The Theoretical Prediction of the Physical Properties of Many-Electron Atoms and Ions. Mole Refraction, Diamagnetic Susceptibility, and Extension in Space, 1927

Linus and Ava Helen Pauling in Copenhagen, May 1927

[Ed Note: Today and in the three posts that will follow, we will be taking a close look at four important scientific articles published by Linus Pauling between 1927 – 1949.]

In this ambitious and hugely influential paper, Linus Pauling applied his theory of screening constants to various problems, including electric polarizability, diamagnetic susceptibility, and the sizes of ions and atoms. Pauling was fundamentally interested in pursuing this topic because of his desire to merge the new quantum mechanics – which embraced wave functions – with older ideas in order to make predictions about molecular properties like mole refraction and diamagnetic susceptibility in space.

Especially during the early phases of his career, one of Pauling’s signature rhetorical tools was to put forth a bold assumption that would serve to simplify the predictions made later on in a given article. This paper is among the best examples of that approach. In it, Pauling developed mathematical relationships that, when applied, could help the reader make generalizations about molecules. But in moving through these calculations, Pauling had to make some assumptions, oftentimes without the aid of hindsight to determine whether or not they were correct. One enduring legacy of this paper is that many of Pauling’s assumptions were indeed correct, and its findings have thus remained relevant across the decades.


Another contributing factor to the paper’s success was that Pauling was in the right place at the right time. While working towards his PhD at Caltech, Pauling enthusiastically followed the rapid development of quantum mechanics in Europe and elsewhere. Pauling was particularly interested in the work of Arnold Somerfield in Munich and Niels Bohr in Copenhagen, and wrote to both to inquire about research opportunities. Bohr never responded but Sommerfeld did and, with his support, Pauling secured a Guggenheim Fellowship that allowed him to live and work in Europe for 19 months. During that period, he spent most of his time with Sommerfeld at the Institute of Theoretical Physics, though he did visit Bohr in Copenhagen as well as Erwin Schrödinger in Zurich.

Pauling’s residency in Europe proved auspicious, in part because Sommerfeld and his colleagues were working on uniting new ideas with old, a task not being readily pursued in the United States at the time. As they moved forward with their work, the European scientists began to solve more and more problems with quantum mechanics, cementing in Pauling’s mind the utility of the approach as a way forward.


Gregor Wentzel (Image credit: Emilio Segre Visual Archives)

One project important to Pauling’s paper was being led by University of Leipzig physicist Gregor Wentzel. A colleague of Sommerfeld, Wentzel was seeking to apply quantum mechanics to x-rays in order to calculate the screening constants of electrons in large and complex molecules. His project had hit a snag however, in that he was unable to find agreement between the observed data and those predicted by theory. After scrutinizing his work, the young Pauling found that Wentzel had made errors in his calculations. Once Pauling had corrected these miscalculations, he found that there was in fact agreement between the observed and predicted data, which meant that Wentzel’s work was actually correct. In so doing, Pauling had confirmed the value of quantum-mechanical calculations in predicting screening constants of electrons in complex molecules.

Armed with this information, Pauling recognized that he could use these same calculations to make predictions about electron arrangement in molecules and the relative size of ions, among other properties. This led to the publication of his paper, The Theoretical Prediction of the Physical Properties of Many-Electron Atoms and Ions. Mole Refraction, Diamagnetic Susceptibility, and Extension in Space, which appeared in 1927, published by the Proceedings of the Royal Society.

In its essence, the article used the wave mechanical feature of quantum mechanics to make predictions about molecules, an approach that emerged directly from Pauling’s exposure to European efforts to unify old ideas with new. And even though it was not the first time that Pauling had written a paper utilizing quantum mechanics, it was certainly his first publication in which he used these novel tools to make predictions about molecular properties. 


Fundamental to these predictions were three key assumptions that Pauling put forth at the beginning of his paper. The first was that,

each electron shell within the atom is idealized as a uniform surface charge of electricity of amount-zi e on a sphere whose radius is equal to the average value of the electron-nucleus distance of the electrons in the shell.

The second assumption stated that,

the motion of the electron under consideration is then determined by the use of the old quantum theory, the azimuthal quantum number being chosen so as to produce the closest approximation of the quantum mechanics.

And the third assumption was that,

since so does not depend on Z, it is evaluated for large values of Z, but expanding powers of zi/Z and neglecting powers higher than the first, and then comparing the expansion with that of the expression containing Z-so in powers of so/Z.

Armed with these assumptions, Pauling was able to issue a collection of predictions about molecules, particularly concerning mole refraction and diamagnetic susceptibility. Prior to his doing so, chemists lacked the necessary tools for making predictions of this sort, meaning that certain chemical properties remained hazy or unknown.

This issue was particularly salient for the hydrogen atom. In the months leading up to the paper’s publication, a huge debate had emerged concerning the polarizability of hydrogen. The prevailing formula had been proven incorrect in 1926, after which time a race ensued to find a new, more suitable equation. Eventually a successor formula was developed, but it was criticized as being “a conservative Newtonian” model. Agreeing that a more robust approach was needed, Pauling set about applying quantum mechanics, and based on his three assumptions, he derived the following:

Knowing full well that the equation was based on his three assumptions, and anticipating resistance, Pauling pre-emptively argued that “it might be thought that these values of ɣ are not correct because of the fact that the electron shells actually do not consist of hydrogen-like electrons, but rather themselves of ‘penetrating electrons.'” However, “as Z [a surface harmonic] increases, the ‘penetrating orbits’ become more hydrogen-like” and therefore should be ignored because any error found would be “negligible.” Having put forth this solution to the problem of hydrogen, Pauling was then able to more broadly demonstrate the utility of his ideas.

Indeed, even though much of the work in the paper made assumptions that were oftentimes crude – such as using data from the valence shell electrons only – Pauling was able to create complex (and, as it turned out, fairly accurate) tables of polarizability of ions, diamagnetism screening constants, and mole refraction, among predictions.

It is clear that Pauling believed strongly in his paper, which he felt would “make possible the accurate prediction of the properties of any atom or ion.” And though the approach would sometimes only yield “approximate values of the physical properties of ions” based on his three assumptions, the importance of the work was not diminished as, oftentimes, directly observed data “may not exist under conditions permitting experimental investigation.”

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

[Part 7 of 7]

“The Nature of the Chemical Bond. VII. The Calculation of Resonance Energy in
Conjugated Systems.” The Journal of Chemical Physics, October 1933

The final paper in Linus Pauling’s earthshaking series on the nature of the chemical bond was the shortest of the seven and made less of a splash than had most of its predecessors. This lesser impact was anticipated and was due primarily to the guiding purpose of the paper: to apply previously developed postulates to compounds that had not been addressed by Pauling in his prior writings. As with the sixth paper in the series, the final publication was co-authored by Caltech colleague Jack Sherman.

In paper seven, Pauling demonstrated how to calculate resonance energy in conjugated systems. A conjugated system is one in which there exists a plane – or alignment – of three or more connecting electrons located in the p orbital. While it was commonly understood by the era’s organic chemists that conjugated systems supplied a compound with more stability than would ordinarily be expected, Pauling’s paper offered the calculations needed to codify this knowledge.

The paper also put forth a collection of rules to help researchers better understand the properties of conjugated systems. For example, Pauling found that “a phenyl group is 20 or 30 percent less effective in conjugation than a double bond, and a naphthyl group is less effective than a phenyl group.” To arrive at these conclusions, Pauling used the equations that he had developed in his previous two papers, applying them this time around to conjugated systems.


Jack Sherman and Linus Pauling, 1935.

Pauling’s seven papers on the nature of the chemical bond came to print over the course of thirty months, from article one in April 1931 to article seven in October 1933. The first three papers laid the groundwork for what was to come by defining chemical bonds in quantum mechanical terms. The fourth paper, published in September 1932, appeared at the midpoint of Pauling’s publishing chronology and also served as a kind of transition paper, connecting the concepts introduced in the first three publications to those in the three more that were forthcoming. (Paper four also contained Pauling’s vital electronegativity scale.) The last three articles were devoted to the concept of resonance and its application to a fuller understanding of the chemical bond.

Taken as a whole, this body of work proved hugely important to the future direction of chemistry. By reconciling and applying the principles of quantum mechanics to the world of chemistry, the articles showed that what had once been mostly a tool for physicists could indeed have great applicability to chemical research. In the process, Pauling and his collaborators also rendered quantum mechanics far more accessible to their colleagues across the field of chemistry. The end result was, to quote Pauling himself, “a way of thinking that might not have been introduced by anyone else, at least not for quite a while.”


This is our forty-eighth and final post for 2020. We’ll look forward to seeing you again in early January!

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

Table of resonance energy calculations for condensed ring systems

[Part 6 of 7]

“The Nature of the Chemical Bond. VI. The Calculation from Thermochemical Data of the Energy of Resonance of Molecules Among Several Electronic Structures.” The Journal of Chemical Physics, July 1933.

In paper number five in his Nature of the Chemical Bond series, Linus Pauling argued that the theory of resonance could be used to accurately discern the structure of many compounds, and he used Valence Bond theory to substantiate that claim. However, much of the argumentation put forth in the paper relied upon fairly generalized calculations, some of which were subsequently shown to be in error.

In his sixth paper, published one month later, Pauling put forth more definitive calculations that used thermochemical data that were more empirically based, and therefore less prone to errors. As with the previous publication, this paper was co-authored. However, instead of G.W. Wheland, Pauling’s collaborator this time around was Jack Sherman, a theoretical chemist who had received his PhD from Caltech the year before.


The data used in the paper weren’t anything new; in fact, they had been used by chemists for years to calculate energy values and to determine bond energies. However, in many cases these calculations failed because chemists, who were rooted in classic organic or physical models, always assumed that the molecules under study were consistently similar.

Relying instead on a quantum mechanical approach, Pauling and Sherman argued that compounds could (and should) be organized into two broad categories. In one group, there resided those molecules that were well-approximated by their Lewis structures (classical representations of molecules using lines and dots to represent bonds and electrons). The other group consisted of compounds whose structures could only be accurately explained through resonance.

By organizing compounds into these two discrete bins, Pauling and Sherman were then able to make more accurate calculations of bond energies. More specifically, the duo was able to calculate energies of formation for various molecules by using extant experimental data on heats of combustion. Pretty quickly they realized that energies of formation could be accurately calculated for Lewis structure (non-resonating) compounds.

For resonating compounds however, the tandem found that calculated energies of formation were much higher than what would have been predicted by theory. Higher energies of formation yield more stable molecules, and the co-authors concluded that the “difference in energy is interpreted as the resonance energy of the molecule among several electronic structures” and that “in this way, the existence of resonance is shown for many molecules.”

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

[What follows is Part 5 of 7 in this series. It is also the 800th blog post published by the Pauling Blog.]

The Nature of the Chemical Bond. V. The Quantum-Mechanical Calculation of the Resonance Energy of Benzene and Naphthalene and the Hydrocarbon Free Radicals.” The Journal of Chemical Physics, June 1933.

With his fifth paper in the nature of the chemical bond series, Linus Pauling communicated a new understanding of the structures of benzene and naphthalene. While it had been long accepted that benzene (C6H6) was arranged as a six-carbon ring and naphthalene (C10H8) as two six-carbon rings, the specific organization of electrons and bonds within these structures were not known. Before the publication of Pauling’s fifth paper, several ideas on these matters had been proposed, but all were viewed as flawed in some way or another. But where others had been stymied, Pauling found success, and he did so by fully embracing and utilizing the theory of resonance.


At the time that Pauling began this work, there were five competing structures for benzene, each burdened by its own problems. The one that was the most accepted, despite its inability to connect theory to experimental data, was the Kekulé model. Put forth several decades earlier by the German chemist August Kekulé, this model centered around a six-carbon ring that possessed alternating double bonds. Because the arrangement of these double bonds could differ, Kekulé’s model was actually proposing two potential isomers for benzene. The standard understanding at the time was that these two isomers constantly oscillated between one another.

One major problem with the Kekulé approach was that scientists of his generation had never found evidence of the oscillating structures. Furthermore, the Kekulé structures should have been quite unstable, which was contrary to what researchers were able to observe in the laboratory. As such, even though it was compelling in the abstract, the Kekulé model was known to be imperfect.

In his paper, Pauling pointed out the flaws in Kekulé’s work as well as four other concepts published by other researchers. In doing so, he suggested that a common hindrance to all of the approaches was a reliance upon the laws of classical organic chemistry, and a concomitant lack of application of the new quantum mechanics. It was Pauling’s belief that the structure of benzene could be explained using quantum mechanics, as could the structures of all aromatic compounds.


In a handful of previous papers, Pauling had used the theory of resonance to explain a variety of chemical phenomena, but in thinking about benzene and naphthalene he committed more fully to its principles. According to Pauling, all observable data that had been collected for benzene, particularly its bond energies, suggested that benzene was much stronger than any models had yet to predict. But none of the previous models had entertained the possibility of a resonate structure, by which he meant an aggregate structure that was essentially a blend of all possible structures. A structure of this sort, Pauling argued, would conform to a lower, more stable energy state, and would accurately map with the observed data.

For Pauling, therefore, the structure of benzene was not the result of rapid isomerization as put forth by Kekulé, but rather a blend of states. “In a sense,” he wrote, “it may be said that all structures based on a plane hexagonal arrangement of the atoms – Kekulé, Dewar, Claus, etc. – play a part” but “it is the resonance among these structures which imparts to the molecules its peculiar aromatic properties.”

To support his theory, Pauling considered all five possible structures of benzene – which he called “canonical forms” – calculating the energy of each structure as well as the combined resonance energy. Having done so, Pauling then noted that it was the resonance energy that most closely matched the observed data.


In addition to its utility, the elegance of Pauling’s approach compared favorably with similar work being published by a contemporary, the German chemist Erich Hückel. Situating this thinking within Molecular Orbital theory, Hückel was able to arrive at a similar conclusion for benzene, but his calculations were quite cumbersome and could not be applied to larger aromatic compounds. By contrast, Pauling was now firmly rooted in Valence Bond theory and his formulae could be applied to all aromatics, not just benzene. In particular, by simplifying some of the calculations that Hückel had made, Pauling was able to overcome some of the mathematical hurdles posed by the free radicals in benzene and other aromatics.

To demonstrate the broad applicability of his ideas, Pauling applied his theoretical framework to naphthalene, which consists of two six-carbon rings and had forty-two canonical structures — a great many more than benzene’s five. Despite this significant difference, Pauling was successful in applying the same basic math to determine that the structure was also in resonance.

Indeed, Pauling was certain that his calculations were relevant to all aromatic compounds, noting specifically that “this treatment could be applied to anthracene [a three-ringed carbon molecule] and phenanthrene [a four-ringed carbon molecule], with 429 linearly independent structures, and to still larger condensed systems, though not without considerable labor.” Were one willing to expend this labor, the calculations would show that the “resonance energy and the number of benzene rings in the molecule would be substantiated” and the structure correctly predicted.


G.W. Wheland

The fifth paper was unique in part because it was the first in the series to be co-authored. The article also marked a switch in publishing forum: whereas the first four had appeared in The Journal of the American Chemical Society, this paper (and the two more still to come) was published in volume 1 of The Journal of Chemical Physics.

Pauling’s co-author for the paper was George W. Wheland, a recent doctoral graduate from Harvard who worked with Pauling from 1932-1936 with the support of a National Research Fellowship. This collaboration proved noteworthy both for the quality of the work that was produced and also because Wheland later became a vocal supporter, advocate and contributor to resonance theory.

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

[Part 4 of 7]

“The Nature of the Chemical Bond. IV. The Energy of Single Bonds and the Relative Electronegativity of Atoms.” Journal of the American Chemical Society, September 1932.

The first three papers published by Linus Pauling in his nature of the chemical bond series were all novel, and the first paper in particular made a significant impact. But it is the fourth paper that has proven to be perhaps the most influential of all. In it, Pauling introduced his idea of the electronegativity scale, a cohesive and logical tool that proved to be of major import to the discipline.


The concept of electronegativity can be understood in terms of the likelihood that an atom will attract a pair of valence (or bonding) electrons. The more electronegative an atom is, the more likely that it will attract electrons. The most electronegative element is fluorine and the least electronegative element is francium.

Pauling was able to develop a scale for electronegativity using insights into valence bond energies. The ideas that he had put forth in his three preceding papers did not always firmly commit to either Molecular Orbital theory or Valence Bond theory, and this vacillation led to significant flaws in paper number two. Beginning with the fourth paper however, Pauling chose to base his work on the tenants of Valence Bond theory.

The electronegativity scale that Pauling developed was also quite intuitive in that it could not be calculated directly, but instead had to be inferred using the atomic and molecular properties of a given element. And even though its creation relied upon a series of assumptions and simplifications, the tool was nonetheless quite sophisticated. Prior to Pauling’s publication of his electronegativity scale, chemists either had to rely upon their own best guesses to determine bond affinities or, if they wanted more precision, compute bond energies for every interaction. Pauling’s scale both standardized and simplified these processes while creating a context where chemists could make predictions of “the energies of bonds for which no experimental data are available.”

Clearly one key piece of utility that the electronegativity scale provided was the ability for chemists to draw conclusions without the need for a lot of computation. For example, based on a molecule’s electronegativity, chemists could roughly deduce the ionic nature of a bond. However, in order to predict the ionic character of a bond, Pauling had first needed to make some assumptions, such as creating an “arbitrarily chosen starting point” to which everything is relative. Even though this approach was not precise, Pauling argued that its usefulness justified the simplification of the approach. And naturally, over time, Pauling’s electronegativity scale became more honed and more specific, an evolution that Pauling also predicted in the fourth paper.


Most of Pauling’s article was devoted to a discussion of how he developed the scale and what kinds of measurements were used in the calculations. To begin, he focused on the qualities of covalent attraction or repulsion in compounds formed by identical elements, such as H:H or Cl:Cl. From there, Pauling used quantum mechanical wave function properties to establish that “energies of normal covalent bonds are additive.” It was from this central theorem that Pauling built out the rest of his conceptual work and also his scale, predicting, for example, bond energies for light atoms and halogens.

Pauling also relied upon others’ helpful calculations in creating his scale, and especially those related to heats of “formation and combustion of gaseous materials” put forth in the International Critical Tables (National Research Council) and elsewhere. The heats of formation were especially useful because they helped to correct for any unknown bond energies. In fact, by using these experimental data for twenty-one different single bond energies, Pauling was able to derive a formula that predicted where a given element should reside on the electronegativity scale. For bonds where data were not available, Pauling used his predictive models to extrapolate approximate energies.


The formula that Pauling derived and published was Δa:b=(χAB)2 where χA and χB represent the coordinates of each atom A and B on an electronegativity map (see Fig. 5 above), and Δ represents the degree of electronegativity.

Here, for example, is how Pauling calculated the electronegativity value for oxygen. He began by establishing the heat of formation of water:

2H + O=H2O(g) +9.493 v.e.

Then, based on the fact that the H:O bond is found to have a bond energy of 4.747 v.e., Pauling further calculated that:

H2O2(l)=H2O(l) + ½ O2 + 1.02 v.e.

Pauling next combined this value with the heat of vaporization of H2O2, which is .50 v.e., and found that:

2H + 2O = H2O2(g) +10.99 v.e.

From there, using his original postulate about consistent bond energies, Pauling subtracted 4.75 v.e. for each H:O bond to yield 1.49 v.e. for the O:O bond. However, since Pauling had previously concluded in his previous papers that O:O was a double bond, the actual electronegativity for the oxygen molecule was found to be 3.47. (The present-day electronegativity value for oxygen has been revised to 3.44.)


Even though it relied in part on a collection of assumptions and simplifications, Pauling’s electronegativity scale has been widely used and stands as a lasting component of his legacy. In addition to its ability to approximate values for a wide variety of compounds, the scale was also important for establishing the idea that electronegativity is not a fixed number that never changes. Instead, Pauling understood that an element’s electronegativity value emerges from its bonding relationships. Because of this, calculating absolute values has been difficult, but Pauling’s scale continues to be useful and predictive.

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

[Part 3 of 7]

“The Nature of the Chemical Bond. III. The Transition from One Extreme Bond Type to Another.” Journal of the American Chemical Society, March 1932.

In his third paper exploring the nature of the chemical bond, Linus Pauling dug into the unsolved question of how molecules transition from one kind of bond type to another. While it had been determined that molecules do switch from one kind of bond to another – from an ionic bond to an electron-pair bond, for example – the specifics of how that transition happens remained elusive.

Prior to the third paper, two prevailing ideas were being debated by chemists. One concept, as Pauling wrote, was that “all intermediate bond types between the pure iconic bond and the pure electron-pair bond” exist in some kind of infinite transitionary state. A contrary viewpoint put forth instead that molecules “transition from one extreme bond type to another” in an abrupt manner. Pauling suggested that the answer lie somewhere in between.


In order to determine how molecules transition, Pauling first needed to establish the bond structures of given molecules in their initial states. He did so by defining the bonding characteristics of molecules, a task that takes up the majority of the paper. But amidst this discussion, Pauling arrived at several key conclusions.

To begin, Pauling described many cases where a relationship existed between atomic arrangement – as determined by x-ray crystallographic analysis – and bond energies. When, for instance, a strongly electropositive and strongly electronegative molecule bonded, it was reasonable to assume that the bond was ionic. This presumed, Pauling then used electron energy curves to show that an example group, the alkali halide molecules, were strongly ionic, and that they might generally be thought to form ionic bonds.

As Pauling pointed out however, these presumptions were faulty. In fact, studies of the bonding in hydrochloric acid (HCl) and hydrobromic acid (HBr) indicated that both molecules were essentially covalent in make-up, whereas hydrofluoric acid (HF) was ionic. So even though it might reasonably have been assumed that the initial states for HCl, HBr and HF would be similar in their bonding, the experimental data indicated otherwise. These findings led Pauling toward the conclusion that there is no single universal answer to the question of how molecules transition, because there is no steadfast rule determining the types of bonds that hold molecules together before they transition.  


Having arrived at the conclusion that one could not lean upon a guaranteed universal bond type, Pauling then turned to his burgeoning theory of resonance to develop more precise thinking about transition mechanisms. Pauling specifically argued that when bonds transition from one type to another, rather than shifting either abruptly or in a continuous state – as the two competing models then prevailing put forth – they instead shift to an intermediate resonant state before switching to a new bond type.

Pauling was in essence suggesting that, in between classically-defined “completed” bond states, there also existed an intermediate bonding state that could best be understood through the theory of resonance. Moreover, Pauling argued that idealized bonds, such as pure covalent bonds or pure ionic bonds, did not technically exist. Rather, bonds might more accurately be described as constantly transitioning through resonant states, some of which more closely approximated a classic bond type.

Pauling understood that the concept he was putting forth was quite theoretical and that, in practical terms, it was hard to work with molecules if they existed in a constant state of transition. As such, Pauling allowed that, for purposes of discussion, it was acceptable to think of molecules as residing in discrete bonding states. He likewise acknowledged the convenience of using more traditional names (ionic, covalent, etc.) when referring to bonds, even if they never fully existed.

Pauling then concluded that, even though bonds were constantly transitioning, for certain bond types – such as “when the normal states for the two extremes have the same number of unpaired electrons” – it could be assumed that they had transitioned in a continuous state. But, of course, continuous state transition was definitely not always the case and could not be universally applied.


In conducting the work that led to his third paper, Pauling had sought to define a universal rule that would govern the transition between bond types. By the time that he delivered his manuscript though, he had recognized that not only was a universal law unattainable, but that what he did find had its limitations. In particular, Pauling suggested of his approach that “It is not possible at the present time to carry out similar calculations for more complicated molecules,” though “certain less specific conclusions can, however, be drawn.”

Regardless, Pauling’s third paper broke new ground on a topic of keen importance to structural chemists. By applying the theory of resonance, Pauling helped chemists to understand that there was a spectrum of polarity, and that bonds were not always strictly of one kind or the other. Importantly, in this same paper Pauling did not fall prey to dogmatism, and allowed that bonds residing near the ends of one spectrum or another might fairly be said to represent so-called “classic” bond types.

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

Linus Pauling, 1931.

[Part 2 of 7]

“The nature of the chemical bond. II. The one-electron bond and the three-electron bond.” Journal of the American Chemical Society, September 1931.

Linus Pauling’s first paper on the nature of the chemical bond made huge waves throughout the field, catching the attention of many. The second paper in the series however, was not quite so memorable. In it, Pauling tried to use quantum mechanics to explain molecules formed by either one- or three-electron bonds. This work stood in contrast to his first paper, which focused solely on electron pair bonds. And though they were similarly novel to Pauling’s first article, the ideas put forth in the second paper did not stand the test of time.


The single-electron and three-electron bonding environments had long proven difficult for chemists to understand. In tackling the challenge, Pauling admitted at the outset that they, “have not the importance of the electron-pair bond, for they occur in only a few compounds.” Nonetheless, they were “of special interest on account of their unusual and previously puzzling properties.”

Pauling’s first step in approaching the problem was to focus first on single-electron bonding, after which he would then apply the rules and mechanisms that he had formulated to the three-electron bond. Like all of the papers in his nature of the chemical bond series, the foundational groundwork for his ideas was based in quantum mechanics.

Accordingly, he began his explanation of the one-electron bond by delving into quantum mechanical principles. In doing so, Pauling argued that resonance – which, simply stated, is the sharing of energies, and a concept that Pauling would detail in greater depth in his fifth paper – could be predicted to arise if two different theoretical states of a bond possessed equal energy.

For example, the two possible bonding states for H2+ were H· H+ and H+ H·. Given that the two configurations possessed equal energies, Pauling put forth that resonating bonds between the two would be found with “essentially the same energy.” In other words, the one-electron bonds holding H2+ together were actually resonating between two different configurations. The mechanisms underlying three-electron bonds were detailed in much the same way.


After offering this explanation for how these bonds might form, Pauling used the rest of his paper to apply the mechanism to known molecules. In doing so, Pauling noted that, to date, it had been difficult to determine which molecules even possessed one- or three-electron bonds. Both types of bonds were known to exist, but this was mostly because observed energy levels for certain compounds were much more stable than would be predicted by models using other types of bonds.

For compounds suspected to be of this type, Pauling used resonance to demonstrate equivalence between observed bond energies and theoretical bond energies. Success in showing that the two sets of bond energies were equal or “differ[ing] by only one or two volt-electrons” would mean that the “criterion for the formation of a one-electron [or three-electron] bond is satisfied,” thus validating his ideas.

In his paper, Pauling applied his theory specifically to the boron hydrides. Once again based upon compatibilities between observed and predicted energy values for these compounds, Pauling found his criteria to be met and concluded that “the one-electron bond is to be expected.” In later years, as Pauling’s thinking matured, his views on these compounds became more sophisticated. But at the time of the second paper, he argued that the hydrogen ion (H+3), and the triatomic hydrogen ion (H+3) in the boron hydrides must be single-electron bonds based on their observed energy levels.

Pauling likewise suggested that the oxygen molecule, the helium ion (He+2), and nitric acid (NO), were all formed by three-electron bonds. For oxygen in particular, Pauling believed that a three-electron bond was required to explain the molecule’s slight magnetic moment. This connection between magnetism and electron bonding was something that Pauling had addressed in his first paper, and remained a topic to which he would turn with some frequency throughout the seven paper series.


As time moved forward, many of the notions put forth in Pauling’s second paper were largely debunked, with Pauling himself eventually speaking out about their irregularities. The primary issue with the work was its reliance upon Molecular Orbital theory to explain how double and triple bonds work. At this early stage in Pauling’s career, Molecular Orbital theory and Valence Bond theory did not stand apart as distinct models and, as such, Pauling’s thinking sometimes blended the two. Later, of course, Pauling’s writings would prove foundational to the advancement of Valence Bond theory.

Despite their limitations, the concepts introduced by the second paper were still important in helping Pauling to frame the larger thrust of his series. Though he sometimes went astray, Pauling more commonly found success in building off of concepts from his preceding papers in his work to create a fundamental understanding of the nature of the chemical bond.

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.


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.


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.


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.


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.


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.


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.

Finding Resources for Basic Science and Medical Research

Linus Pauling, 1949

[Exploring Linus Pauling’s popular writings on the shape of post-war science, part 4 of 5.]

Our job ahead.” Chemical and Engineering News, January 1949

The onset of 1949 brought with it the beginning of Linus Pauling’s one-year term as president of the American Chemical Society, and Pauling’s article “Our job ahead” outlined the message that he wished to convey to the society. In it, Pauling specifically addressed the financial concerns being faced by the ACS as well as the scientific community at large.

The society’s problems centered on the need to manage operating costs and member remunerations in the midst of rising costs of living. More broadly though, Pauling saw for the society a responsibility to try to improve financial conditions for science as a whole. Pauling argued that the destruction of war, in tandem with the massive consumption of natural resources required by the war effort, had resulted in increasing levels of poverty throughout the world. Pauling encouraged the ACS to do its part to combat the problem by supporting and participating in global interdisciplinary scientific cooperation.

Pauling also pushed for ACS support of basic research, believing that work of this sort was most likely to lead to significant breakthroughs. Doing so would be made all the more effective by the creation of a National Science Foundation, which would issue and administer unrestricted grants on behalf of the federal government. It was Pauling’s ultimate vision that the majority of research dollars be provided by the federal government, with supplementary funding being made available by state governments, permanent endowments, private foundations, and industry.


Chemistry and the world of today.” Chemical and Engineering News, September 1949.

The themes put forth by Pauling in his initial message to the ACS – particularly the need for a National Science Foundation – were continued in his presidential address, delivered in fall 1949.

Pauling opened his talk with a broad question, “What can I say under the title ‘Chemistry and the World of Today?'” His answer was “that I can say anything, discuss any feature of modern life, because every aspect of the world today – even politics and international relations – is affected by chemistry.”

Pauling’s all-roads-lead-to-chemistry perspective informed his strong support of a potential National Science Foundation and his firm belief in the value of basic research. He lamented the ongoing struggle for funding faced by so many of his colleagues, and pressed the notion that even applied science was dependent on advances in basic science. Moreover, Pauling suggested that applied science often received the credit for ideas that had initially been discovered or cultivated by basic researchers.

Above all, Pauling believed that, in the post-war era, “…a nation’s strength will lie largely in the quality of its science and scientists.” That noted, Pauling emphasized that government funding for scientific research should not be funneled toward military channels. To this end, it was the responsibility of the ACS, as an organization representing American chemists, to make its voice heard in the fight for the creation of a National Science Foundation.

During Pauling’s presidential year, the concept of the NSF had been put forth in political circles but had not yet been acted upon. Looking forward to that day (which would, in fact, come the next year) Pauling put forth an ideal scenario where the NSF would fund $250 million a year in research, while science-dependent industries would fund an additional $75 million. Of this latter contribution, Pauling believed that private funding ought to be considered as a form of insurance rather than charity, since it was certain to fuel the scientific discoveries necessary to drive industrial development.


“Structural chemistry in relation to biology and medicine.” Second Bicentennial Science Lecture of the City College Chemistry Alumni Association, New York, December 7, 1949. Baskerville Chemical Journal, February 1950. 

At the end of 1949, Pauling gave another high profile public lecture, this time to the City College Chemistry Association in New York. In this talk, he focused on the relationships between structural chemistry, biochemistry, and molecular medicine.

Pauling began by citing the role that chemistry had played in catalyzing immense achievement in medicine over the preceding half-century, referencing in particular the discovery and refinement of chemotherapeutic agents including antibiotics. That said, Pauling was quick to point out that scientists still had a very poor understanding of the principles and structural attributes underlying chemotherapeutic functions. It was Pauling’s belief that “…if a detailed understanding of the molecular basis of chemotherapeutic activity were to be obtained, the advance of medicine would be greatly accelerated,” and that structural chemistry was fast approaching a point where it could produce this understanding. Once done, Pauling suggested that the decade or two that followed would surely offer significant advancements in the scientific understanding of medicine and the development of new pharmaceuticals.

Pauling then identified a collection of major areas where he thought biomedical research should be focused. The first involved developing a detailed molecular structure of 1) chemotherapeutic substances (i.e., antibiotics and other medications), 2) the organisms against which they are directed (bacteria, viruses, etc.), and 3) the human organism which they are meant to protect. A second major program of work should delve into the nature of the forces involved in the intermolecular interactions between the above substances and organisms.

Pauling pointed out that the last quarter century had seen great progress in the first goal – the science of organic chemistry had been developed and the structures of many organic compounds had been confirmed. But progress elsewhere, though promising, had not come about so quickly. For questions related to the physiology of disease-causing organisms and of the human body itself, advancements were fated to be slow simply due to the immensity of the task. In addition, structural chemistry was a fairly new field and, although it was growing quickly, the stock of previous discoveries upon which one might expand was finite (research thus far had mainly focused on the structures of amino acids and peptides).

The latter goal, an understanding of the intermolecular interactions between chemotherapeutic substances and the organisms they are meant to treat or defeat, had seen the least progress of all. It was a complicated task for sure, and though he had very little data in hand, Pauling offered a back of the envelope theory about what might be going on, speculating that

…some drugs operate by undergoing a chemical reaction with a constituent of the living organism, and that others operate by the formation of complexes involving only forces that are usually called intermolecular forces.

Regardless, Pauling felt that work in these areas would prove integral to the conduct of future medical research, and he put forth his own work on sickle cell anemia as an example of how other investigations might unfold. Specifically, Pauling and his team had discovered that the hemoglobin present in the red blood cells of afflicted individuals differed structurally from normal hemoglobin. Were other investigators able to develop a similar molecular understanding of a given disease, producing new treatments would be that much easier, since chemotherapeutic agents could be tailored to fit a particular molecular architecture. Work of this sort would

…represent the first time that a chemotherapeutic agent had been developed purely through the application of logical scientific argument, without the significant interference of the element of chance.

Similar to his call for an NSF, Pauling encouraged the creation of an institute for medical chemistry that would train a new generation of students to apply chemistry to medical problems. Doing so, in Pauling’s view, ought to be prioritized due to its potential significance to the health and happiness of all people.

Molecular Architects, Atomic Blueprints and Medical Progress

The Gibbs Award dinner, June 1946

[An exploration of Linus Pauling’s popular rhetoric on the potential for science following World War II. This is part 2 of 5.]

Modern structural chemistry.” [Acceptance speech for the Willard Gibbs Medal, awarded June 14, 1946 by the Chicago Section of the American Chemical Society] Chemical and Engineering News, July 1946.

In 1946, Linus Pauling was awarded the prestigious Willard Gibbs Medal by the Chicago section of the American Chemical Society for his work in structural chemistry. In thinking about his acceptance speech, Pauling ultimately chose to frame it as an overview of the history of modern structural chemistry.

Pauling began his talk with Lucretius who, in the first century BCE, began thinking about the properties of matter. Lucretius hypothesized that honey was made up of “smooth, round molecules which roll easily over the tongue, whereas wormwood and biting centaury consist of molecules which are hooked and sharp.” From there, Pauling rolled through the work of more contemporary greats including Lomonosov’s explanations of the properties of molecules in solid, liquid, and gaseous states; Dalton’s work on the weight relations of chemical reactions; and Avogadro and Cannizarro’s breakthroughs on chemical bonds.

Next up in the whirlwind tour were Frankland, Couper, and Kekulé’s theory of valence; Kekulé’s subsequent writings on the structure of the benzene molecule; and van’t Hoff and le Bel’s explanation of the right and left-handedness of substances. Rounding out the history lesson were Werner’s work on the spatial arrangement of chemical bonds, and Lewis’ identification of the chemical bond as a pair of electrons shared between two atoms. One outcome of all of these advancements was that the discipline of structural chemistry had moved firmly in the direction of the quantitative as opposed to the qualitative judgments that had permeated Lucretius’ analyses of taste and mouth-feel.

Pauling then noted that some of the most exciting and important developments in the history of modern structural chemistry had occurred during his lifetime. It was, for example, only during the early years of his career that methods for accurately measuring interatomic distances had been developed. Subsequent breakthroughs in methodology had included molecular spectroscopy, x-ray and electron diffraction, and applied quantum mechanics, among others techniques. More recently, new knowledge had been produced about moments of inertia, oscillational frequencies, the elucidation of molecular structures for specific substances including sex hormones and vitamin D, and the discovery of the β-lactam configuration of penicillin. In surveying this work, Pauling was particularly quick to praise the usefulness of x-ray diffraction as a powerful tool.

As he looked ahead, Pauling expressed a belief that the most promising application of modern structural chemistry would be its ability to explain the physiological activity of chemical substances. Previous research in this area had produced few results of importance, but Pauling felt sure that the structures of numerous molecules would soon be elucidated, thus laying the groundwork for new insights into physiological activity and, eventually, medical research on diseases like cancer and cardiovascular illness.  


Molecular Architecture and Medical Progress.” Radio talk broadcast on the New York Philharmonic-Symphony Radio Program and sponsored by the U. S. Rubber Company, October 13, 1946.

The ideas expressed by Pauling in Chicago were taken up again in this radio broadcast, which Pauling used to further explore the relationship between molecular structure and physiological activity. In attempting to make this relationship more understandable to his lay audience, he opened with the example of Penicillin G, a molecule commonly recognized as a powerful antibiotic.

Despite penicillin’s widespread application in medical contexts and its acknowledged significance to human life since its discovery in 1928, the molecule’s physiology, at the time of Pauling’s radio talk, was not well-understood. This circumstance was likewise true of other molecules that had become household names, including DDT, morphine, ether, and adrenaline. While scientists understood their uses and functions, the chemical activity that generates and determines those functions remained out of grasp.

Pauling believed that these connections, and the answers that they might provide, lay in what he called “their molecular architecture.” More specifically, were scientists able to determine the structures of specific molecules, they might then turn their attentions to the structures of the biochemical forms with which the molecule interacts. In the case of the household names molecules – penicillin, morphine and the like – these forms might include enzymes, nerve fibers, and tissues with which the molecules interact to produce a desired effect, such as killing bacteria or numbing pain.


Interatomic distance is one important aspect of molecular structure that Pauling took pains to emphasize to his audience. In order to convey a sense of the scale at which atomic distances are measured, Pauling created a hypothetical world where perspective was shifted in the direction of the commonplace. He began by stating that a single Angstrom – the unit used to measure interatomic distances – is equal to 1/254,000,000th of an inch. In other words, when magnified by a factor of 254 million, one scaled-up Angstrom unit would be equivalent to one inch.

With proportions thus shifted, the average human being in Pauling’s hypothetical world would be about 250,000 miles tall, and a wineglass would be as big as the Earth. Importantly, were this gargantuan wineglass full of liquid chloroform, each individual chloroform molecule would be a mere seven inches across. A molecule of chloroform is made up of one carbon atom, three chlorine atoms, and one hydrogen atom, and on this scale, the carbon atom would be the size of a walnut, each chlorine atom the size of a small orange, and the distance between the walnut and each orange would be 1.76 inches. Scaled back down to its actual size (that is, a wineglass-sized wineglass), that distance would be 1.76 Angstrom units.

Pauling’s point in developing this hypothetical was that, in part because they are both small and complicated, the structures of organic compounds were poorly understood. “This then is the great problem of modern chemistry,” Pauling suggested, “the determination of the molecular architecture of the proteins and other complex constituents of the living organism.”

Indeed, Pauling believed that progress in medicine was particularly dependent upon an improved understanding of molecular structure and physiology. By extension, he saw the future role of the “medical research man” as being equivalent to a “molecular architect.” Armed with an understanding of the molecular structures underlying physiological reactions, this new style of architect would have the ability to create “atomic blueprints” for pharmacological compounds designed specifically to treat particular illnesses.