The Nature of Interatomic Forces in Metals, 1938

Linus Pauling, ca. 1930s

“In recent years I have formed, on the basis of mainly empirical arguments, a conception of the nature of the interatomic forces in metals which has some novel features.”

­-Linus Pauling, 1938

Prior to the publication of this article, which appeared in the December 1938 issue of Physical Review, much about the interatomic forces operating in metals was either unknown, or theoretical predictions did not align properly with observed data. In publishing this paper, Linus Pauling first sought to align the incongruencies between theory and data for the transition metals, such as iron, cobalt, nickel, copper, palladium, and platinum. He was then able to correctly predict properties including “interatomic distance, characteristic temperature, hardness, compressibility, and coefficient of thermal expansion” by discarding previously held assumptions and inserting new – and correct – assumptions about transitions metals.

The most significant idea that Pauling introduced with this paper was the notion that the valence shell electrons – those in the outer shell – play a part in bonding. Previously, scientists believed that these electrons made “no significant contribution” to bond formation. Pauling was able to establish otherwise, and used this breakthrough to both align observable data with theoretical data, and make other predictions about transition metals.

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The 1938 paper was written in the wake of a revolution within the world of chemistry. A raft of new theories brought about by a widening understanding of quantum mechanics was generating intense excitement for scientists world-wide, and the tools that quantum mechanics provided for helping to “correct” previous understandings of the chemical bond were of paramount interest to many. Pauling, of course, was a leader in this area, his body of work ultimately garnering the 1954 Nobel Chemistry Prize for “research into the nature of the chemical bond and its application to the elucidation of the structure of complex substances.”

Within this area of focus, many scientists were especially interested in exploring the ways that metals bonded because, as noted, the observed data did not match up with theory. Pauling sought to mend this gap by using quantum mechanics to look at interatomic forces in a novel way. Prior to the Physical Review paper, chemists believed that when metals bonded, their valance shell electrons played only a small role in the resulting structures. Pauling argued otherwise, and put forth an important new theory that the valence shell electrons contributed to the process through resonance, a theory that he had developed earlier in the decade and continued to champion.

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Because the crux of Pauling’s scientific intervention was to prove that valence shell electrons are involved in bonding, most of the paper is devoted to supporting this claim. The primary tool that Pauling uses to craft his argument is an analysis of temperature predictions. According to the reigning theory regarding metals and valence shell bonds, when bonding occurred, the electrons would bond in a manner that would create a moment of ferromagnetism. Specifically, it was theorized that these ferromagnetic moments would be temperature dependent, meaning that as the temperature of the metal changed, its degree of magnetism would also change in a predictable way. Experiments had shown however, that when metals bonded, their ferromagnetism remained independent of temperature.

Pauling exploited this piece of information and used it to support his theory. According to Pauling, if metals bonded through resonance, they would create ferromagnetic moments that were temperature independent, a hypothesis that correctly aligned with the observed data.

To develop his argument, Pauling made specific use of the element Vanadium, which has an electron configuration of 3d³4s². Under the old model, Vanadium’s valence electrons could only interact weakly in bonding if, at most, two of the 4s² electrons were involved in a bond. This, according to Pauling, would create ferromagnetism which would decrease with increasing temperature, meaning that it was temperature dependent. On the contrary, the experimental evidence showed that Vanadium’s magnetism was temperature independent. This meant, therefore, that weak valence interaction during bonding was not possible.

Pauling’s alternative suggestion was that all of Vanadium’s valence electrons were involved in bonding through resonance; not just the two 4s² electrons, as previously believed. Further, if the valence electrons bonded through resonance, the ferromagnetism of their structure would be temperature independent, a prediction that aligned with the observed data.

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Once Pauling was able to prove that the valence electrons in Vanadium bonded through resonance, he then began to apply the concept to all transition metals. As with the previous example, Pauling continued to support the concept by comparing predicted outcomes with empirical data. And once again, when viewing the bonding through the prism of resonance, predicted outcomes of magnetic moments began to align with the empirical data.

Pauling then took it another step by repeating the exercise with interatomic distances. As demonstrated in his paper, a resonant structure would correctly predict the interatomic distances that had been observed for many bonds. Pauling also claimed that other properties, such as the “compressibility, coefficient of thermal expansion, characteristic temperature, melting point, and hardness” would likewise correctly align with experimental evidence, once resonance was used to explain valence shell bonding.

Though clearly a significant breakthrough, the assertions that Pauling made in his paper were grounded in work done by others — notably the quantum mechanical theory of ferromagnetism developed by Heisenberg, Frenkel, Bloch, Slater, et al., and Wolfgang Pauli’s theory of the temperature-independent paramagnetism of the alkali metals. And while the 1938 article acknowledges these debts, it also attempts to improve upon them.

This was especially so with the quantum mechanical theory of ferromagnetism. As we have seen, Pauling successfully applied the idea of temperature independence and ferromagnetism to support his claims, but he also found one aspect of the theory to be needlessly bothersome. As Pauling noted, in order for much of the theory to work on a mathematical level, scientists were compelled to assign positive numbers to all unpaired valence electrons. Pauling recognized that this was only necessary if it was assumed that valence electrons did not play a large role in bonding for metals. Under a resonant scenario, Pauling was able to show that the math could still work if the valence electrons were negative and that, once again, “this conclusion agrees with the observation.”

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

[Part 1 of 7]

Over the span of just two short years beginning in 1931, Linus Pauling published seven decidedly influential papers on the nature of the chemical bond. In the series, which formed the foundation for his 1939 book, The Nature of the Chemical Bond, Pauling introduced many chemists to the burgeoning field of quantum mechanics and demonstrated its applicability to structural chemistry. As a result of this work, Pauling was awarded the 1954 Nobel Prize in chemistry, “for his research into the nature of the chemical bond and its application to the elucidation of the structure of complex substances.” With today’s post, we begin a series that attempts to explore the scientific advancements and ideas put forth in each of the seven papers.

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“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.” Journal of the American Chemical Society, April 1931.

The first paper in the series was perhaps the most important, in that it set the theoretical foundation for the six papers – some of them more practical than theoretical – yet to come. In it, Pauling sought to lay the groundwork for ideas that he would expand upon in future articles, notably pointing out that “many more results of chemical significance can be obtained from the quantum mechanical equations.” A statement of this sort was necessary because, up until that point, quantum mechanics had mostly been seen as a tool for physicists to use within their discipline. In order to convince chemists of the usefulness of quantum mechanics to their own work, Pauling put forth a conceptual framework consisting of a series of rules as well as guidance on how to apply them to molecular orbitals.

Three of the six rules that Pauling stressed in his paper were already well-known to chemists, but were needed in order to generate “buy-in” for the three additional rules that were new to the field. The most important of these was the fifth rule, which stipulated that when two electrons are in the process of forming a bond, the electron with the larger eigenfunction value will dictate the direction and shape of the bonds that are subsequently created. Pauling argued that this type of electron pairing would result in the most stable bonds possible.

Importantly, Pauling’s rules also combined ideas about wave functions with quantum mechanical thinking in a way that pushed the field forward. Earlier iterations of quantum ideas were not holding up well to certain experimental data. For example, it was known that electrons occupied quanta states, but the observations of the energy associated with these states did not always match what might be predicted by quantum theory. Through his study of both wave theory and quantum mechanics, Pauling recognized that shared bonding energies could explain certain observed bond energies and angles. As such, with his rules, Pauling helped chemists to merge quantum mechanics and wave functions, in the process creating a model that was predictive for all molecules.

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In addition to conceptual rules for electron-pair bonding, the first article also helped to establish rules regarding the splitting or breaking of molecular orbitals, a concept that was completely new. The traditionally held belief was that orbitals were firmly set, but Pauling believed that if this were not true, then a whole new set of tantalizing possibilities was on the table. (Indeed, Pauling’s idea that orbitals could be split or broken formed the germ of his later work on the theory of resonance, which proved hugely influential.)

In this section of his paper, Pauling’s main focus was the s and p orbitals. Prior to his article, these orbitals were thought to occupy discrete quantum states that could not be broken. However, based on his earlier assertions that combined wave functions and quantum mechanics, Pauling argued that quantized states could, in fact, sometimes be broken. In subsequent writings, Pauling would conclude that the hybridization of orbitals allowed for the breaking of quantized states, but in this earlier phase of his thinking, he instead put forth that the orbitals were simply broken.

This was, of course, a big theoretical leap, but throughout his series of seven papers, Pauling often chose to base theory on informed guesses, even if he did not always have a precise understanding of how the rules worked. In this particular instance, Pauling used his fifth rule to rationalize the idea of breaking orbitals, positing that, when bonding, the stronger of two electrons would force the weaker to overlap and ultimately create new bond angles.

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Though he did not yet fully understand all the minutiae of how it could be possible for orbitals to break, Pauling did know that the rules governing chemistry at the time were not sufficient, since they were unable to explain why molecules were sometimes observed to be more stable than predicted. By leaning on the notion that orbitals could break, Pauling was able to devise a set of rules that overlapped almost perfectly with the experimental data. In his paper, Pauling spoke particularly of the tetrahedral carbon atom,

in which only the s and p eigenfunctions contribute to bond formation and in which the quantization in the polar coordinates is broken can form one, two, three, or four equivalent bonds, which are directed towards the corners of a regular tetrahedron.

The idea of a tetrahedral angle is well-known within structural chemistry today, but it was a novel concept in 1931. As such, with his first paper, Pauling was not only proposing that orbitals could do things previously unheard of (i.e. break), but that they also formed angles that were completely new. Pauling knew that these ideas were revolutionary and devoted a significant component of his article to describing the tetrahedral angle in detail.

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The s and p orbitals that Pauling addressed were important to many chemists because they formed the building blocks of carbon atoms. Analysis of larger orbitals however, such as the d orbitals, was often kept separate from discussions of the s and p orbitals, because the chemistry of the time lacked a unified law that could apply to both smaller and larger orbitals alike.

Pauling combated this by explaining that his six rules were constant, and that they could be applied to all scenarios, not just the s and p orbitals. From there he reasoned that, while more complicated molecules might open up additional possibilities for bond angles, the proclivity for bonds to form tetrahedral angles still applied. Pauling further argued that this idea was supported by the experimental data. In the case of cobalt for example, Pauling noted that both the predicted and observed angles are six equivalent sp³d² bonds, and that because of his fifth rule, the bonds are pulled towards the corners of the octahedron that is formed, rather than the center.

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As if that weren’t enough, Pauling also addressed magnetization in his paper, a new concept that had long fascinated him. Even during his years as an undergraduate student at Oregon Agriculture College, Pauling was deeply interested in understanding how it was possible that certain compounds were magnetic, while others were not. What, Pauling asked himself, was causing the difference?

In the first paper, Pauling does not quite offer an answer, but he did lay out a series of observations that would lead to new insights on electronegativity, the subject of his fourth paper in the series. In paper one, Pauling specifically contended that, since unpaired electrons were fundamental to magnetic compounds, a model of the bond types that comprise a given molecule could be built using data on the magnetic properties of the molecule. Offering the transition group elements as an example, Pauling pointed out that, without exception, they pair with CN^–  to form electron-pair bonds; with F^–  to form ionic bonds; and with H₂O to form ion-dipole bonds.

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Later in life, Pauling reflected that his first paper on the nature of the chemical bond was “the best work I’ve ever done,” and indeed it is difficult to overstate the importance of the publication. In a single article, Pauling was able to put forth crucial new ideas on bonding in both simple and complex molecular structures using a standardized set of rules. The paper also began the process of applying the new quantum mechanics to help explain the structure of molecules in ways that better supported experimental observations. And while Pauling was later criticized by some for the assumptions that he had made, the value of the paper increasingly shone through as chemists came to understand the practical utility of the work to their own research.

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

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.

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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.”

“The Best Work I’ve Ever Done”

Linus Pauling, 1931.

[An examination of Linus Pauling’s first paper on the nature of the chemical bond, published in April 1931. This is part 1 of 2.]

“It seems to me that I have introduced into my work on the chemical bond a way of thinking that might not have been introduced by anyone else, at least not for quite a while. I suppose that the complex of ideas that I originated in the period of around 1928 to 1933 – and 1931 was probably my most important paper – has had the greatest impact on chemistry.”

-Linus Pauling, 1977

One of the major film documentaries chronicling Linus Pauling’s life was produced for the long-running NOVA series in 1977. By that point, when asked to look back over the decades of significant work that he had done, Pauling still singled out his insights into the chemical bond as being his most significant contribution to chemistry.

Pauling’s initial 1931 paper in particular marked the first time that he published his revolutionary point of view related to the chemical bond, and reflecting on that period Pauling went so far as to call the article “the best work I’ve ever done.” Indeed, the paper marked the first instance in which Pauling began to spell out the ways in which the burgeoning field of quantum mechanics might be applied to fundamental questions in chemistry. And though first in a lengthy series, Pauling placed major significance on this one paper because it profoundly changed the course of his career and set into motion a period of heavy influenced on the trajectory of an entire discipline.

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G.N. Lewis, ca. 1930.

While an undergraduate at Oregon Agricultural College, Pauling had been taught – and went on to teach his own students – the “hooks and eyes” theory of chemical bonding. In this model, each atom was presumed to have a certain number of hooks or eyes that determined how and to what other atoms it could connect. Though it prevailed at the time, the model was deemed to be outdated and insufficient by many of Pauling’s contemporaries, some of whom were concurrently searching for a more satisfactory replacement.

That said, “hooks and eyes” did serve as a useful precursor to the later concept of valence, because it correctly assumed that each atom possessed a concrete number of electrons to contribute to the formation of bonds with other atoms. The theory also suggested that there were rules governing how chemical bonds worked and how likely it was that two or more atoms might form a bond.

While Pauling was still a student in Oregon, he avidly read G.N. Lewis’ ideas about electron structure and also studied Irving Langmuir’s theory of valence, a tutelage that helped propel his own nascent interest in chemical bonding and atomic structure. Lewis proved to be particularly important. A chemist at the University of California, Berkeley and a future mentor of Pauling’s, Lewis proposed that eight electrons provided a maximally stable environment for a molecule, a tenet known today as the octet rule. Working from this idea, Lewis hypothesized that an atom containing, for example, seven electrons would bond more readily with an atom containing nine electrons, and that the bond that was formed consisted of the electron shared between the two atoms.

Lewis wasn’t the first to chase the nature of the chemical bond. Indeed, the problem had been under attack for a few decades. In 1911, Ernest Rutherford created the first modern atomic model, but ran into trouble because it wasn’t compatible with classical physics. Niels Bohr then updated this model. Less than twenty years after J. J. Thompson had discovered the electron, Bohr suggested that electrons orbited the nucleus in a predictable way, emitting quanta when they moved into lower orbits.

Arnold Sommerfeld, 1928.

From there, others sought to fill gaps in Bohr’s model. In 1915, Arnold Sommerfeld, a physicist with whom Pauling eventually worked, helped to devise what came to be known as the Sommerfeld-Wilson quantization rules. These guidelines provided an explanation for angular momentum by describing electron orbits as ellipses rather than perfect circles.

At the same time, Werner Heisenberg, Erwin Schrödinger and Max Planck (among others) were rapidly embracing a new way to look at physics, expanding the theory and mathematics behind involved in this innovative approach. In 1925, a year before Pauling began an influential trip to Europe, Heisenberg had authored his “Quantum Theoretical Reinterpretation of Kinematic and Mechanical Relations,” which many point to as the true beginning of quantum mechanics. Schrödinger then completed his wave function in 1926. By contrast, the Lewis and Langmuir models were part of an old system that – as soon Pauling discovered – was in the process of being discarded.

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Linus Pauling at the Temple of Neptune, Paestum, Italy, during his legendary Guggenheim trip to Europe. This photo was taken by Ava Helen in April 1926.

An admirer of Sommerfeld’s work, Pauling traveled to Europe on a Guggenheim fellowship to learn as much as he could about quantum mechanics, which at the time was referred to as “new physics.” He was especially keen to learn more about Schrödinger’s equation and to dig into the ways in which the wave function might be applied to a more sophisticated understanding of the chemical bond. Though impressed by Heisenberg, Pauling gravitated toward Schrödinger because he saw more potential for practical application of the wave function, as opposed to Heisenberg’s matrix mechanics. In a note penned during his travels, Pauling wrote specifically that

I think that it is very interesting that one can see the [psi] functions of Schrödinger’s wave mechanics by means of the X-ray study of crystals. This work should be continued experimentally. I believe that much information regarding the nature of the chemical bond will result from it.

These thoughts proved prophetic, as we will see in part 2 of this series.

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Pauling returned to Pasadena in the fall of 1927, bursting with new ideas. While he was away, Caltech chemistry chief A.A. Noyes had sent word that a unique position had been created for his promising young faculty member, one that lined up nicely with Pauling’s new interests. Upon his re-arrival at Caltech, Pauling was to begin working under the title of Assistant Professor of Theoretical Chemistry and Mathematical Physics.

Although Noyes eventually dropped the physics course from the appointment, Pauling liked the idea of hybridizing his interests into one name. It was at that point that he began referring to himself as a quantum chemist.

Linus Pauling’s Polyspheron Theory

[Part 1 of 2]

“I consider the polyspheron theory to be a simple statement about the insight into nuclear structure that is provided by the experimental data and to some extent by the quantum mechanical calculations.” 

– Linus Pauling, 1976

In the early twentieth century, when physicists were gaining knowledge of the properties of atomic nuclei in strides, the still young field of quantum mechanical theory was being used to interpret experimental data. At the same time, chemists were beginning to explore the implications of quantum theory as it pertained to molecular structure, a trend that culminated in Linus Pauling’s groundbreaking book, The Nature of the Chemical Bond, published in 1939.

In the following forty years however, no single theory of the structure of the atomic nucleus emerged that could conceptually account for all the results that chemists and physicists were observing. Nor was there a satisfactory theory that could link the behavior of the most infinitesimal and internal parts of the atom with the much larger scale of molecular behavior and chemical reactions. In other words, there was not yet a single accepted unified theory of quantum physics and chemistry. The pursuit of just such a theory stood as a holy grail of sorts, occupying the hopes, dreams and energy of many a twentieth century scientist.

For parts of five decades, Linus Pauling strove to develop just such a theory, one that could account for the basic structural tendencies and behaviors of the atomic nucleus and prove useful not only for atomic physicists but also for chemists. His efforts resulted in what he called “close-packed spheron theory,” simplified later as “polyspheron theory.”

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Though he had begun work on the topic much earlier, Pauling first revealed his theory to the world on October 11, 1965 at a meeting of the National Academy of Sciences, held at the University of Washington in Seattle. His talk that day was titled “The Close-Packed-Spheron Theory of the Structure of Nuclei and the Mechanism of Nuclear Fission,” and its contents mirrored a pair of similarly titled papers that he published that same year: “The Close-Packed-Spheron Theory and Nuclear Fission,” published in Science, and “The Close-Packed-Spheron Model of Atomic Nuclei and Its Relation to the Shell Model,” which appeared in the Proceedings of the National Academy of Sciences.

In each of these works, Pauling advanced a theoretical framework that incorporated features of three older theories – the cluster, shell and liquid-drop theories – while also accounting for several observed phenomena of atomic nuclei that were difficult to explain at the time, such as asymmetric nuclear fission. Importantly, the close-packed spheron model of the nucleus differed from past models by declaring “spherons” as its units, rather than nucleons. Pauling described his rationale for this choice as having been an outgrowth of his thinking about nuclear fission.

Twenty five years ago a phenomenon of tremendous importance was discovered, nuclear fission. In the uranium nucleus and other heavy nuclei, fissioning produces a lighter and a heavier nucleus, with mass ratio about 2/3, several hundred times as often as two nuclei with equal mass are produced.

Why is fission asymmetric in this way? Here is a simple reason why this might be: I assume that in nuclei the nucleons may, as a first approximation, be described as occupying localized 1s orbitals to form small clusters. These small clusters, called spherons, are usually helions, tritons, and dineutrons: in nuclei containing an odd number of neutrons, a (Helium-3) cluster or a deuteron may serve as a spheron.

Pauling’s basic assumption here was that, in atomic nuclei, the nucleons were in large part aggregated into clusters that are arranged as closely as allowed by the laws of physics. Nuclei with more neutrons than protons were called tritons or dineutrons by Pauling. Likewise, the clusters of neutrons and protons occupying localized 1s orbitals were called spherons.

The most important spherons in Pauling’s conception were aggregates of two neutrons and two protons, which he called helions, though they were already known to physicists as alpha particles. The localized 1s orbitals that these spherons occupied could also be described mathematically as hybrids of the central-field orbitals that are outlined in shell theory. This process of hybridization of orbitals provided a formal basis for relating the cluster model – of which Pauling’s theory was an extreme version – and the shell model.

Pauling also put forth the idea that the spherons in a nucleus were arranged in a series of concentric layers. For a large nucleus, the outer part of the cavity inside the surface layer was occupied by spherons that were in contact with the inner side of the surface layer. These spherons constituted a layer of their own, within which Pauling believed there might reside yet another layer of spherons. To avoid confusion with the “shells” of the shell model, Pauling referred to his spheron layers as follows: “the mantle” for the surface layer, and the “outer core” and “inner core” for the two additional constituents of a three-layer nucleus.

In an effort to assure the scientific rank and file that he was not seeking to upend their entire understanding of nuclear physics, Pauling promised that the quantum mechanical calculations enabled by his polyspheron theory were essentially the same as those that had been made using various other models in the past.

Perhaps unwittingly, this assurance left many colleagues within the field wondering why Pauling was bothering to develop this theory at all. For many physicists, Pauling’s work seemed redundant, or perhaps merely an attempt to change the names of existing terms to new ones that fit more elegantly into Pauling’s conceptual framework of atomic structure.

Pauling countered this skepticism by suggesting that both qualitative and rough quantitative conclusions could be drawn from his model without the aid of extensive calculations. If these conclusions agreed with the experimental evidence, Pauling argued, then detailed calculations of this sort might not always be required in the future, pushing scientists just that little bit closer to the discovery of their holy grail.

The Story of “The Nature of the Chemical Bond”: Coordinating Research & Funding

[Ed. Note: This year marks the 75th anniversary of Linus Pauling’s publication of his landmark text, The Nature of the Chemical Bond.  For the next six weeks we will take a detailed look at the creation, release and impact of a book that changed the scientific world.]

Linus Pauling’s The Nature of the Chemical Bond, first published in 1939, was the product of over two decades of diligence, sacrifice, and collaboration among a broad range of actors that included Pauling’s family, research assistants, professional colleagues and a variety of institutions. Pauling’s prefatory remarks to the book – “For a long time I have been planning to write a book on the structure of molecules and crystals and the nature of the chemical bond” – give an indication of the extent to which this was a long-term objective for Pauling, despite his being only 38 years old.

Looking back at his process, Pauling’s application for a grant from the Carnegie Institute in February 1932 provides a more detailed affirmation of his ambitions. In it, Pauling relayed how his undergraduate research in crystal structures at Oregon Agricultural College between 1917 and 1922 had laid the foundation for his current work by bringing him into contact with contemporary questions in structural chemistry. As a graduate student at Caltech, Pauling began to search for answers to those questions in the newly developing field of quantum mechanics.

In pursuit of those answers, Pauling and his wife Ava Helen, with the support of a Guggenheim Fellowship, left their one-year-old son, Linus Jr., with Ava Helen’s mother in Portland and traveled to Europe in 1926 to study quantum mechanics at its source. There, Pauling deepened his understanding and immersed himself even more by beginning to apply the new physics directly to chemical bonding.

J. Holmes Sturdivant

Upon returning to Caltech in 1927, Pauling began to seek funding so he could continue what he had begun. Let down by the National Research Fund, Pauling supported his work with funding from Caltech and the National Research Council, money which allowed him to hire a full time assistant, J. Holmes Sturdivant, who focused on x-ray crystallography and continued to work with Pauling for many years. Pauling also brought aboard Boris Podolsky for nine months to assist him with the more detailed technical components of connecting quantum mechanics to chemical bonding.

In 1932 Pauling expressed a hope that, with help from the Carnegie Institute, he could expand his work by funding more assistants and purchasing equipment like an “electric calculating machine,” a “specialized ionization spectrometer,” and a microphotometer. The Carnegie Institute was not interested. Luckily for Pauling, the Rockefeller Foundation came through with a general grant of $20,000 per year over two years, to be split between the physics and chemistry departments at Caltech. This allowed Pauling to keep Sturdivant on staff while adding George Wheland, Jack Sherman, and E. Bright Wilson, Jr. to his research team.

This scramble to secure funding and bring new people into the lab came amidst the publication of Pauling’s first four “Nature of the Chemical Bond” articles for the Journal of the American Chemical Society, proof positive that Pauling’s work was bearing fruit. Once the funding was secured and Sherman and Wheland began producing results, Pauling wrote – with Sherman and Wheland as co-authors – three more “Nature of the Chemical Bond” articles the following year, published in the newly established Journal of Chemical Physics. Wheland also worked with Pauling on a monograph discussing the application of quantum mechanics to organic molecules. Wheland finished his part of the book by 1937, but Pauling never got around to his portion: his desire to write a book length treatment of chemical bonds began, more and more, to take center stage.

Warren Weaver

In order to keep the funding coming in through the lean years of the Great Depression, Pauling was compelled to follow the lead of his patrons, the Rockefeller Foundation. Warren Weaver, Director of Natural Sciences for the foundation, told Pauling in December 1933 that the organization was “operating under severe restrictions” and that funding would go to projects “concentrated upon certain fields of fundamental quantitative biology.” That Pauling’s work had “developed to the point where it promises applications to the study of chlorophyll, haemoglobin and other substances of basic biological importance” was key to his potential receipt of continued dollars.

The commitment of Caltech’s chemistry department to continue pursuing the line of research suggested by Weaver helped Pauling to secure funding for the following year. A three-year commitment came after that, providing the Caltech group with a reliable source of support into 1938. Pauling thanked Weaver in February of that year for his direction, writing,

I am of course aware of the fact that our plans for organic chemistry not only have been developed with the aid of your continued advice but also are based on your initial suggestion and encouragement; and I can forsee that I shall be indebted to you also for the opportunity of carrying out on my own scientific work in the future to as great an extent as I have been during the past six years.

Secure funding allowed Pauling to maintain a research group consisting of graduate students and post-doctoral fellows. In his preface to The Nature of the Chemical Bond, Pauling expressed his gratitude to several of these individuals, including Sherman and Sturdivant. Another, Sidney Weinbaum, earned his doctorate under Pauling and continued on afterwards, helping Pauling with quantum mechanical calculations and molecular structures.

Fred Stitt worked as research fellow with Pauling and assisted him in teaching his graduate course on the applications of quantum mechanics to chemistry – an exercise, no doubt, that helped to shape Pauling’s own thoughts on the subject, crystallizing them in preparation for the book.

Charles Coryell and Linus Pauling, 1935.

Charles Coryell worked as a research fellow at the Caltech lab with Pauling on the topic of magnetic susceptibilities, which were central to investigating chemical bonds.  (Coryell also later helped Pauling to construct a magnet for the Caltech labs, based on one already in place at Cornell.)

Edwin H. Buchman, according to a 1985 oral history interview, was self-supporting due to royalties from his synthesis of vitamin B1. Buchman told Pauling in May 1937 that he would assist Pauling “on any problem in which an organic chemist could be useful and for which extra space could be had.”

Once assembled, Pauling’s team helped him to refine his understanding of chemical structures and bonding as the time approached when he could produce a book-length treatment on the subject.

Clarissa Lee, Resident Scholar

Clarissa Lee, January 2013.

Clarissa Lee is the most recent alum of the Oregon State University Libraries Resident Scholar Program, having completed her stay in Corvallis in early January. Lee is a Ph.D. candidate in the Program in Literature at Duke University.

The focus of Lee’s research and writing is the notion of speculation in contemporary quantum theory; or, more generally, “speculative physics.”  While at OSU, Lee dug deeply into the History of Science rare book collection, the History of Atomic Energy Collection and the Ava Helen and Linus Pauling Papers in support of her dissertation.

Lee’s Resident Scholar presentation, “Experiments, Fictions, and the Question of Science-Modeling in Speculative Physics,” gave a glimpse into her ambitious research agenda as it is currently evolving.  From the abstract of her talk

In trying to work out what speculation entails, I have returned to the prehistory of particle physics, to earlier chains of physical epistemological developments in areas such as electricity, radioactivity and nuclear physics, especially in terms of their experimental-instrumental design and the formalistic developments that drive them forward….I will also explore the relationship of specific developments in particle physics to astrophysics and cosmology (with a nod towards the space science of the 1960s) especially over questions of space-time and locality of extra-terrestrial objects (as well as their relationship to String theory and hidden dimensions.)

According to Lee, her time at OSU

helped me shape…the arguments I am making about the freedom and constraints involved in physics speculation, especially through some of the physics problems faced by scientists in moving between theoretical prediction and experiment.

Lee’s research “is also interested in theorizing and constructing models of fiction…through the use of speculative science fiction as well as speculative science fact, for the purpose of extending the imaginative realm of the scientific real.”

To this end, Lee made extensive use of Linus Pauling’s collection of Analog: Science Fact and Fiction paperback periodicals. Along with detective stories and the occasional walk, reading science fiction was Pauling’s favorite leisure activity, and his papers include thousands of dog-eared science fiction monthlies – a much-needed escape for Pauling from the unrelenting pressures that surrounded him for much of his life.

For Lee, sources like Pauling’s Analogs are useful in

trying to formulate some preliminary ideas concerning how fictionalizing can be used as a way for creatively modeling existing scientific ideas, theories and facts that aid scientists in pondering about more speculative areas of science, while also using scientific material to deal imaginatively with interdisciplinary studies of science and the humanities.

The Resident Scholar Program, now in it sixth year, offers research stipends of up to $2,500 in support of researchers wishing to make extensive use of materials held in the OSU Libraries Special Collections & Archives Research Center.  More information about the program, including the application form, is available here. The deadline for 2013 applicants is April 30th.

Polykarp Kusch (1911-1993)

Today marks the centenary of the birth of Polykarp Kusch, an accomplished physicist and Nobel laureate, born in Blankenburg, Germany on January 26, 1911.

In 1912, the Kusch family moved from Germany to the United States, where Polykarp would later build his reputation as a respected and successful scientist. After concluding his pre-college education in the Midwest, Kusch enrolled in the Case Institute of Technology (now the Case Western Reserve University) in Cleveland, Ohio. Although he initially planned to pursue a degree in chemistry, his interests quickly shifted toward physics, and he received his Bachelor of Science in the subject in 1931. Kusch continued his secondary education at the University of Illinois, where he earned both his Master of Science and Ph. D. in 1933 and 1937, respectively.

Upon completing his education, Kusch began a career in scientific research. He held his first position at the University of Minnesota, where he worked as a research assistant. There, he learned the technique of mass spectroscopy and garnered the support of his supervisors, which eventually led to his appointment as an instructor at Columbia University in New York City. At Columbia, Kusch worked in the lab of I.I. Rabi, and had the opportunity to take part in the magnetic resonance spectroscopy research that would later win Rabi the 1944 Nobel Prize in Physics. In 1941, Kusch left Columbia for a few years, during which time he researched and developed microwave generators and vacuum tubes for the Westinghouse Electric Corporation and the Bell Telephone Laboratories.

Around 1946, Kusch returned to Columbia, where he accepted a position as associate professor and conducted research in quantum mechanics. Specifically, he was most interested in the components of the atom – protons, neutrons, and electrons – and the ways in which they interacted with each other. This research would lead to his sharing of the 1955 Nobel Prize in Physics with Willis. E. Lamb. Kusch won his portion of the prize for “his precision determination of the magnetic moment of the electron,” a breakthrough that led to the development of a new field of physics called quantum electrodynamics, which describes how light and matter interact with one another.

In 1949, Kusch was promoted to full professor at Columbia; he would eventually become academic vice president and provost of the university.  In 1972 he decided to leave Columbia for the newly established University of Texas in Dallas, where he assumed a position as professor – he retained this role until his retirement in 1982. As Kusch’s career reached its later stages, he became more interested in societal issues, such as overpopulation and education, and the manners in which they could impact scientific progress. Besides the Nobel Prize, Kusch received many other awards, including the Illinois Achievement award in 1975. He was also a member of several important organizations, such as the National Academy of Sciences, the American Association for the Advancement of Science, and the American Philosophical Society.

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There is little evidence in the Pauling Papers of extensive interaction between Kusch and Pauling.  Two sets of correspondence, however, suggest that the pair did share certain commonalities, and are indicative of the traits that, for better and for worse, tended to define Pauling’s professional life.

In the first instance, Kusch sent a telegram to Pauling dated November 7, 1960 indicating that one A. F. Forance had invited him to appear at an educational gathering but that, “in no event will I speak before his group.  I intend to send a letter of vigorous protest.”  It appears that Kusch’s note was sent in reaction to Forance’s having slighted Linus Pauling – an all too common occurrence for Pauling during this chapter in his life.

As it turns out, Pauling had been scheduled to deliver the principal address at the annual meeting of the Ohio Science Education Association in Columbus, and a second lecture to a smaller group in Cincinnati, both events organized by Mr. Forance.  Two days before the first lecture, Pauling learned from an Associated Press reporter that his Cincinnati appearance had been canceled, due to protests of Pauling’s politics (this was in the wake of Pauling’s SISS hearings) by a local American Legion group.  Pauling had received no official word from Forance however, and flew to Ohio as planned.  In his words

When I arrived in Cincinnati at 5 P.M. Mr. Forance and another teacher…met me at the airport.  We started on the auto trip to the city, and after perhaps fifteen minutes, Mr. Forance mentioned that the address for that night in Cincinnati had been canceled.

Pauling was understandably upset but chose to deliver his Columbus lecture as planned.  In responding to Kusch’s disgust-tinged telegram, Pauling counseled

We have to recognize that high school teachers and people in secondary education are quite vulnerable, and my own feelings about Mr. Forance have softened somewhat with the passage of time.

The second exchange between Kusch and Pauling, initiated some five months later, is indicative of their mutual scientific interests.  In it, Pauling comments on a paper that Kusch had recently co-published in the Journal of Chemical Physics.  Specifically, Pauling requests further information on the electronic magnetic moments, or lack thereof, in molecules of KFeCl₃ and CsFeCl₃. Pauling notes that “the matter is interesting to me because of the evidence that it provides about the iron-chloride bonds.”

Pauling to Kusch, March 30, 1961.

In providing the requested information, Kusch notes that “I am always delighted to have someone read my papers which generally describe an intense interest in a subject but not necessarily an interest of very many scientists in the subject matter.”  Indeed, this trait of intense interests in all manner of scientific topics shows up again and again in Pauling’s exchanges with his colleagues.  Coupled with an extraordinary work ethic, Pauling’s never-ending sense of wonder about the world was, as much as any other trait, the secret to his success.

Pauling Amidst the Titans of Quantum Mechanics: Europe, 1926

Erwin Schrödinger and Fritz London in Berlin, Germany, 1928.

[Ed. Note: Spring 2010 marks the seventy-fifth anniversary of the publication of Linus Pauling and E. Bright Wilson, Jr.’s landmark textbook, Introduction to Quantum Mechanics.  This is post 1 of 4 detailing the authoring and impact of Pauling and Wilson’s book.]

“…the replacement of the old quantum theory by the quantum mechanics is not the overthrow of a dynasty through revolution, but rather the abdication of an old and feeble king in favor of his young and powerful son.”

-Linus Pauling, “The Development of the Quantum Mechanics,” February 1929.

Since 1925 the John Simon Guggenheim Memorial Foundation has annually awarded fellowships to promising individuals identified as advanced professionals who have “already demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the arts.”  The selection process is extremely competitive and recipients are generally esteemed in their chosen field as applicants face rigorous screening and are selected based on peer recommendation and expert review.

Since the first awards in 1925, many Nobel and Pulitzer prize winners have received Guggenheim Fellowships including, but not limited to, Ansel Adams, Aaron Copland, Martha Graham, Langston Hughes, Henry Kissinger, Paul Samuelson, Wendy Wasserstein, James Watson and, of course, Linus Pauling.

As one of the program’s earliest honorees, Pauling was awarded his first Guggenheim fellowship in 1926.  Heeding the advice of his mentors, Pauling had applied for the fellowship in hopes of pursuing an opportunity for international study.  Pauling’s advisers had long been insisting that he go to Europe to study alongside the leading experts in the budding field of quantum physics, and the Guggenheim funding provided Pauling with the opportunity to do just that.  It was this fellowship that allowed Pauling to travel abroad in order to learn from the European geniuses of quantum physics and to later become one of the early American pioneers of the new field of quantum mechanics.

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Linus and Ava Helen Pauling’s apartment in Munich, Germany. 1927.

“The subject of quantum mechanics constitutes the most recent step in the very old search for the general laws governing the motion of matter.”

–Linus Pauling and E. Bright Wilson, Introduction to Quantum Mechanics, 1935.

The mid-1920s – the time during which Pauling was awarded the prestigious Guggenheim fellowship – was an exciting period to begin an exploration of quantum theory.  The tides were dramatically shifting in this field of study and the acceptance of the old quantum theory was rapidly declining.

Linus and Ava Helen left for Europe on March 4, 1926, arriving in Europe in the midst of what was a great quantum theory reform.  At the inception of quantum theory, physicists and chemists had attempted to apply the classical laws of physics to atomic particles in an effort to understand the motion of and interactions between nuclei and electrons.  This application was grossly flawed as the classical laws, such as Newton’s laws, were originally generated to represent macroscopic systems.   Theorists soon discovered that the classical laws did not apply to atomic systems, and that the microscopic world does not consistently align with experimental observations.

A series of breakthroughs by prominent theorists in the early- to mid-1920s accelerated the decline of the old quantum theory.  In 1924 Louis de Broglie discovered the wave-particle duality of matter, and in the process introduced the theory of wave mechanics.  Then in 1925, just one year before Pauling began his European adventure, Werner Heisenberg developed his uncertainty principle and thus began applying matrix mechanics to the quantum world.

In 1926, shortly after the Paulings arrived in Europe, Erwin Schrödinger combined de Broglie’s and Heisenberg’s findings, mathematically proving that the two approaches produce equivalent results.  Schrödinger then proceeded to develop an equation, now know as the Schrödinger Equation, that treats the electron as a wave.  (The Schrödinger Equation remains a central component of quantum mechanics today.)  The adoption of wave and matrix mechanics led to the development of a new quantum theory and the overwhelming acceptance of a burgeoning field known as quantum mechanics.

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Arnold Sommerfeld and Ava Helen Pauling in Munich, Germany. 1927.

“Where the old quantum theory was in disagreement with the experiment, the new mechanics ran hand-in-hand with nature and where the old quantum theory was silent, the new mechanics spoke the truth.”

–Linus Pauling, February 1929

Pauling began his work in Munich at Arnold Sommerfeld‘s Institute for Theoretical Physics, a scholarly environment described by biographer Thomas Hager as “a new wave-mechanical universe for Pauling.”  It was this atmosphere that opened the door for Pauling to leave his mark as a pioneer of quantum mechanics.

In the fall of 1926, Pauling began applying the new quantum mechanics to the calculation of light refraction, diamagnetic susceptibility, and the atomic size of large, complex atoms.  Through these types of applications, Pauling developed his valence-bond theory, in the process making significant advancements in the new field of quantum mechanics and expanding our understanding of the chemical bond.

Two Years on the Pauling Beat

Today marks the second anniversary of the launching of the Pauling Blog.  In two years we have generated 214 posts, garnered over 63,000 views (not counting those accruing from syndication, which WordPress doesn’t include in its total statistics) and been graced with nearly 7,400 spam comments, most of which, thankfully, have been kept at bay by the good folks at Akismet.

We’re a bit less philosophical today than was the case one year ago, but we do want to take this moment to reflect back a bit.  Our readership has grown substantially over the past year and, as we enter our terrible twos, we figure this is a good opportunity to take another quick look at some writing that many of our readers may have never seen.  Here then, are ten worthwhile posts from the early days of the blog.

1. Visiting Albert Schweitzer:  a review of the Paulings’ trip to Schweitzer’s medical compound in central Africa – in Linus Pauling’s estimation, “one of the most inaccessible areas of the world.”
2. Pauling and the Presidents: the first in a series of three posts on Pauling’s relationship with this nation’s Commanders in Chief and with the office of the Presidency itself.  The other two posts focus on Pauling’s complicated interactions with John F. Kennedy, and with his own brief flirtation with the idea of running for the office himself.
3. Pauling’s Rules: among Pauling’s major early contributions to science was his formation of a set of rules used to guide one’s analysis of x-ray diffraction data in the determination of crystal structures.
4. The Guggenheim Trip: a three-part series detailing Linus and Ava Helen’s adventures as they toured through Europe for a year, meeting major scientific figures and absorbing the fledgling discipline of quantum mechanics.
5. The Darlings: Maternal Ancestors of Linus Pauling:  an entertaining look at the colorful characters residing further down Pauling’s family tree.  We also featured Pauling’s paternal ancestry as well as Ava Helen’s lineage in separate posts.
6. A Halloween Tale of Ice Cream and Ethanol:  Pauling’s typically detailed and ultra-rational recollection of a hallucination experienced late one November night.
7. Clarifying Three Widespread Quotes:  three quotes attributed to Linus Pauling are scattered across the Internet.  This post investigates whether or not Pauling actually authored them.
8. Pauling in the ROTC:  often accused of anti-Americanism due to his pacifist beliefs, few people know that Pauling actually served in the Reserve Officers Training Corps, ultimately rising to the rank of Major.  This post was among the first in our lengthy Oregon 150 series, celebrating Pauling’s relationship with his home state.
9. Mastering Genetics: Pauling and Eugenics:  a post that delves into what was among the more controversial stances that Pauling ever took.
10. Linus Pauling Baseball:  we can’t help it – the video is priceless.

As always, thanks for reading!