What is Resonance Theory?

Linus Pauling, 1931.

[Ed Note: In 2009, we dipped our toes into an unusual Pauling controversy involving the theory of resonance and Soviet scientific dogma. Today we begin a much more detailed look at the “Soviet Resonance Controversy,” beginning with a discussion of the scientific work that resided at the heart of the matter. This is Part 1 of 7.]

Linus Pauling’s resonance theory helped to unify the classical roots of organic chemistry with the new field of quantum physics. In so doing, the theory provided a hugely important framework for understanding observed atomic behaviors that did not correlate with then-known mathematical explanations or models of the atom.

The theory would also help to usher in an onslaught of new approaches to organic chemistry and the nature of the chemical bond, lifting, in Pauling’s words, “the veil of mystery which had shrouded the bond during the decades since its existence was first assumed.” It was, in short, one of the most adaptive and applicable postulates ever put forth by Pauling.

But the theory of resonance was not immune to controversy. Specifically, it was initially not widely accepted within the scientific community in the United States and, in a very different way, abroad in the Soviet Union. The disputes surrounding the theory were ultimately short-lived though, and Pauling’s ideas on resonance continue to inform today’s understanding of molecular architecture.

August Kekulé

Pauling’s ideas on resonance were grounded in the work of several other scientists but most notably August Kekulé and Werner Heisenberg, both of whom were also interested in the structure of molecules.

Kekulé (1829-1896), a German chemist, notably devised a proposed structure for benzene, an aromatic hydrocarbon of interest to many. Kekulé’s model put forth a structure consisting of six carbon atoms forming a ring, with hydrogen atoms attached externally to each carbon. Though intriguing, this basic structure did not explain where, on the interior carbon ring, double bonds were located. Partly because of this, Pauling would later lament that, “the Kekulé structure for benzene is unsatisfactory.”

Shortly after Kekulé published his basic benzene structure, multiple isomers – or alternative structures – of the same compound were predicted and even isolated by Kekulé. But even these breakthroughs were not enough to explain the “correct” model of benzene. Recognizing as much, in 1872 Kekulé posited that, in actuality, benzene “oscillates” between the various isomers, and that all isomers may in fact be regarded as “correct.”

This notion of oscillation between isomers was hugely important, but despite its utility Kekulé never succeeded in accurately predicting the “true” structure of benzene. The solution to the benzene puzzle would lie in waiting for nearly sixty more years and would rely heavily upon Pauling’s resonance breakthrough.

Despite its shortcomings in accurately predicting a structure for benzene, Kekulé’s oscillation theory served well in disrupting traditionally held beliefs regarding the number of valence electrons that must be present in aromatic compounds. This, in turn, helped to usher in new theories about the chemical structure of aromatic compounds more generally.

By the 1920s, a community of American, British and German chemists had developed a set of theories related to aromatic compounds that built on Kekulé’s ideas. The group’s basic hypothesis was that, instead of molecules oscillating between various isomers, perhaps all isomers actually existed simultaneously. This idea of simultaneous existence piqued Pauling’s interest because it seemed related to work that he was doing with quantum mechanics — specifically, ideas related to quantum resonance that had been introduced by Werner Heisenberg in 1926.

Werner Heisenberg

Heisenberg (1901-1976), a contemporary of Pauling’s, was working to understand the wave mechanics of subatomic particles. As part of this work, he theorized that, on the subatomic level, molecules exist in quantum states – meaning discrete states – and that the actual wave function of a given molecule can be described as the sum of its various quantum states. Heisenberg coined the term resonance to refer to this process — e.g., the summation of various quantum states to comprise a molecule’s wave function.

Pauling was intimately familiar with Heisenberg’s theory of quantum resonance as well as the hypotheses proposed by the British, American, and German contingent. Thus equipped, he began to construct a theory of his own that would prove crucial to building a “truer” understanding of molecular architecture and chemical bonding.

Pauling built and circulated his resonance theory in a series of papers that were published from 1931 to 1933. In them, he reasserted the ideas stated above, before emphasizing that

the actual normal state of such a molecule does not correspond to any one of the alternative reasonable structures, but rather to a combination of them, their individual contributions being determined by their nature and stability.

In other words, the individual isomers of a given molecule should not be viewed as existing in a state of rapid switching from one to another. Instead, a hybrid of every isomer is, in fact, the “true” form of the molecule.

The distinction that Pauling drew between rapidly switching isomers – which was known as tautomerism – and isomer hybrids was conceptually difficult for many scientists to grasp, but Pauling was able to cite experimental evidence in support of his theory. Namely, Pauling had found that resonating molecules existed at a much lower energy state than tautomerism would predict. Pauling believed that these lower energy states resulted in more stable molecules, an effect that lent support to the viability of resonance – as opposed to tautomerism – as an operating theory.

The experimental data continued to be important to Pauling as he pushed his theory forward. Some had argued that there was no real difference between resonance and tautomerism, because the classical understanding of tautomerization portrayed isomers as switching so rapidly as to be in a virtual hybrid state of their own accord. But the data showed that Pauling was describing something different and that, to use Pauling’s words, “it is easy to distinguish between the two.”

In a 1946 speech delivered to a private industry group, Pauling restated the basics of his theory using language that is useful for summarizing here. For a hypothetical molecule known to have two isomers, “neither the first structure nor the second structure represents the system. Instead, the molecule is ‘a combination’ of the two structures.” And importantly, when scientists

can write two structures, neither one actually represents the state of the molecule but both of them together represent the state of the molecule. The molecule is more stable actually than it would be if it had any of the structures that you can assign to it.

Benzene calculations in Pauling’s research notebook from June 1934

Though he faced early resistance, Pauling was eventually able to persuade most of his colleagues to align with his thinking on the theory of resonance, and he did so in part by using the theory to solve the elusive structure of benzene.

One of the reasons why chemists knew that Kekulé’s model of benzene was incorrect was because the observed energy level of the molecule was much lower than the number that Kekulé would have predicted. Something else, then, was causing the energy of benzene to be lower (and thus more stable).

Pauling’s theory suggested that resonating hybrids exhibit lower energies, and ultimately he was able to use his ideas to build a structure of the molecule that fit with the energy data. Once the model was accepted, the benzene breakthrough did much to secure resonance theory as a valuable and accurate tool for understanding molecular structure.

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.

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.

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.

The Heisenberg Uncertainty Principle

Werner Heisenberg

Werner Heisenberg

I learned mathematics from Born and physics from Bohr, and from Sommerfeld I learned optimism.”
– Werner Heisenberg

While the Bohr-Sommerfeld atom had proved revolutionary in the mid-1910s, a decade later the model was considered disordered and highly paradoxical. For years, researchers had tried to rebuild mathematics to fit the atomic model of the day.

Instead of struggling along the same path as his contemporaries, Werner Heisenberg, a young German physicist, chose to entirely ignore visual models and focus on the mathematics of spectral data. Over the course of several days, by limiting himself to hard, verifiable data, Heisenberg created the basis for matrix mechanics. In cooperation with Max Born and Pascual Jordan, he was able to refine his work, allowing scientists to approach particles as evolving matrices rather than stale, immobile ball-and-stick models. Through his study of particles using matrix mechanics, he was able to develop a detailed theory suggesting that it was impossible to pinpoint both the momentum and the exact location of any given particle at a specific point in time. Instead, he argued, it was possible to create a probability distribution which could be used to calculate the likelihood of a particle achieving an exact momentum and position at a particular moment.

In late March of 1927, Heisenberg published a manuscript entitled “On the perceptual content of quantum theoretical kinematics and mechanics.” The paper detailed the terms of his probability theory, eventually known as the indeterminacy principle, or more commonly, the Heisenberg Uncertainty Principle. According to David Cassidy, author of Uncertainty: The Life and Science of Werner Heisenberg, Heisenberg’s paper, coupled with Bohr’s complementarity principle and Born’s statistical interpretation of Schrodinger’s wave function, formed an integral part of the Copenhagen interpretation of quantum mechanics. Cassidy calls the Copenhagen interpretation “an explication of mechanics that fundamentally altered our understanding of nature and our relation to it,” and an event that “marked the end of a profound transformation in physics that has not been equaled since.” In this way, Heisenberg was able to reshape scientists’ understanding of the world at the molecular level.

Linus Pauling had the great fortune of touring Europe on a Guggenheim Fellowship during the time of Heisenberg’s discovery. During his stay in Germany, Pauling visited the Göttingen Institute of Physics, the home of Max Born, Arnold Sommerfeld, and of course, Werner Heisenberg. The institute’s renowned scientists, determined to educate their students on the newest developments in their fields, were known for presenting cutting-edge research in their day-to-day lectures. In true Göttingen fashion, Max Born, the famed physicist and mathematician, presented the young visitor with a pre-publication copy of Heisenberg’s paper. We are pleased to note the final pre-publication proof sheets, item corr155.1, is a part of the Ava Helen and Linus Pauling Papers.

Listen: Pauling discusses his contacts with some of Europe’s finest scientists in the mid-1920s

As groundbreaking as the Heisenberg Uncertainty Principle was, Pauling and many of his fellow scientists found the matrix approach to be frustratingly mathematical. Much of Pauling’s work was heavily influenced by Heisenberg’s discoveries and he commonly introduced some of the concepts in his lectures, but ultimately he struggled with the abstract, intangible aspects of the math-based matrix mechanics.

“Uber den anschauclichen Inhalt der quantentheoretischen Kinematik und Mechanik.” March 23, 1927.”

Erwin Schrödinger’s work, which complemented Heisenberg’s complex mathematics, was comparatively simple and conducive to visual representation. As such, it was much more widely adopted by the researchers of the day. Both individuals quickly became known as titans of twentieth-century science.

Learn more at the website “Linus Pauling and the Nature of the Chemical Bond: A Documentary History,” or by clicking on the multimedia link below.

“Valence and Molecular Structure”