New Insights into Metals and More

Linus and Peter Pauling at Warwick Castle, England. 1948.

[The Paulings in England: Part 3 of 5]

In his lab, a five minute walk from his office at Balliol College (where he was once caught boiling an egg on his electric space heater), Linus Pauling’s research took a turn from the contents of his lectures – intermolecular forces and biological specificity – and he found himself devoting his research time to metal theory. Pauling had planned to revise the index for his newly published freshman text, General Chemistry, during his Eastman Professorship, but couldn’t seem to get metals off his mind.  As he wrote in a letter to his Caltech colleague J. Holmes Sturdivant, “I thought that I would be doing work in connection with my freshman text while in England, but it has turned out that I have devoted all of my time, and presumably shall continue to do so, to work on the theory of metals and intermetallic compounds.”

He was aided in his lab by three other researchers – David Shoemaker, Hans Kuhn, and a young man from Holland, Dr. F. C. Romeyn. Pauling’s circumstances were proving to be highly productive, and in a March letter to Robert Corey, Pauling wrote of the impact that the change of setting was having in stimulating his thoughts:

I have been having wonderful success in my development of a theory of metals. I think that it has really been very much worthwhile for me to get away for this period of time, under circumstances favorable to my thinking over questions and trying to find their solution. The problem of metals has been on my mind for a number of years, and I haven’t been able to leave it alone, so it is a good thing that I have now managed to get it solved.

This new theory of metals was an extension of Pauling’s valence-bond approach to determining the structure of molecules, as initially developed in the late 1920s. Pauling was first exposed to quantum mechanics as an undergraduate at Oregon State University (then known as Oregon Agricultural College) and retained that interest as he transitioned to graduate studies and faculty employment at the California Institute of Technology.

In 1926 Pauling traveled on a Guggenheim Fellowship to study the developing field of quantum mechanics with physicists in Europe, and especially Germany. He brought these new ideas back to Caltech in the form of quantum chemistry, which he used to compute the electronic structures of molecules. This intuitive valence-bond approach was quickly judged a success and had been popular since the 1930s as a simple model for studying the electron dispersal in the bonds between molecules.

But all the while another chemist, Robert Mulliken (recipient of the 1966 Nobel Prize for Chemistry) had been steadily fostering a rival approach: the molecular orbital theory. While the Pauling family enjoyed springtime in Paris at the beginning of April, Pauling and Mulliken met head to head at a conference on Isotopic Exchange and Molecular Structure. There an entire day was devoted to the comparison of the two theories before a group of quantum chemists. Pauling had written earlier that molecular orbitals were confusing to students, but he learned at this meeting that one always has to stay one’s toes: with more mathematics under their belts, advanced chemistry students were increasingly hungry for the more quantitative approach that Mulliken’s theory offered.


Sometimes ideas come upon the great thinker at surprising times, and Pauling experienced just such a eureka moment during one of his twice-weekly Oxford lectures in February.  As he wrote to Holmes Sturdivant,

I have just had a great stroke of luck. While giving my lecture on Tuesday I suddenly realized that a calculation about resonance energy of metals that I had just made and was reporting contained the key to the strange valence numbers and numbers of atomic orbitals and unused orbitals that have turned up in my theory of valency of metals.

Notes on intermetallic compounds by Linus Pauling, March 1948.

Pauling worked out his ideas on electron theory and the structure of metals and intermetallic compounds through pages and pages of careful handwritten calculations. In looking at each manuscript now, Pauling presents a hypothesis about some aspect of metal theory and then proceeds to calculate, revise, and recalculate until the theory and the experimental x-ray diffraction data line up. For instance, on one day in March, Pauling was exploring intermetallic compounds from several different angles.  He writes “I shall now treat intermetallic compounds, with my new ideas – resonance of bonds when an extra orbital is available, importance of n=1/2, 1/4 etc., concentration of bonding electrons into strong bonds (Zn-Zn, etc as compared with Na-Na) , transfer of electrons with increase in valence.” Hybrid orbitals, bond lengths, and the overall stability of structures were other items on Pauling’s research agenda.

Of course, not every idea is a winner and a few theories led Pauling down the wrong path; in one manuscript Pauling set out to, as he wrote, “consider sp hybridization – how can we set up a secular equation to give the results given by my bond-strength postulate?”  In the end Pauling found that “the ratio does not come out as desired. It is evident that my assumption that the energies can be taken proportional to ‘bond strengths’ is not right.”  Missteps such as these didn’t deter Pauling from pressing on with his research, for as he often said, “The way to have good ideas is to have lots of ideas, and throw away the bad ones.”


Chemistry boasts its own special language, or nomenclature, and chemists like Pauling are to thank for the terms that make chemical jargon unique. As research advances, sometimes an entire new word is needed to describe an innovative concept. While tackling the nuances of metal theory at Oxford, Pauling wrote to Sturdivant about this very problem.

By the way, I think that we should do something toward improving the nomenclature. For example, coordination number is an awkward and unwieldy expression – we need one short, precise word for this concept. Perhaps ligancy could be used. It would fit in well with ligand and the verb to ligate. We also need some general words to express the bonds between one atom and the surrounding atoms – we now use the word bond to refer both to the electron pair bond that is resonating around among alternative positions and to the fraction of an electron pair bond that is a portion to a particular position. I have also felt troubled about using the word position in this way – to mean the region between two atoms. If we do introduce any change in nomenclature, it must be very well thought out, and must not involve too great a strain on the memory, or too great a departure from the past.

New fields also call for innovations in instrument development and research programs. Pauling was in constant communication with his colleagues back home about new tools that might be constructed to aid the researchers. He admired the Cavendish’s vast x-ray crystallography laboratory and also gained new insights from reading British journals devoted to scientific instrumentation. He would frequently send word back as to how Caltech workers could improve on a complex apparatus such as the specialized cameras for x-ray diffraction of metallic crystals.

Pauling was likewise intrigued by the English system of graduate education, wherein graduate students would take class work completely during the first year and then spend practically 100% of their time on research during the other two years. Pauling was always looking to improve upon existing programs, but as appealing as the English system was, he acknowledged that in implementing it one would run the risk of not knowing whether a student was an apt researcher for their entire first year!

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Pauling’s Rules

Studio portrait of Linus Pauling. 1930.

Studio portrait of Linus Pauling. 1930.

“I am enclosing a copy of a manuscript which Mr. Sturdivant and I have prepared, dealing with the structure of brookite. We feel rather confident in our structure, and are pleased to have begun work in the field which you recently opened — the study of complex ionic crystals.”

– Linus Pauling. Letter to William Lawrence Bragg. May 31, 1928.

X-ray diffraction, as discovered by Max Theodore Felix von Laue, is the process of examining a crystalline substance by tracking the scattering of x-rays upon contact with a given material. The process goes something like this: An x-ray photograph is taken, releasing x-rays which then interact with the sample and subsequently interfere with one another. This interference results in an image, known as a Laue photograph, of a diffraction pattern in which the x-rays that have passed through the crystal appear as small black dots. A trained crystallographer can then use this photograph as the basis for deriving the molecular structure of the sample crystal.

In the late 1920s, x-ray diffraction appeared to have reached the peak of its usefulness. Crystallographers had pinpointed the structure of most simple, few-atom crystals and were left to struggle with increasingly complex molecules. Unfortunately, with the addition of only one or two atoms, a crystal’s structure became considerably more difficult to derive. In complex molecules, the diffraction patterns were much more intricate, allowing for a large number of theoretically possible structures. Crystallographers, with the help of their lab assistants, were forced to wade through pages of complex mathematics in search of the correct structure. Pauling and J. Holmes Sturdivant, who were working together on complex crystals, had taken to hiring teams of students to crunch the calculations necessary for this sort of approach.

Pauling was dissatisfied with this process and felt that there had to be another way to attack the problem. He noted that many researchers involved in the field had discovered similar molecular structures and bonding patterns between different crystals, which suggested a limited number of structural possibilities. With this in mind, Pauling believed it possible to develop a guide which would help researchers derive molecular structures of complex crystals via the x-ray diffraction technique.

Supplementing his knowledge of crystalline structures and quantum mechanics with existing research, Pauling attacked the problem. In a short time, he was able to develop five simple guidelines for eliminating scores of theoretical structures, thereby greatly reducing the difficulty of solving molecular structures.

Pauling’s Rules, first published in 1928 as a part of his paper “The Principles Determining the Structure of Complex Ionic Crystals,” are still considered valid by today’s scientific community. They are as follows:

1. A coordinated polyhedron of anions is formed about each cation, the cation-anion distance is determined by the sum of ionic radii and the coordination number (C.N.) by the radius ratio.

2. An ionic structure will be stable to the extent that the sum of the strengths of the electrostatic bonds that reach an anion equal the charge on that anion.

3. The sharing of edges and particularly faces by two anion polyhedra decreases the stability of an ionic structure.

4. In a crystal containing different cations, those of high valency and small coordination number tend not to share polyhedron elements with one another.

5. The number of essentially different kinds of constituents in a crystal tends to be small.

After developing these rules, Pauling began to apply them in his own research. In 1929 and 1930, he worked at solving the structures of groups of silicates, including but not limited to mica and talc. Using his new system of rules, as well as an x-ray powder diffraction apparatus that he had built, Pauling was able to decipher previously unknown bonding patterns. His work with zeolites, for example, uncovered the basis of their unique gas-absorption properties, a problem that had baffled many of his contemporaries.

Pauling’s Rules propelled the young researcher to the forefront of the crystallographic community. In a very short time, he had become a major player in a reputable branch of structural science. Moreover, his use of both the crystallographic and quantum mechanical disciplines hinted at a possible meshing of the fields unlike anything seen before. The young scientist was well on his way to international fame on a grand scale.

Learn more about Pauling’s Rules on the website “Linus Pauling and the Nature of the Chemical Bond: A Documentary History.”