewis’ rules about electron pairs. Pauling used this collection of guidelines to explain relative bond strength, finding that the strongest bonds occurred on the lowest energy level and where orbitals overlap. He also developed a complete theory of magnetic moments and ended the paper stressing the important role that quantum mechanics had played in his formulation of the rules and theories expressed in the work.

The paper, titled “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,” was accepted and published in record time. The subject matter was so new and the ideas so fresh that Arthur Lamb, the editor of JACS at the time, had trouble finding a group qualified enough to review it. Even so, he scheduled the article for the April issue and in so doing published Pauling’s paper a mere six weeks after he had received it.


In 1926, whether he knew it or not, Linus Pauling embarked down a path toward the transformation of chemistry and the way that it would be studied for generations to come. The ideas that he began developing during this time gradually became the standard model for those studying chemistry while simultaneously launching Pauling to dizzying heights. His April 1931 paper, the first in a series of seven, also became the basis for his 1939 book, The Nature of the Chemical Bond, which was almost immediately recognized as a classic of twentieth-century scientific writing.

Largely on the strength of the April JACS article, Pauling also received the 1931 Langmuir Prize from the American Chemical Society, and used the money that came with the prestigious award to further his research. Now that he was interested in molecular structure, he saw it’s promise everywhere within a rapidly expanding research program. In fact, the chemical bond work of the late 1920s and early 1930s laid the foundation for his subsequent program of hemoglobin research, which in turn led to his sickle cell anemia discovery almost twenty years later. In hindsight, it is easy to see how Pauling could have looked back on the achievements of early 1931 as being “the best work I’ve ever done.”

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The Guggenheim Trip, Part III: Unexpected Colleagues

Walter Heitler, Fritz London, and Ava Helen Pauling in Europe. 1926.

Walter Heitler, Fritz London, and Ava Helen Pauling in Europe. 1926.

The paper of Heitler and London on H2 for the first time seemed to provide a basic understanding, which could be extended to other molecules. Linus Pauling at the California Institute of Technology in Pasadena soon used the valence bond method. . . . As a master salesman and showman, Linus persuaded chemists all over the world to think of typical molecular structures in terms of the valence bond method.” – Robert Mulliken. Life of a Scientist, pp. 60-61. 1989.

After Linus Pauling’s publication of “The Theoretical Prediction of the Physical Properties of Many-Electron Atoms and Ions,” he was ready for an even greater challenge – the problem of the chemical bond was a tantalizing enigma for Pauling, and he wanted more time in Europe to work on it. In the winter of 1926, he applied for an extension of his Guggenheim fellowship and with the help of a particularly complementary cover letter from Arnold Sommerfeld, Pauling was granted six more months of support.

Boosted by this news, he quickly began planning visits to Copenhagen and Zurich, both cities boasting of some of Europe’s finest research facilities. His first stop was Copenhagen, where he hoped to visit Niels Bohr’s institute and discuss ongoing research with the renowned scientist. Unfortunately, he had arrived uninvited and found it almost impossible to obtain a meeting with the physicist. Bohr, with the help of Werner Heisenberg and Erwin Schrödinger, was deeply engaged in research on the fundamentals of quantum mechanics, and was specifically attempting to root out the physical realities of the electron, in the process developing a theory which would eventually be termed the “Copenhagen Interpretation.”

Pauling did, however, did make one valuable discovery in Denmark — that of a young Dutch physicist named Samuel Goudsmit. The two men quickly became friends and began discussing the potential translation of Goudsmit’s doctoral thesis from German to English. Their work did eventually get them noticed by Bohr, who finally granted Pauling and Goudsmit an audience. Unfortunately for the pair, Bohr was neither engaging nor encouraging. Nevertheless, the two continued to work together, their cooperation eventually culminating in a 1930 text, The Structure of Line Spectra, the first book-form publication for either scientist.

In 1926 though, frustrated by his unproductive time in Copenhagen, Pauling departed, stopping briefly at Max Born’s institute in Göttingen before traveling to Zurich where other advances in quantum mechanics promised an interesting stay. Unfortunately, the man Pauling was most interested in, Erwin Schrödinger, proved to be just as unavailable as Bohr. The quantum mechanics revolution was consuming the time and thoughts of Europe’s leading physicists and Pauling, a small-fry American researcher, simply wasn’t important enough to attract the interest of men like Bohr and Schrödinger.

Fritz London

Fritz London

As a result, Pauling chose to converse and work with men of his own status in the scientific community. Fritz London and Walter Heitler, acquaintances of the Paulings, had spent the past several months working on the application of wave mechanics to the study of electron-pair bonding.

Heitler and London’s work was an outgrowth of their interest in the applications and derivations of Heisenberg’s theory of resonance, which suggested that electrons are exchanged between atoms as a result of electronic attraction. Heitler and London determined that this process, under certain conditions, could result in the creation of electron bonds by cancelling out electrostatic repulsion via the energy from electron transfer. Their work on hydrogen bonds likewise agreed with existing theories, including Wolfgang Pauli’s exclusion principle and G.N. Lewis’ shared electron bond. The Heitler-London model was well on its way to contributing to a new truth about the physics of the atom

Walter Heitler

Walter Heitler

Pauling used his time in Zurich to experiment with the Heitler-London work. While he didn’t produce a paper during his stay, the new model made a great impression on him and he returned to Caltech with a renewed sense of purpose. He was preparing to tackle the problem of atomic structure, in all its manifestations, and make history as one of the greatest minds of the twentieth century.

For more information, view our post “Linus Pauling and the Birth of Quantum Mechanics” or visit the website “Linus Pauling and the Nature of the Chemical Bond: A Documentary History.”

Linus Pauling and the Birth of Quantum Mechanics

Linus and Ava Helen Pauling in Munich, with Walter Heitler (left) and Fritz London (right), 1927.

Linus and Ava Helen Pauling in Munich, with Walter Heitler (left) and Fritz London (right), 1927.

My year in Munich was very productive. I not only got a very good grasp of quantum mechanics — by attending Sommerfeld’s lectures on the subject, as well as other lectures by him and other people in the University, and also by my own study of published papers — but in addition I was able to begin attacking many problems dealing with the nature of the chemical bond by applying quantum mechanics to these problems.”
– Linus Pauling, 1992

In the spring of 1926, funded by a Guggenheim Fellowship, Linus and Ava Helen Pauling embarked on their first trip to Europe, scientific tourists beginning a journey that would revolutionize modern chemistry and physics.

The Paulings travelled through the continent, stopping at the famed institutes of modern science in Munich, Göttingen, and Zurich, among others, and meeting with scientific giants including Arnold Sommerfeld, Max Born and Erwin Schrödinger. It was at this time that quantum mechanics, the branch of science devoted to the study of the atom’s physics, was being revolutionized by the ideas of Schrödinger and Werner Heisenberg. It wasn’t until Pauling left Germany for Switzerland however, that he was introduced to a ground-breaking idea – the combination of Schrödinger’s wave mechanics with the study of structural chemistry.

In Zurich, the German researchers Walter Heitler and Fritz London explained to Pauling the concept of “electron resonance” as developed by Heisenberg. At its core, the theory suggested that electrons could be attracted to one another, to the point where they would eventually switch back and forth between two given atoms. This exchange of electrons would, in turn, release energy, in the process drawing the two atoms together and creating a chemical bond. This revolutionary concept agreed with certain known principles of the hydrogen atom – the atom on which Heitler and London were conducting their calculations – and appeared to support the Pauli exclusion principle which, as Pauling later put it, “states that no two electrons in the universe can be in exactly the same state.”

After his return to Caltech in September of 1927, Pauling worked on several projects, including his first published book and a class on the Heitler-London work. In the process of defining his research program as a young member of the Caltech faculty, Pauling decided that, rather than continuing to dabble in theoretical physics, he would instead return to his roots in chemistry. With that, he set out to combine what he had learned in Europe with his continuing interests in structural chemistry.

He began his work on the chemical bond, figuring calculations and comparing his results to existing experimental data. He affirmed that Heitler and London’s work meshed comfortably with G. N. Lewis‘ theory of the shared electron pair and he published articles on the subject, in the process introducing many chemists to the notion of using quantum mechanics as a tool for the study of non-physics problems. In early 1928, he suggested that quantum mechanics could answer the question of carbon bonding – a revolutionary idea at the time. Unfortunately, while the preliminary mathematics were promising, the sheer mathematical computing power required did not exist for Pauling to fully solve the problem.

In 1930 M.I.T. physicist John C. Slater succeeded in simplifying Schrödinger’s mathematical description of the types of changes experienced by any quantum system over time — an important mathematical model known as the Schrödinger Wave Equation. By slightly restructuring Slater’s set of simplified equations, Pauling was able to utilize the concept of wave functions to describe new orbitals that matched the known traits of the carbon-tetrahedron bond. Not only did these new methods allow Pauling to calculate the data for basic tetrahedral bonds, they also provided stable footing for detailing the precise structures of a series of complex molecules. This was the genesis of valence-bond theory — a hugely important marriage of quantum physics and structural chemistry.

In early 1931, Pauling released a paper detailing six rules, later known as “Pauling’s Rules,” that dictated the basic principles governing the molecular structure of any given molecule. He presented his findings in the simplest language possible, avoiding complex mathematics in order to make the concepts accessible to his fellow chemists. This paper, of course, was titled “The Nature of the Chemical Bond” and would serve as the basis for his immensely popular textbook of the same name.

In 1954 Pauling won the Nobel Prize in Chemistry “For research into the nature of the chemical bond and its application to the elucidation of complex substances.” The award was granted in recognition of the work that began during his first trip to Europe and blossomed in the decade that followed. Pauling’s innovative application of quantum mechanics had resulted in his receipt of the highest possible scientific honor and the subsequent worldwide recognition of his talents.

Learn more about this story by visiting the website “Linus Pauling and the Nature of the Chemical Bond: A Documentary History.”