by Thomas Hager
Finally, after several weeks in Copenhagen, Pauling was summoned to Bohr's office, along with Goudsmit. Bohr had heard they were doing calculations together, and asked them to describe their work. As the two young men talked, he sat, impassive, his heavy eyelids drooping, occasionally saying, "Yes. Yes." When they were finished, he said, "Very well." They were dismissed. It was the only time Pauling saw Bohr during his month's stay.
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On their way to see Schroedinger in Zurich, the Paulings spent a few days at Max Born's institute in Goettingen, the dominion of rigorous mathematics, the spiritual home of so many young theorists—Heisenberg, Pauli, Dirac, and Jordan—that it became the storied land of Knabenphysik (boy physics). It was also a magnet for young Americans; more Guggenheim fellows in the sciences during this period ended up in Goettingen than anywhere else. Pauling was able to meet many of the major players in the quantum revolution: Dirac, Heisenberg, Jordan, and briefly, Born himself. He also ran across and spent quite a bit of time talking to a nervous, thin young research fellow from Harvard who was in Goettingen working on his doctorate, J. Robert Oppenheimer.
Pauling hoped that Schroedinger would be more accessible than Bohr, but he was disappointed. Over the course of the preceding year, wave mechanics had proved so powerful in approaching all sorts of problems that everyone was trying to learn about it. Schroedinger was asked to give lectures all over Europe, and in the spring of 1927 he toured America, including a pleasurable stop at Caltech, with side trips arranged by Paul Epstein to Hollywood and the beach at Santa Monica. While he enjoyed much of the United States, he generally disliked Americans, whom he viewed as unsophisticated, acquisitive, and pushy. All the Statue of Liberty needed, he said, was a wristwatch below the torch to make the picture complete, and Southern California, he thought, would have been much improved it if had been left to the Indians and Spaniards. Worst of all was the Prohibition-caused difficulty in getting a glass of beer or wine. Soon after Pauling arrived in Zurich for the summer semester, Schroedinger was offered the most prestigious position in German science, the Berlin chair in theoretical physics being vacated by Max Planck. He had become, at age thirty-nine, an overnight scientific superstar, and he was enjoying playing the part. It included little time for visiting Americans.
By August, Pauling was feeling frustrated. "I have rather regretted the nearly two months spent here," he wrote a colleague, "for I have been unable to get in touch with Schroedinger. I saw him about once a week, at a seminar. I tried very hard to find out what he is doing, and I offered to make any calculation interesting him since he was not interested in my work; but without success. ... As a result of two months here, I have no news regarding new developments in physics to give you."
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But there was exciting news in chemistry. Immediately upon arriving in Zurich, Pauling found out that two young Germans, Walter Heitler and Fritz London, had found a way to apply wave mechanics to the electron-pair bond in the hydrogen molecule.
Pauling and Ava Helen had been friendly with Heitler and London while in Munich, where the four of them had celebrated one night at the Neue Boerse restaurant, toasting Heitler's new doctoral degree with champagne. They had talked about the problem of the quantum nature of the chemical bond then, but none of them had a clear answer. The breakthrough happened for Heitler and London a few months later, when they went to Switzerland to work as postdoctoral fellows with Schroedinger.
When Pauling got to Zurich, he looked them up, and they began talking. The key to Heitler and London's success, he learned, was an idea developed by Heisenberg the year before, which he called electron exchange, or "resonance." The basic idea was that under the right circumstances electrons could switch places with one another very rapidly; Heisenberg had used it to explain some odd spectral lines in helium. Heitler and London expanded the concept to the chemical bond: They imagined two identical hydrogen atoms, each with its own electron, approaching each other. As they neared, the chances would increase that an electron from one could find itself attracted to the nucleus of the other. At a certain point, an electron would jump to the new atom, and an electron exchange would begin taking place billions of times every second. In a sense, the electrons would be unable to tell which nucleus was their own. It was this interchange, Heitler and London believed, that provided the energy to draw the two atoms together. Their calculations indicated that the electron density tended to concentrate in the area between the nuclei, thus lessening the electrostatic repulsion between the two positively charged cores. At a certain point, that positive-positive repulsion would balance the energy of the electron exchange, setting up a chemical bond with a definite length.
This idea of an electron exchange was a new concept in chemistry—before Heisenberg there had been nothing like it in physics, either—but it seemed to work. The calculations based on the system very roughly corresponded to the experimental values of several technical constants for the hydrogen molecule, and the Heitler-London model made sense in other ways as well. Pauli's exclusion principle stated that two electrons could share the same orbit only if they had opposite spin, a state that Heitler and London found was necessary for their bond to occur in the hydrogen molecule. Paired electrons forming the cement between atoms: This was Lewis's shared electron bond, now given a strong quantum-mechanical foundation, a mathematical explanation. Again the new physics had pointed the way to a strange new reality.
Pauling was excited when he saw Heitler and London's results, and he spent most of his time in Zurich working with their ideas.
While he talked a great deal with Heitler and London, typically he worked on his calculations alone. He didn't produce a paper during that period. But by the time he set sail on the first of September to return to America, he was committed to applying Heitler and London's resonance interpretation of chemical bonding to all types of questions about chemical structure. It would form the basis of much of his work for the next decade.
CHAPTER 6
The Bond
Tetrahedra
Caltech was booming when Pauling returned. Under Robert Millikan's aggressive leadership, the number of students had grown to six hundred by the fall of 1927, including one hundred graduate students. The Caltech physics department now published more papers per year than any group in the nation. George Ellery Hale was negotiating a stupendous grant to build the world's biggest telescope atop Mount Wilson. A department of geology had been started, and an aeronautics laboratory was on the drawing board. Most important, word had just been released that the nation's most renowned geneticist, Thomas Hunt Morgan, was coming to start a biology division. Biology, along with physics and chemistry, would complete the triumvirate of sciences at Caltech, and Morgan, the man who had narrowed the site of the gene down to individual chromosomes—and in doing so made his experimental model, the fruit fly, famous—was the perfect leader. He was a top player, well connected and well funded, and had been lured from Columbia University in typical Caltech style, with promises of his own laboratory building and a substantial research endowment. His arrival in 1928 immediately made Caltech a national force in biology.
Pauling, Ava Helen, and Linus junior moved into a small rental house at 320 South Wilson Street, two blocks from campus, and Pauling readied himself for his first official year as a professor. But he would not carry the grand title of assistant professor of theoretical chemistry and mathematical physics that Noyes had written him about in Munich. The "mathematical physics" part had been dropped. "I don't know what happened with the physics," Pauling remembered. "Whether Millikan objected to my having a joint appointment or whether Noyes . . . may have decided that he didn't want me to be associated with the physics department in any way, that perhaps I would shift. I didn't care." The title he ended up with, assistant professor of theoretical chemistry, was, perhaps not coincidentally, the same Noyes had had for years at MIT.
Pauling was put in charge of the Caltech x-ray laboratory, which Roscoe Dickinson had abandon
ed to move on to other studies. His first office was a desk in the corner of the x-ray lab, from which he could directly oversee the activities of his first official graduate student, a diligent young chemist fresh from Texas named J. Holmes Sturdivant. Pauling began preparing for his first course as an assistant professor—"An Introduction to Wave Mechanics with Chemical Applications"—by writing out 250 pages of notes in longhand. He would later turn them into a book on the subject.
The rest of his energy went to his own scientific work. As always, his mind ranged over several problems at once. Before leaving Europe, Pauling had made arrangements with Samuel Goudsmit to translate and help expand his Dutch doctoral thesis into a book on spectroscopy. The two young theorists completed the book by correspondence, with Goudsmit writing some chapters; Pauling wrote others and handled the final editing. It was published in 1930 as The Structure of Line Spectra, Pauling's first book but one that already carried the stamp of his unquenchable self-confidence: At least one reviewer complained that the authors' assured tone gave the impression that there was little more to be learned about line spectroscopy. Other reviews were positive, and the book became a moderate success.
But the book with Goudsmit was also a work of pure physics, which raised questions about Pauling's position at Caltech. After it was published, Pauling taught a course based on the book in the chemistry department, but it was offered only once before Noyes shut it down. He told Pauling that Millikan had complained about physics courses being taught in the wrong division, but Pauling later guessed that Noyes made the decision on his own in order to keep him focused on chemistry.
The incident underlined a problem for Noyes. Pauling was interested in many things, perhaps too many things, including theoretical physics. That was fine as far as it went—Noyes had, after all, sent him to Europe specifically to learn the new physics—but the plan now was that Pauling apply his lessons to chemistry rather than leap into physics.
For a few months after returning from Europe, Pauling was tempted to focus on pure theoretical physics. Quantum mechanics was fascinating, and Sommerfeld had given him the tools he needed to do well in the field, especially in America, where quantum physicists were hard to find. On the other hand, he had seen that the Heisenbergs and Paulis and Diracs, with their dazzling mathematics and philosophical insights, were well ahead of him in making major discoveries. Pauling was, in fact, for perhaps the only time in his life, intimidated by the competition.
He wanted to accomplish something significant, and the place to do that, he realized, was in the zone between the new physics and chemistry. There might be few quantum physicists around, but the number of American researchers who could apply quantum mechanics to chemistry in the late 1920s was even smaller. Most of them were not chemists at all, but physicists with an interest in chemistry. Pauling was unique in combining both deep mathematical and physical knowledge with the training and worldview of a chemist. Quantum mechanics had opened up a new vista here, promising a vast new field of chemical applications, especially in relation to the question of the chemical bond. The field was wide open and unexplored, a place to discover something big, to make a name. "I thought there was a possibility of doing something better, but I didn't know what it was that was needed to be done," Pauling remembered. "I had the feeling that if I worked in this field I probably would find something, make some discovery, and the probability was high enough to justify my working in the field." Within a few months of returning to Caltech, Pauling wrote a colleague, "I am sure that I shan't be led astray by the will-o'-the-wisp of theoretical physics." Chemistry would be his focus, but a new type of chemistry, one transformed by the new physics.
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His work proceeded rapidly. On the chemical bond question, for instance, he thought there was still much left to do. Heitler and London's resonance breakthrough with the hydrogen molecule was just a first step, to Pauling's mind, and their attempts with more complex molecules left much to be desired. These were physicists, after all, not chemists, so they could not be expected to understand how their exchange-energy concept related to the huge cornucopia of chemical phenomena, most of which they knew nothing about. Even though they had beaten Pauling to the first successful quantum-mechanical attack on the chemical bond, there was still much he could do to expand and rework their original insight.
One of the first things he did was to prepare a long article for Chemical Reviews in which he introduced the Heitler-London chemical bond work and added some new insights of his own into its application to the one-electron hydrogen molecule-ion. This was the first that most chemists had ever seen of the quantum mechanical approach to their field, and it marked Pauling's entrance onto the American scientific stage in his new role of quantum-chemist.
Then he made a daring leap. In the spring of 1928 he wrote a brief note to the Proceedings of the National Academy of Sciences in which he outlined what he called Heitler and London's "simple theory" of the chemical bond and noted that it was "in simple cases entirely equivalent to G. N. Lewis's successful theory of the shared electron pair." Nothing new there. But at the end, in a single paragraph, he announced a significant advance. His calculations, he said, showed that quantum mechanics could explain the tetrahedral binding of carbon.
This woke readers up. Carbon was a much-studied element, the linchpin of all of organic chemistry. Strings of carbon atoms formed the backbone of proteins, fats, and starches—the major constituents of living systems. Carbon chemistry was the chemistry of life.
But physicists and chemists could not agree on carbon's electronic structure. It was known that each carbon atom carried a total of six electrons, the first two of which had nothing to do with forming bonds, since they paired to re-create the two-electron inner-electron structure of helium. The remaining four electrons should be, in theory, at the next energy level, in the so-called second shell of the atom. Chemists knew that carbon offered four bonds to other atoms and that in nature these were almost always the same size and strength and oriented to the corners of a three-sided pyramid, or tetrahedron.
But physicists said this should not happen. The most recent spectroscopic studies showed that carbon's four binding electrons existed in two different energy levels, or subshells. The two lower-level electrons should pair with each other, leaving only two to make bonds with other atoms. Carbon, the physicists said, should have a valence of two. And there were rare cases where it did: carbon monoxide, for instance, where the carbon is double-bonded to a single oxygen atom.
Reconciling the physicists' carbon and the chemists' was a major challenge, and Pauling was determined to meet it. The physicists' spectroscopic evidence was undeniable, as was the chemists' tetrahedron. Both groups somehow had to be right.
In his 1928 note, Pauling proposed an explanation based on Heitler and London's exchange energy. Each time a new bond was created, new exchange energy was involved. The exchange energy resulting from forming four tetrahedral bonds, he wrote, was sufficient to break carbon's four binding electrons out of the physicists' subshells and allow them to assume new forms.
This was an exciting idea, but one that would have to be backed up with considerable mathematics. Pauling didn't present any in his note, however, writing that "the detailed account of the material mentioned in this note will be submitted for publication in the Journal of the American Chemical Society." He then sent a proof copy of his note to Lewis with a letter saying: "It pleases me very much that in the new atomic model the salient features of the Lewis atom have been reproduced as much as those of the Bohr atom."
Nearly three years would pass before Pauling's "detailed account" appeared. In 1928 he had worked out enough convoluted calculations to convince himself, at least preliminarily, that his idea was right, but "it was so complicated that I thought people won't believe it," he said. "And perhaps I don't believe it, either. . . . Anybody could see that quantum mechanics must lead to the tetrahedral carbon atom, because we have it. But the equations were so complicated th
at I never could be sure that I could present the arguments in such a way that they would be convincing to anybody."
Today, with computers to run the equations, precise answers are possible. But in 1930, completely solving the equations for virtually any molecular system was impossible. Pauling, like every theoretician working to apply wave mechanics to complex systems, was forced to find shortcuts, various assumptions and approximations, schemes for further simplifying the mathematics.
The same hurdle was stalling London and others interested in the field. The difference with Pauling was that he was confident enough that the mathematics would fall into place to publish his preliminary thought, thus ensuring scientific priority. He then set his graduate student, Sturdivant, an able mathematician in his own right, to work on the tetrahedral-wave-function problem. When Sturdivant got nowhere after weeks of work, Pauling, now on to other problems, set the carbon problem aside.
Pauling's Rules
Caltech continued to lure the world's foremost theoretical physicists to California for visits, and in the late 1920s, Pauling helped to welcome Heisenberg, Sommerfeld, and Dirac. He maintained a strong interest in their work and turned out a few papers of his own on physics oriented topics, such as the momentum distribution of electrons and the influence on them of light and x-rays.
He spent most of his time, however, solving molecular structures using x-ray crystallography, and here he found himself stymied. If a structure in which he was interested involved more than a few atoms, it was almost impossible to solve. The problem was again in part mathematics, this time the terrific calculations needed to translate into a three-dimensional structure the patterns that diffracted x-rays sprayed on a photographic plate. The more atoms involved in the molecule, the more complex the pattern and the more structures were theoretically possible. Each added atom greatly increased the difficulty.