by Thomas Hager
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When the new semester started in the fall of 1926, Pauling took Sommerfeld's first official lecture section on wave mechanics—history's first full-semester lecture course on the subject—in which Sommerfeld systematically explained the powerful mathematics of Schroedinger's wave picture of the atom. As was often the case when he presented new material for the first time, Sommerfeld taught himself about the advances along with his students. He would later remember, "My first lectures on this theory were heard by Linus Pauling, who learned as much from them as I did myself."
A new wave-mechanical universe began opening up for Pauling. One of the great failures of the Bohr-Sommerfeld atom was its inability to predict anything more than the spectra of the simplest atoms; it did not lend itself to useful explanations of other properties, such as paramagnetism, polarity, three-dimensional structure, and chemical bonding. There was much to be done expanding the approach to include more complex atoms and more varied chemical properties.
The problem was that although Schroedinger's wave equation was relatively straightforward in calculating the energy levels of a single electron around a single nucleus, each additional element had to be calculated individually, along with the effects of each on the others. Precise mathematical solutions quickly became impossible. By working with the techniques he developed in correcting Wentzel's paper and calculating screening constants, however, Pauling simplified the picture. He concentrated on the outermost electrons only. This made it possible for Pauling to use wave mechanics to calculate light refraction, diamagnetic susceptibility, and the sizes of larger, more complex atoms—the first time wave mechanics had been applied to many of these problems and a pioneering advance in the field.
By late December he was in his room banging out a draft of a long paper on an old German typewriter, thus avoiding the double fees Munich typing agencies charged for papers in English. Ava Helen listened and waited and peered over his shoulder. "Are you sure this line on this curve should go the way it's drawn?" she asked him at one point, pointing at a figure he had created to illustrate the paper. "Of course I'm sure. I drew it," he replied. Then he looked at it again, thought a moment, and changed it.
Finally, it was ready to give to Sommerfeld. The director was impressed. He used his position as a foreign member of the Royal Society of London to offer Pauling's paper, "The Theoretical Prediction of the Physical Properties of Many-Electron Atoms and Ions," for publication in the society's Proceedings. In a cover note Sommerfeld wrote, "I am persuaded that these questions, which are fundamental for the structure of the atom, have never before been treated with such thoroughness and completeness."
Pauling knew he had written a good paper as well and was ready to take his screening-constants idea even further. "I believe that this work is of considerable value," he wrote Noyes. "The possible extensions and applications of the method are numerous; for example, I am now working on the sizes of ions in crystals, and the question of the occurrence of different types of crystals."
By bringing his new quantum-mechanical tools back to the study of crystals, Pauling was closing an important loop in his interests. At Caltech he had been frustrated by the inability of x-ray diffraction to solve the structures of any but the simplest crystals. To get beyond this limitation, the Braggs and other crystallographers had been building tables of the sizes of ions—electrically charged atoms such as the sodium and chlorine atoms in table salt—based on their work with simple crystals. The hope was that such tables could be used to discover some general rules or patterns that could be extended to solve the structure of crystals too complex to attack directly. Whoever came up with the most useful set of rules would make it possible to solve hundreds of these more difficult crystal structures.
Pauling was now able to attack the problem from a different angle, using quantum mechanics and the technique he had developed to correct Wentzel's paper. Within a few weeks of his Royal Society contribution, Pauling finished another major paper. The sizes of ions, he wrote, are determined by their outermost electrons; these outer electrons behave in ways determined in great part by how well more inner lying electrons shield them from the nucleus. The distances between ions in a crystal are also affected by the repulsion between the two positively charged nuclei, another factor affected by electronic shielding. Using his new screening constants, Pauling was now able to build a table of ionic sizes firmly based in quantum mechanics, and he used the values he determined to start building a set of general rules underlying crystal structures.
These two papers, both published in early 1927, helped establish Pauling's international reputation and pointed the way toward future work. In both of them he used a semiempirical method: calculating theoretical values for properties, comparing them to what was known from experiment, then correcting the theory to more closely match reality. True to Sommerfeld's teachings and his own temperament, he used whatever worked—the Royal Society paper included elements from classical, old quantum theoretical and new quantum-mechanical physics. More important, he consummated the marriage of two powerful scientific tools, x-ray crystallography and wave mechanics, by using each to check the accuracy of the other. "I think that it is very interesting that one can see the [psi] functions of Schroedinger's wave mechanics by means of the x-ray study of crystals," Pauling wrote Noyes. "This work should be continued experimentally. I believe that much information regarding the nature of the chemical bond will result from it."
Heitler and London
The chemical bond was one problem with which Pauling was not making much headway. He wanted more time in Europe, and that winter he applied for a six-month extension of his Guggenheim fellowship in order to further investigate "the atomic model obtained from Schroedinger's interpretation of his wave mechanics, especially with reference to the use of this model in the explanation of the chemical bond in molecules and in crystals." He planned to leave Munich in mid-February for two weeks in Goettingen with Born, then to Berlin to study crystal-structure techniques, then to Copenhagen to see Bohr for six weeks, Zurich for the three-month summer semester with Schroedinger, and finally a quick visit with the Braggs in England on the way home in September. Sommerfeld added a cover letter to Pauling's request, writing, "My colleagues and I have the impression that he is an extraordinary, productive scientist with many interests, in whom it is justified to place the greatest expectations." Pauling was granted the extension.
There remained the question of what he would do when he came back to the United States. Just after Christmas of 1926 he wrote Noyes, "I have just realized that the time will soon be here when [Caltech], as well as other universities, makes its decisions regarding the staff for the next year; so that definite arrangements regarding my position and salary will also soon be made. I have had no offers from any one, for I have thought, and accordingly expressed myself as believing, that I would return to the Institute." A week later he wrote to G. N. Lewis, hinting that he might be available for the right price: "So far I have no definite position for next year; but I promised Dr. Noyes that I would return to the Institute next year unless I received from some one else an offer better than theirs (how good it will be I do not know)." It was some months before Lewis wrote back; "I had some hopes that you might be offered a position in our Physics department, but different plans have been made, for this year at least," he wrote. "In any case I am afraid that Dr. Noyes would be quite disappointed if you did not return to him."
Lewis's looking to the physics department was logical. Pauling had thrown himself into the study of theoretical physics with such enthusiasm that there was some question as to whether he was still a chemist. During nearly a year in Munich he had never visited the university's Institute of Physical Chemistry, and with the exception of a few chats with its director, Kasimir Fajans, he ignored the chemistry faculty altogether. All his contacts and all his research were in theoretical physics.
But his own temperament and skills led him back to chemistry. At OAC and Caltech,
Pauling had become accustomed to being one of the quickest and brightest students. But in Europe he found himself a lesser-known among a muster of brilliant young men about his age (including Pauli, Heisenberg, Dirac, and Jordan). "I had something of a shock when I went to Europe in 1926 and discovered that there were a good number of people around that I thought to be smarter than me," he remembered, mentioning Heisenberg, Pauli, and Bethe in particular. He was beginning to feel the limits of his mathematical abilities as well, which he felt were good enough for the semiempirical approach he took to chemical questions but were not of the caliber required for rigorous mathematical physics.
On the other hand, "I got to thinking that I know some things—a lot about chemistry—that other people don't know," he said. After a year in Munich, Pauling wrote Noyes: "Most people seem to think that work such as mine, dealing with the properties of atoms and molecules, should be classed with physics, but I . . . feel that the study of chemical substances remains chemistry even though it reach the state in which it requires the use of considerable mathematics. The question is more than an academic one, for the answer really determines my classification as a physicist or chemist." Regarding his own work, he wrote, "One can hardly class this with Physical Chemistry, as ordinarily understood; possibly Molecular Chemistry would be a suitable designation."
There had never been such a thing as a "molecular chemist" before. Perhaps, Pauling seemed to suggest, he was in a field of his own. But designations didn't matter to Noyes; he wanted Pauling. Physicists wanted to discover the laws underlying atomic reality; Pauling wanted to use those laws to make chemistry more rational, more mathematical. It was the same dream that had driven Ostwald and then Noyes: chemistry illuminated by the light of physics. Only now the physics had fundamentally changed. And Pauling had the skills to make sense of it all.
In the late spring of 1927, Noyes wrote Pauling, offering him a position at Caltech with an unusual title that reflected his hybrid interests: assistant professor of theoretical chemistry and mathematical physics.
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A few weeks after Pauling learned he had gotten the extension of his Guggenheim, he and Ava Helen were in Copenhagen at Niels Bohr's institute, the epicenter of the quantum revolution. It was already a place of legend. People talked about Der Kopenhagener Geist (the spirit of Copenhagen) that permeated Bohr's institute: a spirit of cooperation, collaboration, and friendship, of endless talks in which ideas from the new physics were teased out as far as they could go. Pauling had come without a formal invitation after hearing from a colleague that one didn't arrange to attend Bohr's institute; one simply appeared and was enlightened. It turned out to be bad advice. Pauling found that it was almost impossible to see the great man; Bohr's mind was on larger questions.
During the spring and summer of 1927 quantum mechanics was entering a new phase. Late in the previous year Schroedinger and the English prodigy Paul Dirac had begun healing the rift between wave and matrix mechanics by showing that the two systems were mathematically equivalent, that they gave the same answers to the same questions. But what physical reality lay behind the numbers? After a marathon meeting with Bohr, Schroedinger gave up the idea that his wave equation described an actual electron "smear," as he had originally proposed. The work of Born and others indicated that instead of an actual wave, his equation described not a physically apprehensible "thing" but a statistical probability, the mathematical likelihood of finding an electron within a certain area.
Schroedinger and Heisenberg had succeeded not in describing the atom but in trapping it with numbers, taming it so that its behavior could be predicted. This predictive ability was powerful and vitally important. With stunning swiftness, it became clear to open-minded physicists that the new quantum mechanics worked, that it pointed the way to new findings in cases where the old system had simply failed. But Heisenberg and Schroedinger would continue to argue over the reality behind the numbers.
For instance, there was the problem of how an electron could simultaneously be both a wave and a particle. After months of hammering away at the question, after countless mind-numbing discussions with Schroedinger and especially Heisenberg, Bohr decided that both descriptions had to be right. Atomic reality was (at least) two-faced: The electron you found depended on how you chose to observe it. Both wave and particle descriptions were correct, and both were needed. They were complementary. The refinement of this "Copenhagen interpretation" of quantum physics took up much of Bohr's time during the period Pauling was in Denmark.
That description also seemed to beg the question. What was an electron? It was not a tiny planet whizzing around the nucleus. It was not a wave, exactly, nor was it exactly a particle. It was becoming clear that no one could describe it in a way that could be visualized. The wave/particle duality and quantum jumps were unlike anything anyone had ever experienced; at the atomic level, things behaved in ways deemed impossible at the level of the senses. After endless discussions with Bohr, Heisenberg would go for long walks alone and wonder: Can nature possibly be as absurd as it seems to us in these atomic experiments?
Physics was now merging into philosophy, a process given popular impetus when Heisenberg posited his "uncertainty principle" in March 1927. In a fairly straightforward extension of his matrix ideas, Heisenberg showed that it was impossible for an observer to know both the precise position and velocity of an electron. All you could know for certain was the statistical likelihood of an electron being in a certain area, with no guarantee it would actually be there. His thoughts were practical at their core: Anyone trying to observe an electron would require some sort of light energy to do it, and even the smallest packet of light would knock the electron around, affecting the observation. We could never be certain in looking at electrons. We had reached, at the level of the atom, the limits of observability.
This raised larger questions about the understanding of nature. If what Heisenberg was saying was true, then not only had we reached the limits of precise observation, but cause-and-effect, as it was then conceived, didn't hold within the atom: You couldn't say an electron definitely caused something if you could only say it was "probably" somewhere in the vicinity. Physics up to this time had been built upon determinism. If the sizes, velocities, and angle of collision of two billiard balls were known, a prediction could be made about what would happen after they hit. In the same way, according to Newton's classical physics, the current positions and velocities of the particles in the universe would determine, through cause and effect, the future positions and velocities of every particle. The future was held in the present. But Heisenberg's uncertainty principle said you couldn't predict the future of a single electron, much less the universe.
Ever the pragmatist, Pauling found these discussions pointless. Heisenberg had given Pauling proof sheets of his paper on the uncertainty principle, and Pauling was aware that the idea was spurring a lot of speculation about philosophical questions such as predestination. But, he decided, none of this meant much to everyday existence. "Even if this were a classical world, it would be impossible for us to determine the positions and momenta of all the particles of the universe by experiment," Pauling pointed out in a later interview. "Even if we did know all of them, how would we carry out the computations? We can't even discuss in detail a system involving, say, 1020 particles or 1010. I think it is meaningless to argue about determination versus free will, quite independent of the uncertainty principle." Any question that did not lead to a real-world experiment or observation was not important to Pauling. If it had no operational significance, "it becomes just a matter of semantics," he said. As a result, "I have never been bothered by the detailed or penetrating discussions about interpretation of quantum mechanics."
The long talks about philosophical issues at Bohr’s institute left him cold, and he wasn't having much success in Copenhagen with his own calculations on the chemical bond. Early in 1927 a young Danish physicist named Burrau had published what appeared to be a successful applic
ation of Schroedinger's wave equation to the simplest possible molecule: the hydrogen molecule-ion, two hydrogen nuclei bound by a single electron. Burrau's results showed that the electron distribution tended to concentrate between the two nuclei, with the electron's attraction for the nuclei balancing their repulsion. It was the first crack in the door, an indication that the wave equation could help solve the chemical bond, and Pauling worked to extend Burrau's ideas to the next step, the hydrogen molecule with two electrons and two nuclei. But he got nowhere. The wave equation was hard enough to use in describing electrons in individual atoms, as Pauling had done in his paper on the sizes of ions. Going to the next step of complexity was much more of a challenge. You had to consider and calculate the repulsion of the two nuclei, the attraction of each electron for each of the nuclei, the repulsion of the electrons by each other; it quickly became a mathematical impossibility. Simplifications and assumptions about the form of the molecules had to be made. Heisenberg and Dirac already had tackled the problem without success. And during the time he was in Copenhagen, Pauling was frustrated as well.
He did, however, make a valuable contact among the crowd of researchers flocking around the great Bohr: Samuel Goudsmit, one of the young codiscoverers of electron spin, who was just finishing his doctoral thesis. Pauling hit it off with "Sem," as everyone called him. Goudsmit was interested in explaining the fine structure of spectra in quantum-mechanical terms, and Pauling helped him with some theoretical calculations. Before long Pauling was suggesting to his new friend that he help translate Goudsmit's doctoral thesis into English.