Mulliken, Robert Sanderson

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(b. Newburyport, Massachusetts, 7 June 1896; d. Alexandria, Virginia, 31 October 1986)

quantum chemistry, molecular orbital theory, molecular structure.

Mulliken is counted as one of the founders of theoretical quantum chemistry, along with Linus Pauling. Mulliken, instrumental in the definition of basic concepts and methods to study molecular structure and spectra, as well as in the shaping of its language and nomenclature, was awarded the Nobel Prize in Chemistry in 1966 for his “fundamental work concerning chemical bonds and the electronic structure of molecules by the molecular orbital method.” Working within the boundary of two scientific disciplines, Mulliken left his imprint in an area that during his lifetime gradually shifted from physics to chemistry. From experiment he moved toward theory, as his contributions also brought mathematics and computers into the realm of chemical practice.

Education and Career The son of Samuel Parsons Mulliken, an organic chemist from the Massachusetts Institute of Technology (MIT), Robert, like his father, attended MIT, receiving an undergraduate degree in chemistry in 1917. After graduation, he accepted a wartime job as a junior chemical engineer for the U.S. Bureau of Mines, and he conducted research on poison gases at the American University in Washington, D.C. Following World War I, he worked as a chemist at the New Jersey Zinc Company until 1919, when he opted for university life and enrolled at the University of Chicago in order to work with the physical chemist William Draper Harkins. In 1921 he earned his PhD in chemistry with a dissertation on the partial separation of mercury isotopes by evaporation (and other methods). He stayed one more year as a National Research Council Fellow, working on an extension of his former research in the attempt to obtain bigger isotope separations with mercury by using improved equipments and methods. In the process, he built the first “isotope factory,” an apparatus that took advantage of the slightly different behaviors of isotopes during evaporation and diffusion through a membrane.

Mulliken still held a National Research Council Fellowship when he moved in 1923 to the Jefferson Physical Laboratory at Harvard University. In 1926 he became an assistant professor of physics at New York University. He became an associate professor of physics at the University of Chicago in 1928, where he stayed until his death, with a dual appointment at Florida State University as a Distinguished Research Professor of Chemical Physics from 1964 to 1971. The year after his return to Chicago in 1929, he married Mary Helen Von Noé; they became the parents of two daughters. Mulliken became a full professor in 1931 and was elected as a member of the National Academy of Sciences in 1936.

During World War II, Mulliken collaborated on the Manhattan Project as the director of the Information Division of the Plutonium Project at the Metallurgical Laboratory at the University of Chicago. While he valued first and foremost his scientific work, which he pursued until the end of his life, he also viewed science as having a renewed role in a society facing new challenges during and after the war. In 1955 he served as scientific attaché at the U.S. Embassy in London. From 1956 to 1961 he was Ernest DeWitt Burton Distinguished Service Professor of Physics, and he was the Distinguished Service Professor of Physics and Chemistry at the University of Chicago from 1961 to 1985. Mulliken received several medals and awards from the American Chemical Society—the G. N. Lewis Gold Medal, the Theodore William Richards Gold Medal, the Peter Debye Award, the John Gamble Kirkwood Award, and the J. Willard Gibbs Medal—before being awarded the Nobel Prize.

Molecular Physics, Electrons, and Molecular Spectra Since his high school days, Mulliken was intrigued by the role that electrons played in the architecture of matter. In 1913, the year of the publication of a new hybrid model of the atom by the Danish physicist Niels Bohr, Mulliken presented at his high school graduation ceremony an essay titled “Electrons: What They Are and What They Do.” The elucidation of the role played by electrons in the structure, behavior, and spectra of molecules became a central and recurrent theme in his scientific life.

In the years when atomic physics was coming of age and increasing in importance as a topic at the forefront of research for European scientists, American physicists chose instead to concentrate on molecular physics. Mulliken moved to Harvard University and joined a group of physicists, including Edwin Crawford Kemble and Raymond Thayer Birge, that exemplified this trend. Molecules, not atoms, became their main target. The experimental work on isotope separation prepared Mulliken to move smoothly into spectroscopy, and specifically into the analysis of molecular spectra, starting with diatomic molecules and looking for evidence of the existence of different isotopes in their spectra (isotope effect).

Mulliken assisted Kemble and Birge in the preparation of their 1926 comprehensive report on the spectra of diatomic molecules for the National Research Council, written together with Walter F. Colby and Francis Wheeler Loomis. More complicated than the spectra of elements, band spectra (then the current designation for molecular spectra) were classified on the basis of three types of contributions associated with the three different components of the energy of a molecule (due to nuclear rotations, nuclear vibrations, and electronic motions). By implication, an isotope effect in the spectra could be the result of three contributions: rotational, vibrational, and electronic. Mulliken began to look for evidence of vibrational contributions in visible and ultraviolet spectra. His experimental work enabled him to identify a new molecular fragment—nitric oxide (NO)—and to suggest the existence in molecules of an energy at a temperature of zero degrees Kelvin (zero point energy), a concept that was soon to find a theoretical justification within the framework of the new quantum mechanics.

Mulliken then shifted to the consideration of the electronic distribution in molecules. He found evidence that diatomic molecules with the same number of electrons shared similar spectroscopic properties with the element in the periodic table having the same number of electrons. This analogical behavior has occurred in one form or another for scientists such as Rudolf Mecke and Hertha Sponer in Germany, as well as Birge in the United States, and became the starting point for the development of a classificatory scheme for diatomic molecules in order to group them into different families. Subsequently, this classifying scheme led to the suggestion that similar electronic structures were associated with corresponding systems of energy levels.

The two years Mulliken spent at New York University were particularly productive. An active group of students gathered around him, working along the lines of his new research program. At the same time, he became recognized as an international leader on the classification of band spectra.

This was a period in which quantum mechanics emerged, wave and matrix mechanics were formulated and proved mathematically equivalent, and the Copenhagen interpretation of the behavior of the miscroscopic realm, grounded on Bohr’s complementarity principle and Heisenberg’s uncertainty principle, came into view. Mulliken began a lifetime friendship with Friedrich Hund, the German theoretical physicist who introduced quantum mechanics into the study of molecular structure. Even though molecular rotations and vibrations had been studied by Mulliken and others within the framework of the old quantum theory, Hund used quantum mechanics to show that the electronic quantum states of a diatomic molecule could be interpolated between two limiting cases: the situation in which the two atoms are separated, and the opposite situation in which their two nuclei are considered to be united into one. This work gave theoretical support to Mulliken’s former hypothesis that electronic quantum numbers could change drastically in the process of molecule formation, and to his subsequent successful attempt to assign individual quantum numbers to electrons in molecules.

Mulliken’s work on the interpretation of spectra of diatomic molecules ended with the preparation of three classic review articles (1930–1932) in which he introduced his famous correlation diagrams, which enabled one to visualize the state of a molecule in relation to the separated atoms and the united atom descriptions. The correlation diagrams were considered by the physicists John Hasbrouck Van Vleck and Albert Sherman, in their famous 1935 review paper, to play a role relative to diatomic molecules equivalent to that played by Mendeleev’s periodic table for atoms. The visualization of the properties of diatomic molecules went hand in hand with Mulliken’s effort to secure an international agreement on notation for diatomic molecules, which he managed successfully to accomplish in 1930. In 1955, an agreement on notation was also secured for polyatomic molecules.

Molecule Formation and Chemical Bonding The assignment of quantum numbers to electrons in molecules (1928–1932), as suggested by the study of their electronic


spectra, was directly linked to Mulliken’s initial analysis of the conditions of molecule formation in diatomic molecules. This led to the proposal of a novel approach to the question of molecule formation and chemical bonding, abandoning the notion of chemical bonds and valence, and dispensing with the conceptual framework of classical valence theory. Mulliken set forward a theoretical scheme in which molecule formation was analyzed in terms of each electron’s motions in the field of two or more nuclei as well as that of other electrons, in what he called molecular orbitals. To counteract the established view of a molecule as an aggregate of atoms, Mulliken contended, in the same manner as Gertrude Stein, that “a molecule is a molecule is a molecule.” He refused to reduce a molecule to an aggregate of atoms, and instead built it from nuclei and electrons. Mulliken’s new approach to valence theory, which came to be known as the molecular orbital (MO) theory, was the result of a painstaking analysis of band spectra data. Starting as a largely phenomenological theory based on the extension of Bohr’s building-up principle to molecules, according to which the molecules were pictured as being formed by feeding electrons into orbits (or orbitals) that encircled all nuclei, it soon became integrated into the framework of quantum mechanics, through the participation of other scientists. In addition to Hund, Erich Hückel, and Gerhard Herzberg, from Germany, the British entered the field. In 1929 John E. Lennard-Jones suggested the physical simplification that consisted of representing molecular orbitals by a linear combination of atomic orbitals, a step that in itself proved fundamental to the mathematical development of MO theory within the framework of quantum mechanics.

Mulliken’s extension of the idea of molecular orbitals to small polyatomic molecules (1932–1935) brought about several important new results. Whereas the physicist John Clarke Slater had shown that group theory was not essential to the analysis of atomic spectra, Mulliken demonstrated that it was indispensable in dealing with polyatomic molecules. As molecular symmetry varies with electronic state, group theoretical methods proved to be an indispensable tool in the classification of the states of highly symmetrical molecules like benzene. Mulliken also developed a quantum theory of the double bond along the lines suggested by Hückel and introduced a scale of absolute electronegativities (1934), which was intended to be a reply to Pauling’s scale of relative electronegativities.

The Genesis and First Decades of Quantum Chemistry: Mulliken versus Pauling Mulliken’s proposal to attack the problem of molecule formation was opposed by Linus Pauling, who had put forward an alternative method to study molecular structure and chemical bonding. Contrary to Mulliken’s approach, Pauling’s valence bond (VB) approach was based on a resonance theory of the chemical bond, which was meant to extend classical structural theory. It thus envisioned molecules as aggregates of atoms bonded together along privileged directions.

Originated in the joint work on the hydrogen molecule by the German physicists Walter Heitler and Fritz London (1927), the method was extended to other molecules by Slater (1931) and, especially, by Pauling himself, who based his semiempirical approach on ideas such as hybridization of atomic orbitals to form bond orbitals that possessed directional character and resonance among several valence-bond structures. He came to believe that bonds are formed as a result of the overlapping of two atomic orbitals, and that the stronger bond is formed by the atomic orbital overlapping the most with a certain atomic orbital in the other atom. The bond direction is defined as the direction in which the concentration of individual bond orbitals is highest. The strength and directional character of bonds is thus explained as a result of the overlapping of individual bond orbitals, which is itself a reflection of a greater density of charge concentrated along a particular direction. Under certain conditions, during bond formation, atomic orbitals must be combined and the new hybridized orbitals—which are formed as linear combinations of atomic s, p, and d orbitals—are particularly suited for bond formation. Pauling came to believe that bonds are formed as a result of the overlapping of two bond orbitals, and that the stronger bond is formed by the bond orbital overlapping the most with a certain bond orbital in the other atom. The bond direction is defined as the direction in which the concentration of individual atomic orbitals is highest. The strength and directional character of bonds is thus explained as a result of the overlapping of individual atomic orbitals, which is itself a reflection of a greater density of charge concentrated along a particular direction. Furthermore, in those compounds for which no single structure seemed to represent adequately all its properties, Pauling suggested that the molecule could be represented as a hybrid of two or more conventional forms of the molecule—a situation that he dubbed “resonance among several valence-bond structures.” Introduced in “The Nature of the Chemical Bond” series (1931–1933), these ideas were further developed and presented to a wider audience in the famous book, The Nature of the Chemical Bond (1939).

The differences in outlook of Pauling’s and Mulliken’s proposals, which Mulliken himself characterized as reflecting two opposite points of view—Pauling’s following “the ideology of chemistry,” his own departing from it (Mulliken, 1935)—may well account, together with factors such as personality, rhetorical skills, and communication strategies, for the immediate and widespread success of VB theory when compared to MO theory. Although Pauling and Mulliken thought differently on how the newly developed quantum mechanics could, in practice, be applied to the problem of the chemical bond, they shared a common outlook on how to construct their theoretical schemata, on the character of the constitutive features of their theories, on what the relation of physics to chemistry should be, and on the discourse they developed to legitimate their respective theories.

Seen from this vantage point, the genesis and development of quantum chemistry as an autonomous subdiscipline was dependent on those scientists who, like Mulliken, were able to realize that what had started as an application of physics was becoming an integral part of chemistry. According to Charles Alfred Coulson’s words in a symposium commemorating fifty years of valence theory (1969), those who managed to escape successfully from the “thought forms of the physicist” (Coulson, 1970, p. 259) by implicitly or explicitly addressing issues such as the role of theory in chemistry and the methodological status of empirical observations helped to create a new space for chemists to go about practicing their discipline.

The Internationalization of Quantum Chemistry Throughout a period extending to the late 1950s, the VB method dominated quantum chemistry for reasons that were not entirely due to its superiority. In sharp contrast with Mulliken, who was neither a persuasive writer nor an eloquent teacher, Pauling’s ability to present the theory of resonance as an extension of former chemical theories, and to show its explanatory power when dealing with a broad range of chemical phenomena involving ground state properties, especially in small molecules, accounted for the initial popularity of the VB method. Furthermore, endorsing explicitly two main aspects of chemical tradition, Pauling emphasized model building and visualizability as constitutive features of his chemical theory of the bond, a choice that proved decisive to its adoption.

The ascendancy of the MO theory accompanied the downfall of the VB theory. It was largely associated with the contributions of Coulson, an advocate of the MO theory whose rhetorical and pedagogical skills equaled those of Pauling. In a sense, Coulson’s textbook Valence (1952) played the role of a book that Mulliken never wrote, since it counterbalanced the approach followed in Pauling’s The Nature of the Chemical Bond. The MO theory also proved easily adapted to the classification of the excited states of molecules—one of the realms of molecular spec-troscopy—and above all, suitable for computer programs.

Beginning in the mid- and late 1930s, when quantum chemistry was already delineated as a distinct subdiscipline, the contributions of a group of British theoreticians proved rather decisive. Lennard-Jones, D. R. Hartree, and Coulson were the best-known members of this group. In different ways, they were all strongly influenced by Mulliken’s legacy. Of the three, Coulson was the most vocal and the person whose work encompasses all those trends characteristic of what has been called the “British approach” to quantum chemistry (Simões and Gavroglu, 1999; Simões, 2003). If the “German approach” inaugurated by London, Heitler, Hund, and Hückel stressed the application of first principles of quantum mechanics to chemistry, and if the “American approach” of Pauling, Mulliken, Van Vleck, and Slater was characterized by a pragmatism together with a creative disregard for the strict obeisance to the first principles of quantum mechanics, the British perceived the problems of quantum chemistry first and foremost as calculational problems, and by devising novel calculational methods they tried to bring quantum chemistry within the realm of applied mathematics. For the members of this group, Coulson in particular, to make a discipline more rigorous meant to incorporate applied mathematical techniques that would serve in practical situations to offer solutions. They would become constitutive to the discipline itself. But, simultaneously, Coulson’s pedagogical activities pushed forward the idea that chemists with no mathematical training could follow the discipline’s trends.

After the war, molecular physics quickly lost ground in relation to other emerging specialties within physics, such as nuclear and particle physics. Mulliken returned to his former work. Supported by the Rockefeller Foundation and the Office of Naval Research, as well as other granting agencies, Mulliken’s group, named after 1952 the Laboratory of Molecular Structure and Spectra, continued to produce high-quality work on the experimental and theoretical study of molecular structure and spectra. Among Mulliken’s postwar contributions, the following works stand out: the development of a charge-transfer interpretation of spectra of donor-acceptor molecular complexes; the calculation of spectral intensities and the explanation of the selection rules that characterize transitions in molecular spectra; the theory of hyperconjugation (pseudo-triple bond) in organic molecules; the “magic formula,” an attempt to quantify Pauling’s criterion of maximum overlapping by defining bond strength in terms of the overlap integral (the integral over all space of the product of two atomic orbitals, each coming from different atoms); and the concept of population analysis, in which the concept of overlap population (the electron population between atoms) was put forth as the best measure of the strength of a chemical bond.

Mulliken became a pivotal player in launching quantum chemistry as a genuinely international enterprise. In this new phase, the organization of meetings and conferences became crucial to the discipline’s consolidation. At home, Mulliken participated in a meeting organized by the Division of Physical and Inorganic Chemical Society honoring G. N. Lewis (1947), where he delivered a review paper assessing the past and present state of development of the application of quantum mechanics to problems of molecular structure and spectra. Believing that the time was ripe for a “new emphasis on the use of semi-empirical methods” in quantum chemistry and molecular spectroscopy, he offered a classification and description of available methods, contrasted the VB and the MO approaches, pointing out their advantages and drawbacks, and concluded that in the realm of molecular spectroscopy, in which there still exists a vast body of empirical data on the spectra of complex molecules rather unsystematically or poorly organized, there were “rich possibilities” for theoretical interpretations (Mulliken, 1947).

The next year, both Mulliken and Pauling were invited speakers and guiding stars at the 1948 Paris Colloque de la Liaison Chimique, jointly organized by the Centre National de la Recherche Scientifique (CNRS) and the Rockefeller Foundation. The first to be held in France after the war, this conference was the meeting point of practically all active quantum chemists. Besides Mulliken and Pauling, Coulson, J. D. Longuet-Higgins, L. E. Sutton, Lennard-Jones, and M. Polanyi stood among those attending the meeting. Marking the beginning of quantum chemistry in France, the strategy of its local promoters was to move the discussion to complex problems of quantum biochemistry. In the meeting, they probed the possibilities of the VB and the MO methods, but gradually shifted to the MO method, developing the technique of “molecular diagrams” and managing to reinforce the recourse to visual imagery in the framework of MO theory.

At about the same time, the successful utilization of digital computers in quantum chemistry to compute wave functions and energy levels was prepared by a program discussed and agreed upon at the Shelter Island Conference (1951), organized by Mulliken and considered to be a “watershed” in his autobiography (Mulliken, 1989). The program aimed at obtaining formulas for the “troublesome” integrals needed for the integration of Schrödinger’s equation, and then making them available to the community of quantum chemists in standardized tables.

The outcome of this conference reinforced the move of Mulliken’s group away from semiempirical calculations toward wholly theoretical (ab initio) calculations. Active participants of this group included C. C. Jo Roothan, Klaus Ruedenberg, and Bernard J. Ransil. In semiempirical calculations the computation of molecular properties was carried out by setting up a theoretical framework; then, at certain points, integrals that were difficult to compute were replaced by experimentally determined quantities. The adaptation to molecular problems of the scheme of the self-consistent-field approximation, which had been widely used for atomic problems, implemented the program outlined at the shelter island conference. The use of computers to calculate the time-consuming integrals of the increasingly sophisticated versions of the MO method also opened the way to the investigation of molecules that were otherwise inaccessible to experimentation. At the experimental level, computers in many instances replaced laboratory experiments as sources of new data.

By 1959 a conference on molecular quantum mechanics was convened in Boulder, Colorado, to debate the impact of computers in quantum chemistry, with Mulliken again at center stage as a member of its steering committee. The splitting of the community into two groups—ab-initionists and those advocating semiempirical methods, essentially dependent on diverging views concerning the use of large-scale electronic computers— was assessed by Coulson as pointing to deep, perhaps irreconcilable, divisions among the practitioners of quantum chemistry.

As in all scientific disciplines, quantum chemistry evolved through time, its practice being shaped by its founders and their immediate followers. In a 1998 paper in Nature, the 1981 Nobel laureate Roald Hoffmann summarized poetically the different sorts of inputs in affirming its tradition: “American and British chemists had secured a place for quantum mechanics in chemistry, through the charismatic exposition of Linus Pauling, the quieter and deep reflections of Robert Mulliken, and the elegant, perceptive teaching of Charles Coulson” (1998, p. 750). As exemplified by Mulliken’s career, the ability to “cross boundaries” between disciplines was, perhaps, the most striking and permanent characteristic of those who, like Mulliken himself, consistently contributed to the development of quantum chemistry.


Mulliken’s papers, correspondence, and other manuscript materials are deposited in the Joseph Regenstein Library of the University of Chicago. Letters and an interview with Mulliken, conducted by Thomas S. Kuhn in 1964, are held in the Archives for the History of Quantum Physics in the American Institute of Physics and in the American Philosophical Society.


“Electronic Structure of Polyatomic Molecules and Valence. VI.

On the Method of Molecular Orbitals.” Journal of Chemical Physics 3 (1935): 375–378.

“Quantum-Mechanical Methods and the Electronic Spectra and Structure of Molecules.” Chemical Reviews 41 (1947): 201–206.

“The Path to Molecular Orbital Theory.” Pure and Applied Chemistry 24 (1970): 203–215. One of Mulliken’s recollections.

“Spectroscopy, Molecular Orbitals, and Chemical Bonding.” In Nobel Lectures in Chemistry 1963–1970, 131–160. Amsterdam: Elsevier, 1972.

Selected Papers of Robert S. Mulliken. Edited by D. A. Ramsay and Jürgen Hinze. Chicago: University of Chicago Press, 1975. Selection of Mulliken’s most important papers on molecular structure and spectra.

Robert S. Mulliken: Life of a Scientist, an Autobiographical Account of the Development of Molecular Orbital Theory with an Introductory Memoir by Friedrich Hund. Edited by Bernard J. Ransil. Berlin: Springer-Verlag, 1989. Mulliken’s autobiography, edited posthumously.


Assmus, Alexi. “The Americanization of Molecular Physics.”

Historical Studies in the Physical and Biological Sciences 23 (1992): 1–34.

Butler, Loren. “Robert S. Mulliken and the Politics of Science and Scientists, 1939–1946.” Historical Studies in the Physical and Biological Sciences 25 (1994): 25–45.

Coulson, Charles Alfred. “Recent Developments in Valence

Theory.” Pure and Applied Chemistry 24 (1970): 257–287.

Gavroglu, Kostas, and Ana Simões. “The Americans, the Germans and the Beginnings of Quantum Chemistry: The Confluence of Diverging Traditions.” Historical Studies in the Physical and Biological Sciences 25 (1994): 47–110.

Hoffmann, Roald. “Kenichi Fukui (1918–1998).” Nature 391 (1998): 750.

Longuet-Higgins, Hugh Christopher. “Robert Sanderson

Mulliken.” Biographical Memoirs of the Fellows of the Royal Society 35 (1990): 329–354.

Löwdin, Per-Olov, and Bernard Pullman, eds. Molecular Orbitals in Chemistry, Physics and Biology: A Tribute to Robert S. Mulliken. New York: Academic Press, 1964. A commemorative volume assessing Mulliken’s contributions to quantum chemistry.

Park, Buhm Soon. “The ‘Hyperbola of Quantum Chemistry’: the Changing Practice and Identity of a Scientific Discipline in the Early Years of Electronic Digital Computers, 1945–1965.” Annals of Science 60 (2003): 219–247.

Simões, Ana. “Chemical Physics and Quantum Chemistry in the Twentieth-Century.” In Modern Physical and Mathematical Sciences, vol. 5, edited by Mary Jo Nye, 394–412. Cambridge, U.K.: Cambridge University Press, 2003.

_____. , and Kostas Gavroglu. “Quantum Chemistry qua Applied Mathematics. The Contributions of Charles Alfred Coulson (1910–1974).” Historical Studies in the Physical Sciences 29 (1999): 363–406.

Ana Simões