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.

An Electronegativity Breakthrough

Linus Pauling, ca. early 1930s.

Exciting news from the laboratories of Oregon State University: a group of researchers here have developed a method that simplifies the scientific understanding of electronegativity, a concept introduced and greatly advanced by Linus Pauling in the 1930s with his “electronegativity scale.”  We’ve written about Pauling’s electronegativity work before and since we’re in an interviewing mood lately, we thought we would catch up with the authors of this new breakthrough to find out what it’s all about.

Below are the fruits of our conversation with OSU’s Ram Ravichandran and Brian Pelatt, both doctoral candidates in electrical and computer engineering and co-authors of this important new paper, “Atomic Solid State Energy Scale.” (J. Am. Chem. Soc., 2011, 133 (42): 16852-16860.)

Pauling Blog: In layman’s terms, what is electronegativity?

Brian Pelatt: Electronegativity as defined by Pauling is “the power of an atom in a molecule to attract electrons to itself.” When two atoms come together to form a molecule, the electronic charge will distribute itself so that one of them will be positively charged and the other negatively charged. Electronegativity is a way to explain that charge redistribution and quantify which atoms will more likely become negatively charged.

In the solid state energy framework, the electronegativity would be a measure of how good an atom is at taking, or “stealing”, electrons (negative charge) from other atoms. As an example, fluorine is the most electronegative element and has the largest solid state energy, so it will almost always take negative charge from another element when they bond.

Electronegativity calculations by Linus Pauling, ca. 1930s.

What was Linus Pauling’s contribution to our understanding of electronegativity?

Ram Ravichandran: The concept of electronegativity was first proposed by Pauling in 1932. In an effort to explain chemical bonding, Pauling looked at chemical bond energy data derived from thermochemical measurements. He noticed that the bond energy of dissimilar atoms was greater than the covalent bond of similar atoms. This difference, what he called the ionic character of the bond, gave rise to the electronegativity scale. However, his scale was arbitrary. He assigned a value of 4.0 to fluorine and then proceeded to use that value to calculate his electronegativity scale.

What has your group done now to further the concept of electronegativity?

Pelatt: Our group has furthered the concept of electronegativity by simplifying it in the Solid State Energy (SSE) framework. Now, instead of an element having an arbitrary number assigned to it as the electronegativity, it has a solid state energy that is based on experimental measurements and easy to understand. As can be seen from the electronegativity definition given earlier, electronegativity is a difficult concept both for students and teachers; this work simplifies the concept significantly. This approach can be used to simplify difficult chemical concepts such as the Hard-Soft Acid-Base Principle, chemical hardness, covalent vs. ionic bonding, and acidic/basic oxides.

The SSE approach is also a way to predict the band gap of a material, which is a fundamental property of materials and determines the behavior of the material, whether it behaves as a conductor, semiconductor, or insulator. Another advantage of the SSE approach is that it is based on solid state measurements, rather than gas phase measurements. Solid state electronics is the foundation of modern devices, having a scale that is tailored to the solid state is a huge advantage of the SSE concept.

How long have you been working on the problem?

Pelatt: We have been working on this for about a year, with most of the time collecting and interpreting data.

What methods did your group use to arrive at your conclusions?

Ravichandran: At the beginning, we did not anticipate working on electronegativity. We began looking at doping trends and energy band offsets of compounds to see if we could come up with an ability to predict properties of new materials.

A concept that connects chemistry and device engineering is the position of energy bands. In chemistry, these bands are known as HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) which translate to the valence band and conduction band in device engineering. The separation between the bands is the energy band gap. The position of these bands is a measurable quantity known as ionization potential, IP (for HOMO, or valence band) and Electron Affinity, EA (for LUMO, or conduction band).

We started tabulating the values for EA and IP for about 69 compounds, and when plotted against the band gap, we noticed a curious trend. The values were centered around 4.5 eV, which corresponds to the standard hydrogen potential commonly used in electrochemistry and is also the bond strength of a hydrogen atom. This led us to conclude that hydrogen could serve as a universal energy reference position.

In chemistry, for a binary A-B compound, the HOMO is predominantly anion derived (mostly B), while the LUMO is cation derived (mostly A). Since the EA is related to the LUMO, by collecting and averaging the EA values for a cation such as aluminum, we were able to come up with a new “solid state energy” (SSE) value for aluminum. Similarly, by collecting and averaging IP values for nitride materials, we were able to calculate an SSE value for nitrogen.

When we then organized these SSE values for 40 elements in an increasing order along with the universal energy reference, common chemistry concepts such as oxide clarification, electronegativity, chemical hardness and ionicity became easier to interpret.

Where do you go from here?

Ravichandran and Pelatt: That is a very interesting question. Within our group, we are already utilizing this concept to be able to predict properties of new compounds. Dr. Michael Lerner and Dr. Richard Nafshun in the Chemistry department are both excited about incorporating this concept in graduate and undergraduate chemistry courses. We believe that the SSE concept has a wide reaching audience, from those trying to understand chemistry concepts to using this scale to investigate properties of new materials with applications in battery technology, water splitting and solar cells, amongst others.

Another exciting path is to see where the scientific community at large takes the SSE concept. The SSE values can be refined and this should spark a lot of conversation about measurement techniques. Doing so would provide a lot of subtle information about chemical bonding that is not readily apparent. The SSE scale helps to quickly estimate important properties of new materials, enabling rapid material development for applications. As a result, the most exciting aspect of SSE is how the community is going to use this scale in the search for materials with novel applications.

For more on this breakthrough in our understanding of electronegativity, see this press release issued by OSU.

The Pauling Electronegativity Scale: Part 2, Inspired by Biology

Linus Pauling’s electronegativity scale was inspired by Biology. In the early 1930s, chromosomal genes were being mapped out by measuring how frequently two independent traits were inherited together; the idea being that the closer the genes were, the more likely that they would stay linked during genetic crossover.

Pauling tested this idea with chemical compounds, finding that bonds between similar elements were not as strong as bonds between dissimilar elements. He attributed this discovery to ionic contributions in the stronger bonds, and correlated the ionic nature of certain elements with further spreads on his electronegativity scale. For example, the bond between Lithium and Fluorine was almost one-hundred percent ionic – therefore, he placed Lithium on one end of his scale and Fluorine on the other end.

From there, Pauling assigned arbitrary values for each known element based upon their position on the accepted ‘map’ of ionic bond proclivities. Later, he explained that his calculation of each electronegativity value was an estimate of the covalent contribution to an element’s bond subtracted from the actual bond energy, as per the following formula:


In this formula,  Δ is a measure of excess ionic energy – the value that Pauling used to arbitrarily assign electronegativity values to elements. Again, the higher the ionic bond energy measured within an element, the more electronegative the element was to be considered.

In terms of chemistry, Pauling’s electronegativity scale was one of his least theoretically well-founded theories.  On the very same token, it was also one of his most influential ideas in that it allowed chemists to make assumptions about bonds and molecules that could give rise to new interesting and useful correlations.

Indeed, Pauling’s electronegativity scale was very practical.  He used electronegativity to explain chemical bonding characteristics, including the changes in the energy of atoms that occur as electrons rearrange their placement in the atoms’ orbitals. By comparing these values, researchers could predict the properties of a given bond without ever needing to know the bond’s complicated wave equation from quantum mechanics.

Pauling’s faith in his scale was such that he used it to theorize that Fluorine was so electronegative, it would form compounds with an inert gas – something that, at the time, was thought to be impossible. Inert gasses simply did not bond.  However, he couldn’t prove the relationship, and it frustrated Pauling. Eventually though, some thirty years later, he was proven correct by another team of scientists. In their discussions of Pauling’s “stochastic method,” biographers have shown that much of Pauling’s research followed the Fluorine example:  more often that not, his intuition about chemical systems was correct, despite his inability to empirically prove his ideas with hard data.

Electronegativity data, 1930s.

Electronegativity data, 1930s.

In 1932, Linus Pauling published his original paper proposing a thermochemical method of assigning relative electronegativity values. He applied his system to ten nonmetallic elements.  As with Berzelius’ earlier attempts at developing an electronegativity scale, Pauling failed to clearly define how he established his proposed values.  (For the contemporary student, his later calculations regarding electronegativity are contained in his 37th research journal, though to most readers the journal is difficult to follow due to it being more of a stream-of-conscious study as opposed to a series of well-explained experimental argument.)

All of this noted, and despite many additional attempts at determining a rigorous electronegativity scale in the years following his work, Pauling’s 1932 scale is still the one most-commonly in use today.

Learn more about electronegativity on the website Linus Pauling and the Nature of the Chemical Bond, available at the Linus Pauling Online portal.

The Pauling Electronegativity Scale: Part 1, Historical Background

Linus Pauling lecturing on Amedeo Avogadro, Rome, Italy, June 6, 1956

Linus Pauling lecturing on Amedeo Avogadro, Rome, Italy, June 6, 1956

The development of an accurate electronegativity scale was one of Linus Pauling’s many major contributions to the study of chemistry.  In this two part series, we’ll first look at the electronegativity research that preceded Pauling’s breakthrough, before analyzing the details of the scale that Pauling ultimately derived.

The concept of electronegativity is measured along a relative scale that compares the degree to which atoms of different elements tend to attract electrons from their surrounding environment. Because the electronegativity scale is a qualitative measurement – meaning that there is no measurable constant value for electronegativity – the scale itself has been both difficult and interesting to develop. The electronegativity scale we use today was formalized by Linus Pauling, and was first published in 1932. However, the idea of electronegativity existing between atoms was established well before Pauling, dating back to the early 1800s.

In 1809, Amedeo Avogadro published a paper connecting the correlations between the neutralization that occurs with acids and bases, and the neutralization that occurs between positive and negative electrical charges. Avogadro claimed that these cancellation relationships could be applied to all chemical interactions; between both simple substances and more complex compounds. From this, he proposed the creation of what he termed an “oxygenicity scale” on which every element could be placed – its location dependent upon the element’s tendency to react with other elements – in order to compare the properties of elements that had not yet been tested together.  This was, of course, the forerunner of the modern electronegativity scale.

To determine the relative “oxygenicity” values of elements, Avogadro relied upon contact electrification experiments published by two fellow scientific giants, Humphrey Davy and Alessandro Volta, as well as the work of a German-Danish researcher named Christian Heinrich Pfaff (pdf link).  These experiments found that when two bodies are electrified on contact, the potential between them becomes a value that can be measured.  These sets of values were, in turn, the units that Avogadro used to develop his oxygeniticity scale.

As it turned out, a significant problem with Avogadro’s method is that measures of contact electricity are very easily affected by outside factors, such as moisture or impurities.  As a result, Avogadro’s oxygenicity values turned out to be inconsistent and inaccurate.  Into this void stepped the important Swedish chemist Jöns Jakob Berzelius.

Portrait of Jöns Jacob Berzelius.  Image courtesy of the Michigan State University department of Chemistry.

Portrait of Jöns Jacob Berzelius. Image courtesy of the Michigan State University department of Chemistry.

In 1811, Berzelius published an article detailing his own ideas on electrochemistry. He utilized much of the same groundwork as Avogadro, but, crucially, used the term “electronegativity” instead of “oxygenicity.”

Besides their names, a major difference between the two scales lies in their focus on heat evolution in chemical reactions – while Avogadro never mentions the concept, it is central to Berzelius’ theory, which, indeed, he presented as a new theory of chemical combustion. Berzelius assumed that both heat (or “caloric“, as it was conceived of at the time) and electricity were fluids.  As such, Berzelius attempted to connect heat to his electronegativity scale because he believed that caloric was created by the combination of negative and positive electricity.

Unfortunately for the theory, this assumed connection failed to account for half of all possible chemical reactions (endothermic association and exothermic dissociation), and was eventually discarded in favor of more modern views of the electronegativity scale. However, Berzelius did provide an almost-complete listing of his measured electronegativities, which coordinate remarkably well with both Pauling’s modern thermochemical definition as well as the current Allred-Rochow force definition. Berzelius’ electrochemical theory eventually failed despite its similarities with current systems because it could not account for increasingly complex organic molecules, and was incompatible with Michael Faraday‘s laws of electrolysis – laws that were already generally-accepted during his time.

Learn more about electronegativity on the website Linus Pauling and the Nature of the Chemical Bond, available at the Linus Pauling Online portal.  For more on the early history of electrochemistry, see Dr. Roderick MacKinnon’s lecture “Ion Channel Chemistry: The Electrical System of Life.”