Van Vleck, John Hasbrouck

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(b. Middletown, Connecticut, 13 March 1899; d. Cambridge, Massachusetts, 27 October 1980)

magnetism, quantum theory of solids, spectroscopy, chemical physics.

Van Vleck was the only child of a wealthy family. Of Dutch extraction, the Van Vlecks had settled in America early in the 1600’s. Van Vleck’s paternal grandfather, John Monroe Van Vleck, was a professor of astronomy at Wesleyan College, and his father, Edward Burr Van Vleck, a professor of mathematics there when John Hasbrouck was born. Van Vleck’s mother, Hester Laurence Raymond, was from Lyme, Connecticut; the Raymonds had come to America about 1700. Both parents were domineering individuals, and as a boy their son (known to the family as Hasbrouck) had a retiring personality.

In 1906 Edward Van Vleck took a position at the University of Wisconsin, where he taught for the remainder of his career. That same year Hasbrouck took up a hobby that occupied him for the rest of his life. While sick in bed during a trip to Europe that summer, he was given an Italian railway timetable to study. He memorized it, and subsequently memorized railway passenger schedules for all of Europe and the United States. His impressive memory served him throughout his life.

Van Vleck attended public schools in Madison and lived with his parents until his graduation from the University of Wisconsin (a semester early) in 1920. He majored in physics, but it was only when he enrolled as a graduate student at Harvard University in the spring semester of 1920 that he decided to make a career of science. Having so made up his mind. Van Vleck was able to complete his Ph.D. degree in the spring of 1922. During these years at Harvard he acquired the sobriquet “Van,” by which he was known thereafter.

Van Vleck’s doctoral dissertation topic was to calculate the ionization energy of the “crossed-orbit” model of the helium atom, a model suggested by his adviser, E. C. Kemble, and also by Niels Bohr. The dissertation was the first in the United States to deal with a purely theoretical topic in the (old) quantum theory. Kemble supposed that the helium atom consisted of two electrons orbiting the nucleus in quantized Keplerian orbits of the same size, but in planes that crossed one another. The solution of the problem required calculating the energy arising from the mutual repulsion of the electrons. Van Vleck developed an approximation technique that allowed him to calculate this energy as a function of the inclination of the orbits with respect to one another. The ionization energy that he obtained agreed with one calculated in a similar fashion by Bohr’s assistant H. A. Kramers, but it exceeded the empirical value.

Although it did not agree with experiment, Van Vleck’s work did earn him his doctorate, and was published in Philosophical Magazine, then the leading English-language journal for physics. In addition, a brief report he gave on it at a meeting of the American Physical Society drew the attention of physicists at the University of Minnesota. After spending the year 1922–1923 as an instructor at Harvard, he taught at Minnesota from 1923 until 1928.

In the fall of 1923 Gregory Brett joined Van Vleck as an assistant professor, and the two enjoyed the privilege of teaching only graduate courses in theoretical physics. Breit left Minnesota after one year but did not overburden Van Vleck with teaching duties. Van Vleck found sufficient time during the years he spent at Minnesota for the research that established him as a physicist; he “came of age” a few years ahead of the physics profession in America.

Van Vleck made his greatest contribution to the old quantum theory in 1924, when he conceived his correspondence principle for absorption. He demonstrated that in the limit of high quantum numbers there would be a correspondence between absorption by classical, multiply periodic systems, and by their quantum analogues. His proof depended on interpreting net absorption in the quantum theory as the difference between gross absorption and stimulated emission of radiation (an interpretation prompted by a remark of Breit’s). Van Vleck was particularly pleased that his classical theory reproduced the quantum result without the need for stimulated emission, which he referred to as “negative absorption.”

Van Vleck’s theory of absorption by multiply periodic systems was consistent with the newly derived Kramers theory of dispersion, and it convinced Bohr that his correspondence principle applied not only to emission but also to absorption. Further, Van Vleck’s 1924 calculation made use of several of the ideas that Werner Heisenberg used in his matrix mechanics a year later. Van Vleck’s work, however, did not lead in the direction of matrix mechanics. His intent was to explain quantum phenomena (especially “negative absorption”) in classical terms rather than to devise an internally consistent quantum theory.

A larger project that Van Vleck completed while at Minnesota was his report for the National Research Council, Quantum Principles and Line Spectra. Both matrix and wave mechanics had appeared by the time of its publication in April 1926, so in a narrow sense it was obsolete. However, it was not so regarded at the time. It quickly sold out its initial printing of 1,000 copies, and an additional 300 copies were printed in 1928. Its success no doubt helped to bring Van Vleck two promotions at the University of Minnesota, and the offer of permanent positions at three other universities in 1926 and 1927.

The success of Quantum Principles and Line Spectra contrasted with Van Vleck’s original research in 1926. While he quickly learned the techniques of matrix mechanics that spring, others were ahead of him; four or five of the original calculations that he worked out between May and December 1926 were duplicated by other theorists. (He withheld much of that duplicated work from publication.) Overlap was to be expected in theoretical work in 1926, for many old problems could be solved in a relatively short time by anyone familiar with the new developments. Nonetheless, the situation was particularly frustrating for Van Vleck. He had begun a three-year term as an editor of Physical Review in January 1926, and thus he was abreast of American work, but he could not stay ahead of the Europeans, even with the help of a stay in Europe during the summer of 1926.

Early in 1927 Van Vleck at last found a line of inquiry in which his work was not duplicated, In January of that year he discovered a way to generalize the theory of susceptibilities of simple dipolar gases that he had written about the previous August. His analysis depends on a division between “normal,” or closely spaced, energy levels (atomic or molecular energy levels that differ by energies small compared with the thermal energy kT) and “excited,” or widely spaced, energy levels. This division applies to most free molecules. The sum of contributions to the electric or magnetic polarization from the closely spaced levels gives a susceptibility that is inversely proportional to the temperature of the gas. Contributions to the polarization from widely spaced levels yield a quantity independent of temperature. The electric or magnetic susceptibility of a gas can therefore be represented by the simple formula

in which N is the number of molecules per unit volume, μ is the electric or magnetic moment of the molecule, and α is a constant. This result had been known in the classical theory of susceptibilities, and Van Vleck’s note of August 1926 had demonstrated that the factor 1﹨3 could be carried over from the classical to the quantum theory. What had not previously been realized was that there is always a positive contribution to a from the excited states. This terra is now known as Van Vleck paramagnetism.

Not all molecules fit Van Vleck’s narrow-wide dichotomy. One that does not is the nitric oxide molecule (NO), which has two states of electronic angular momentum separated by an energy that (at room temperature) is comparable with kT. Consequently its magnetic moment appears to vary with temperature. Van Vleck’s theory predicted the form of variation, which was not known in 1927. Experimental results that appeared in 1929 confirmed his predictions, establishing the validity of his general theory.

Four further points about Van Vleck’s theory of susceptibilities deserve mention. First, he calculated entirely with the matrix formalism, which he always preferred to the wave formalism. Second, a sum rule called the principle of spectroscopic stability played a major part in his analysis. Mentioned in Van Vleck’s August 1926 note on dipolar gases, the rule establishes that the sums of certain matrix elements are independent of the way in which the system is quantized. Throughout the rest of his career, Van Vleck displayed a fondness for rules involving invariant sums. Third, Van Vleck derived his summation over closely spaced levels (which produces the 1﹨T susceptibility) by a direct analogy with an integration in the analysis of susceptibility in classical (multiply periodic) systems. In other words. Van Vleck turned around his procedure of 1924 and derived a quantum formalism from the classical formalism. He was thus able to use his experience with the correspondence principle to explore a new area of the quantum theory. Finally, this general theory of susceptibilities (rather than the calculations he had made in 1926) established his lasting interest in magnetism.

If Van Vleck was discouraged with his progress at the close of 1926, the discovery of his general theory of susceptibilities restored his spirits in 1927. When he accepted an appointment to lecture at Stanford University during the summer, he took the opportunity to make the trip his honeymoon. He and Abigail June Pearson were married in Minneapolis on 10 June. Soon after, Van Vleck was promoted to the rank of professor at the University of Minnesota. He was twenty-eight years old.

Several phenomena besides magnetism attracted Van Vleck’s interest in the 1920’s, among them molecular spectroscopy. One result of his early calculations was the discovery of what is now called lambda-doubling. In the lowest approximation, the energy of a diatomic molecule depends on the square of Λ, λ being the component of electronic angular momentum perpendicular to the axis of the molecule. Hence there is a degeneracy in energy for each value of Λ. In higher approximations, states with positive and negative values of Λ couple differently to the rotational angular momentum of the molecule, and so the energy degeneracy is broken. The degeneracy disappears only in the second order of the perturbation calculation, however, and to treat this situation Van Vleck developed what is now known as Van Vleck degenerate perturbation theory. In the words of Robert Mulliken, Van Vleck’s theoretical description of diatomic spectra fitted the experimental data “like a glove.”

Beginning in the summer of 1927, Van Vleck had negotiated for a professorship with the University of Wisconsin, which he finally accepted early in 1928. The principal attraction was that a foreign theorist was to visit Wisconsin for a semester each year. Van Vleck had supervised three graduate students at Minnesota (two of whom were Elmer Hutchisson and Vladimir Rojansky), but there had been no other experienced theorist at the university since Breit’s departure in 1924. Hence, while he remained an editor through 1928, Van Vleck was willing to distance himself somewhat from the Physical Review (edited by John T. Tate at Minnesota) to teach at Wisconsin. The first visiting theorist at Madison (in the spring of 1929) was P. A. M. Dirac. He and Van Vleck enjoyed hiking around Madison (and later in the Rocky Mountains), but they did not collaborate on any calculations.

At the University of Wisconsin, Van Vleck supervised several more graduate students than he had at Minnesota (nine in all, between 1928 and 1934). Two of these students were J, V. Atanasoff and Robert Serber. He also had five postdoctoral students during those years.

Soon after Van Vleck began teaching at Wisconsin, he undertook the writing of his second book, The Theory of Electric and Magnetic Susceptibilities. He wrote a large portion during a leave of absence in Europe in 1930. Also during that leave he attended the sixth Solvay Congress (on magnetism); he was the only American invited.

The new text was published in the spring of 1932. Early chapters discussed the classical theory of electric susceptibilities and gave considerable attention to current problems in understanding experimental data. The middle chapters principally concerned Van Vleck’s general theory of gas susceptibilities. There appeared a discussion of the gas nitric oxide along with experimental data confirming the theoretical description of its susceptibility. Later chapters sketched out subjects that Van Vleck (and his students) subsequently explored.

In one of those chapters Van Vleck explicated Heisenberg’s fundamental theory of ferromagnetism in terms of Dirac’s vector model of spins. By characterizing spin Hamiltonians as scalar products of vectors, rather than simply as antisymmetric wave functions, he made the alignment of atomic magnetic moments that occurs in ferromagnetism more easily visualized. The vector model has become common in textbook discussions of ferromagnetism, and Van Vleck subsequently found other uses for it. He and his students at Madison applied the Dirac model to calculations of complex spectra of atoms.

In another chapter of Susceptibilities, Van Vleck gave a qualitative discussion of how the para-magnetism of transition-metal ions in salts would be altered front what appeared in free atoms; he and his students William Penney, Robert Schlapp, and Olaf Jordahl soon explored the field quantitatively, and in so doing developed the crystal field theory.

The calculations done at Madison dealt with hy-drated salts of elements in the rare earth and transition metal groups. These salts were supposed to contain water molecules of hydration that surround the paramagnetic ions in a roughly cubic array. The incomplete inner shells of these ions (the 4f shell in rare earths, and 3d shell in the transition metals) are largely shielded from bonding with other ions in the crystal, but they do feel electrostatic repulsion from the electrically polar water molecules. Orbitals with differing spatial arrangements feel different amounts of repulsion, and so their energies are altered by different amounts. The crystal field theory is a method for evaluating this electrostatic perturbation. The mathematical apparatus of the crystal field theory, which includes the use of the rotation group, and of trace-invariance arguments, marks the scheme clearly as Van Vleck’s.

Penney, Schlapp, and Jordahl were able to match current data on susceptibilities in their early calculations. This success is less of an achievement than it might seem, however. Crystal field theory does not work ab initio, but sets the symmetry and strength of the crystalline field according to experimental data (on susceptibilities, in the case of this early work). Subsequent experimental results cast doubt on some of the fundamental assumptions of Penney, Schlapp, and Jordahl. The roughly cubic fields supposed for the salts of the rare earths probably do not exist, although cubic fields may exist in salts of the transition metals.

In 1932 Van Vleck wrote his first paper on the crystal field theory, It explained the results of Schlapp’s calculations, which seemed to demand that salts containing nickel and cobalt (adjacent elements in the periodic table) have radically different crystal structures. Using a brief argument with trace infvariances. Van Vleck showed that the inversion of energy levels found by Schlapp arose in the mathematics of the calculations rather than in an inversion of the crystal structure. This calculation, he pointed out years later, was the favorite of his entire career.

In 1935 Van Vleck extended the crystal field theory to the case where covalent bonding of the paramagnetic ion to the surrounding crystal is strong enough to overcome the usual Russell-Saunders coupling of orbital angular momentum of individual electrons in the ions. The result is abnormally low magnetic moments. Van Vleck’s handling of this “strong field” case has since developed into ligand field theory. Crystal field theory and ligand field theory did not mature, however, until after World War II, when the technology of microwave spectroscopy became available to explore the structure of paramagnetic crystals.

In 1932 and 1933, while his students worked on magnetic salts, the major part of Van Vleck’s efforts was devoted to three-part study of the methane molecule, both on the basis of localized bonds (the method of Linus Pauling) and on the basis of molecular orbitals (the method of Robert Mulliken). In the first part he presented a general contrast of the two methods. Van Vleck found the molecular orbital approach had too “ionic” a character (electrons were too mobile), and too much charge tended to accumulate on individual atoms. Treatment by localized bonds specifically excluded the highly ionic terms from consideration. However, the symmetry of wave functions was then inappropriate to the tetrahedral structure of methane.

In a later part of the study Van Vleck demonstrated that, for four mathematically tractable cases, the tetrahedral structure is the most stable. None of these cases is a close representation of the methane molecule, but they circumscribe the mathematically intractable real case.

Van Vleck wrote two other notable papers on molecular physics, in 1935. The first, a long review article on valence theory written with Albert Sherman, concerned the connections (and contrasts) between localized bonds and molecular orbitals. Its general conclusion was that only results obtainable by both methods were trustworthy.

In his second paper of 1935, Van Vleck demonstrated that the localized bond scheme could be obtained from molecular orbitals by transforming from an irreducible to a reducible representation of the symmetry group appropriate to the molecule in question. Hence, he proved formally what he had suggested in his previous papers: The two approaches were simply different starting points for perturbation calculations. Both were approximations, and adding higher-order corrections would eventually merge the two.

By 1935 Van Vleck had moved from Wisconsin to Harvard University. He had at first balked at the Harvard offer (a joint appointment in the physics and the mathematics departments) because it was an associate professorship, and when he received it in 1934 he had already been a full professor for nearly seven years. Only when he was assured that he would soon be promoted did he accept the offer. He became a full professor at Harvard in 1935 and taught there until his retirement in 1969.

In his early years at Harvard, Van Vleck continued to explore dielectric phenomena and molecular spectra, and ventured into nuclear physics. In May 1939 he delivered a series of lectures at the Institut Henri Poincare, on current theories of magnetism. (Publication of these lectures, delivered in French, was delayed until 1947 by World War II.) Van Vleck also considered new areas in the theory of magnetism, two of which will be described here.

Experimental work carried out in the late 1930’s in the Netherlands showed that the relaxation times for various paramagnetic crystals (the time required, roughly, for a system of spins to reach temperature equilibrium with the surrounding crystal lattice) were one to four orders of magnitude less than could be explained by theory. In 1939 Van Vleck traced this behavior (in alums of titanium, chromium, and iron) to a direct interaction between spins and the lattice. At temperatures near 80 degrees absolute, this strong interaction between spins and the lattice could be explained by means of the Jahn-Teller effect.

The Jahn-Teller effect arises from degeneracy in the energy levels of an atom within a crystal. As a consequence of this degeneracy, the spatial coordinates of the water molecules of hydration enter the perturbation calculation in the first, rather than in the second, order. The presence of first-order terms indicates a strong interaction of spins and lattice, and hence a short relaxation time.

The strong interaction of spins and lattice that occurs for salt crystals near 80 degrees absolute does not occur at lower temperatures. Van Vleck demonstrated in 1941 that for the alums he had considered, there should actually be a phonon bottleneck; relaxation of a single spin moment will release only a small quantum of energy, and lattice modes of oscillation with such small energies are too few to carry the available energy. To put it another way, the speed of sound is too small to allow the requisite number of phonons to flow to the walls of the container of the crystal. Hence Van Vleck could not explain the short paramagnetic relaxation times observed at low temperatures. In spite of its validity, Van Vleck’s idea of the phonon bottleneck was not pursued until the 1950’s.

Antiferromagnetism drew Van Vleck’s attention in 1940. In an antiferromagnet, atoms that are nearest neighbors have spins that align antiparallel, rather than parallel (as in a ferromagnet). The resultant moment for the crystal as a whole is therefore quite small. An antiferromagnetic susceptibility increases with temperature to the Néel point (the temperature above which magnetic ordering vanishes) and then falls with further increases in temperature.

Van Vleck did not attempt to explain why nearest neighbors should have antiparallel spins; he assumed it to be the case, and applied the Dirac vector model to a calculation of susceptibility. By combining two previously derived results, he found that the susceptibility at zero temperature should be two-thirds the susceptibility at the Neel temperature. This relation often agrees well with experimental data.

In 1941 Van Vleck and R. Finkelstein considered the excited states of the chromium ion in chrome alum. They found that (for a predominantly cubic field within the crystal) there was a doublet stale about 2.25 eV above the ground level, which was consistent with recent experimental data. The energy of the doublet was fairly low, due to the contributions of matrix elements nondiagonal in the quantum number L. Van Vleck and his students in 1932 had developed the crystal field theory to deal with the ground state of atoms in crystals, and in 1937 he had considered excited states qualitatively. The quantitative calculation of the energy of an excited state of an atom in a crystal was novel, however. More than twenty years later the equivalent excited state in the ruby crystal became important in the development of the ruby laser.

In the summer of 1942 Van Vleck joined a theoretical study group (headed by J. Robert Oppen-heimer, and including Hans Bethe, Felix Bloch, Robert Serber, and Edward Teller) that concluded that a fission bomb was technically feasible. Van Vleck’s work in this study group was his greatest contribution to the atomic bomb, although he had occasional contact with the project in 1942 and 1943.

From the fall of 1942 Van Vleck spent most of his time on radar research in Cambridge, Massachusetts. He became director of the Theory Group at the Radio Research Laboratory at Harvard in 1943. This laboratory was associated with the MIT Radiation Laboratory but dealt with radar coun-termeasures rather than radar development. Two of the other members of the Theory Group were Felix Bloch and Julian Sehwinger.

Several reports that Van Vleck wrote during the war were subsequently published in the open literature. One of them, by Van Vleck and his assistant at the Radio Research Laboratory, David Middleton, established that for both visual and aural detection of repeated pulsed signals in the presence of noise, the best filter to apply to the incoming signal is the Fourier transform of the pulse being sought.

A second report concerned the absorption of radiation by water vapor. Van Vleck concluded that there would be a transition between two rotational states of the water molecule corresponding to a wavelength of about 1.3 cm, and consequently that there would be strong absorption of radiation near that wavelength. Late in the war, radar apparatus operating near 1.3 cm was developed. It proved useless because of the strong absorption predicted by Van Vleck.

As the war neared its end, Van Vleck returned to pure research and entered a new field. He and Victor Weisskopf developed a quantum theory of the collision broadening of spectral lines based on the classical theory of H. A. Lorentz. The derivation of the quantum theory from the classical employed, in essence, the correspondence principle. It was Van Vleck’s last major use of the concept.

In a further study of line breadths (1948), Van Vleck calculated broadening by dipole-dipole coupling between electronic or nuclear magnetic moments. Exact expressions for the shapes of lines are difficult to derive, but Van Vleck obtained moments (the root mean square and root mean fourth power) of the frequency distribution. He proved (as he had noted in an earlier paper with C. J. Gorter) that exchange effects for electronic moments can appreciably narrow a spectral line.

Van Vleck’s exploration of line shapes was a major contribution to the theoretical understanding of nuclear magnetic resonance and of the other magnetic resonance spectroscopies developed after the war. Philip Anderson (a student of Van Vleck’s in the late 1940’s) points out that Van Vleck maintained close ties to relevant experimental work, such as the research of Edward Purcell at Harvard on nuclear magnetic resonance that earned Purcell the Nobel Prize.

Anderson argues that Van Vleck was a pivotal figure in early developments in the area now known as quantum electronics. He was an expert in atomic and molecular spectra (being, for instance, one of the few theorists to note the detection of the 1.25 cm inversion line of the ammonia molecule), and his work on line breadths was crucial to the invention of the maser and the laser.

In another field, about 1950 Van Vleck and his student Thomas Kuhn developed the quantum defect method for calculating cohesive energies of alkali metals. Rather than constructing a potential for an ion in a crystal lattice and integrating Schrödinger’s equation through it to obtain the binding energy, they made use of the known energy levels of free alkali atoms. The few lowest energy states of the atom define its behavior, and the energies of those states (which are the quantum defects) can be used to construct a wave function for the outer region of an atom in a crystal. The potential in the outer regions of the atom is hydrogenic. The wave function is therefore a combination of confluent hypergeo-metric functions, similar to the wave function of a hydrogen atom. With boundary conditions appropriate to a crystal, rather than a free atom, the hydrogenic wave function determines the cohesive energy of the crystal.

Old concerns continued to interest Van Vleck; in the late 1940’s and early 1950’s he wrote about an “intermediate” model of ferromagnetism. In it he supposed each atom in a metal to be in one of two states of ionization. Electrons are thus less mobile than they are in band theory (where each atom can take on several states of ionization) but are more mobile than in Heisenberg’s first model of ferromagnetism (where each atom has a fixed complement of electrons). As in his earlier work on valence theory, Van Vleck took pleasure in constructing a bridge between two distinct theoretical descriptions of a phenomenon. His “intermediate” model of ferromagnetism was, however, quite difficult to use for calculations.

Although Van Vleck had returned to research at the end of the war, administrative and professional work took a great deal of his time from 1945 through 1957. As chairman of the physics department at Harvard from 1945 to 1949, his principal concern was to build up the faculty. There were many able young physicists available in the postwar period. Among those hired during Van Vleck’s chairmanship were the future Nobel laureates Edward Purcell and Julian Schwinger.

In 1951 Van Vleck was appointed Hollis professor of mathematics and natural philosophy and, somewhat reluctantly, first dean of the Division of Engineering and Applied Physics (created by the merger of the Engineering School and the department of engineering science and applied physics). Funds bequeathed by the industrialist Gordon McKay made possible the equipping of the McKay Laboratory and the hiring of new faculty. One of the first appointments during Van Vleck’s tenure as dean was Nicolaas Bloembergen, also a future Nobel laureate.

In 1952 and 1953 Van Vleck served as president of the American Physical Society. By the early 1950’s it had established divisions that met separately. Van Vleck had opposed this balkanization of the society, a consequence of its postwar growth, but by 1953 the trend could not be reversed.

From 1951 to 1956 Van Vleck was a member of the Visiting Committee of the National Bureau of Standards. He was vice president of the American Academy of Arts and Sciences (1956–1957) and vice president of the International Union of Pure and Applied Physics (1958–1960).

Van Vleck resigned his deanship at Harvard in 1957 and was again able to enjoy extended travel abroad. In 1960 he was Lorentz professor at the University of Leiden, and in the year 1961–1962, Eastman professor at Oxford University.

Van Vleck published about fifty papers between 1957 and his retirement in 1969, and about fifteen more in the decade after he retired. He continued to explore the spectroscopic and magnetic properties of the rare earths. A new concern was the magnetism of garnets (ferrimagnetic silicate crystals containing cations of two chemical elements). In his later years Van Vleck frequently lectured on the half-century of physics he had taken part in. The one project that he never completed was a second edition of his Susceptibilities, which had achieved the status of a classic, but was outdated. The field of susceptibilities had grown too large for a single author, and Van Vleck could find no one willing to collaborate with him.

In his later years nearly a score of medals and awards found their way to Van Vleck. In 1963 he was the first recipient of the Michelson Award of the Case Institute of Technology; in 1970 he was made a chevalier of the Legion of Honor; in 1974 he won the Lorentz Medal of the Royal Netherlands Academy of Arts and Sciences; and in 1977 he shared the Nobel Prize with Philip Anderson and N. F. Mott.

Van Vleck’s mathematical talent was considerable, and his physical intuition impressive, but he was not an arrogant or distant man; quite the contrary: he was approachable, and also exceedingly generous with his talents. Typical of his generosity is the fact that many of his ideas were first published by his students, without his name attached. The papers of Jordahl, Penney, and Schlapp on the crystal field theory are the best examples.

Other aspects of Van Vleck’s character are not evident in his scientific work. As a young man he played the flute, and while he was unathletic, he enjoyed watching football (particularly when Wisconsin or Harvard was playing). He shared his parents’ taste for art, and from them he inherited a collection of several thousand Japanese prints, which he in turn gave to the University of Wisconsin. Van Vleck also had a dry wit.

Van Vleck remained active until his death from heart failure. With funds that he bequeathed, the John Hasbrouck Van Vleck chair of pure and applied physics was established at Harvard University.


I. Original Works. Van Vleck published more than 180 papers in his lifetime. Consult the following complete bibliographies: Philip W. Anderson, “John Hasbrouck Van Vleck,” in Biographical Memoirs, National Academy of Sciences, 56 (1987), 501–540; “Bibliography of J. H. Van Vleck,” in International Journal of Quantum Chemistry, Symposium, no. 5 (1971), vi-xi; and Brebis Bleaney. “John Hasbrouck Van Vleck,” in Biographical Memoirs of Fellows of the Royal Society, 28 (1982), 627–665.

Works concerning the old quantum theory include “The Normal Helium Atom and Its Relation to the Quantum Theory,” in Philosophical Magazine, 44 (1922) 842–869; “The Absorption of Radiation by Multiple Periodic Orbits, and Its Relation to the Correspondence Principle and the Rayleigh-Jeans Law,” in Physical Review, 24 (1924), 330–365 (“Part I. Some Extensions of the Correspondence Principle,” was reprinted in B. L. van der Waerden, ed., Sources of Quantum Mechanics [Amsterdam, 1967; repr. New York, 1968]); “Absorption, Emission, and Line-breadths: A Semihistorical Perspective,” in Reviews of Modern Physics, 49 (1977), 939–959, with David L. Huber; and Quantum Principles and Line Spectra, Bulletin of the National Research Council, no. 54 (1926).

Early calculations in the quantum theory, on susceptibilities, and molecular spectroscopy: “Magnetic Susceptibilities and Dielectric Constants in the New Quantum Mechanics,” in Nature, 118 (1926), 226–227; “The Dielectric Constant and Diamagnettsm of Hydrogen and Helium in the New Quantum Mechanics,” in Proceedings of the National Academy of Sciences, 12 (1926), 662–670; “On Dielectric Constants and Magnetic Susceptibilities in the New Quantum Mechanics. I. A General Proof of the Langevin-Debye Formula,” in Physical Review, 29 (1927), 727–744; “On Dielectric Constants and Magnetic Susceptibilities in the New Quantum Mechanics. II. Application to Dielectric Constants,” ibid., 30 (1927), 31–54; “On Dielectric Constants and Magnetic Susceptibilities in the New Quantum Mechanics, III. Application to Dia- and Paramagnetism,” ibid., 31 (1928), 587–613; and “On A-Type Doubling and Electron Spin in the Spectra of Diatomic Molecules,” ibid., 33 (1929), 467–506.

In the early 1930’s Van Vleck (or his students) wrote the following works on susceptibilities: The Theory of Electric and Magnetic Susceptibilities (Oxford, 1932); “The Influence of Crystalline Fields on the Susceptibilities of Salts of Paramagnetic Ions, I. The Rare Earths. Especially Pr and Nd,” by William Penney and Robert Schlapp, in Physical Review, 41 (1932), 194–207; “Influence of Crystalline Fields on the Susceptibilities of Salts of Paramagnetic Ions, II. The Iron Group, Especially Ni, Cr, and Co,” by Robert Schlapp and William Penney. ibid., 42 (1932), 666–686; “Theory of the Variations in Paramagnetic Anisotropy Among Different Salts of the Iron Group,” ibid., 41 (1932), 208–215; “The Effect of Crystalline Electric Fields on the Paramagnetic Susceptibility of Cupric Salts,” by Olaf M. Jordahl. ibid., 45 (1934), 87–97; and “Valence Strength and the Magnetism of Complex Salts,” in Journal of Chemical Physks, 3 (1935), 807–813. Papers on chemical physics include “On the Theory of the Structure of CH4 and Related Molecules, Part I,” Journal of Chemical Physics, 1 (1933), 177–182; “On the Theory of the Structure of CH4 and Related Molecules. Part II,” ibid., 219–238: “On the Theory of the Structure of CH4 and Related Molecules, Part III,” ibid., 2 (1934), 20–30; “Note on the Sp3 Configuration of Carbon, and Correction to Part III on CH4. ibid., 297–298; “The Quantum Theory of Valence,” in Reviews of Modern Physics, 7 (1935), 167–228, with Albert Sherman; “The Group Relation Between the Mulliken and Slater-Pauling Theories of Valence.” Journal of Chemical Physics, 3 (1935), 803–806.

Works from the late 1930’s and early 1940’s on magnetism and spectroscopy: “Quelques aspects de la théorie du magnetisme,” in Annates de IlnstHut Henri Poincare, 10 (1947), 57–187; “On the Magnetic Behavior of Vanadium, Titanium, and Chrome Alum,” in Journal of Chemical Physics, 7 (1939), 61–71; “The Jahn-Teller Effect and Crystalline Stark Splitting for Clusters of the Form XY6,” ibid., 72–84; “Paramagnetic Relaxation Times for Titanium and Chrome Alum,” in Physical Review, 57 (1940), 426–447; “Errata: Paramagnetic Relaxation Times for Titanium and Chrome Alum,” ibid., 1052; “Paramagnetic Relaxation and the Equilibrium of Lattice Oscillators,” ibid., 59 (1941), 724–729; “Calculation of Energy Exchange Between Lattice Oscillators,” ibid., 730–736; “On the Theory of Antiferromagnetism,” in Journal of Chemical Physics, 9 (1941), 85–90; “The Puzzle of Rare-Earth Spectra in Solids,” in Journal of Physical Chemistry, 41 (1937), 67–80; and “On the Energy Levels of Chrome Alum,” in Journal of Chemical Physics, 8 (1940), 790–797, with R. Finkelstein.

Radar-related papers: “A Theoretical Comparison of the Visual, Aural, and Meter Reception of Pulsed Signals in the Presence of Noise,” in Journal of Applied Physics, 17 (1946), 940–971, with David Middleton; and “The Absorption of Microwaves by Uncondensed Water Vapour,” in Physical Review, 71 (1947), 425–433.

Calculations on line shapes: “On the Shape of Collision-Broadened Lines,” in Reviews of Modern Physics, 17 (1945), 227–236, with Victor F. Weisskopf; “The Role of Exchange Interaction in Paramagnetic Absorption,” in Physical Review, 72 (1947), 1128–1129, with C. J. Gorter; and “The Dipolar Broadening of Magnetic Resonance Lines in Crystals,” ibid., 74 (1948), 1168–1183.

Discussions of the quantum defect method, and of ferromagnetism: “A Simplified Method of Computing the Cohesive Energies of Monovalent Metals,” in Physical Review, 79 (1950), 382–388, with T. S. Kuhn; “The Cohesive Energies of Alkali Metals,” in Proceedings of the International Conference of Theoretical Physics, Kyoto and Tokyo, September 1953 (1954), 640–649; “A Survey of the Theory of Ferromagnetism,” in Reviews of Modern Physics, 17 (1945), 27–47; and “Models of Exchange Coupling in Ferromagnetic Media,” ibid., 25 (1953), 220–227.

The bulk of Van Vleck’s papers are held by the American Institute of Physics’ Center for History of Physics; papers relating to the administration of Harvard University are retained by the Harvard University Archives. Van Vleck was interviewed by Thomas Kuhn (in 1963) as a part of the Archive for History of Quantum Physics, and by Charles Weiner and Gloria Lubkin (in 1966 and 1973) for the A1P Center for History of Physics. Van Vleck’s excellent memory made him a reliable historical source.

The best overview of Van Vleck’s early career is presented in his address, “The First Decade of Quantum Mechanics,” in International Journal of Quantum Chemistry, Symposium, no. 5 (1971), 3–20.

Secondary Literature. The biographical memoirs by Anderson and Bleaney (cited above) discuss his entire career. Van Vleck’s career to 1934 is treated in depth in Frederick Fellows, “J. H. Van Vleck: The Early Life and Work of a Mathematical Physicist” (Ph.D. diss., University of Minnesota, 1985).

H. A. Kramers’ research in the old quantum theory is discussed at length by Max Dresden in his H. A. Kramers: Between Tradition and Revolution (New York, 1987). Katherine Sopka explores the growth of the American physics profession in Quantum Physics in America, 1920–1935 (New York, 1980). Spencer Weart recounts the division of the American Physical Society in “The Birth of the Solid-State Physics Community,” in Physics Today, 41 (July 1988), 38–45. The International Project in the History of Solid State Physics has produced a history of the emergence of the discipline: Lillian Hoddeson, Ernest Braun, Jürgen Teichmann, and Spencer Weart, eds., Out of the Crystal Maze: Chapters from the History of Solid State Physics (New York, 1990).

Frederick Fellows

Van Vleck, John Hasbrouck

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John Hasbrouck Van Vleck

American physicist John Hasbrouck Van Vleck (1899-1980) won the 1977 Nobel Prize for work that laid the foundation for the quantum theory of paramagnetism. Van Vleck is considered the founder of modern theoretical physics, and enjoyed a long career as both researcher and mentor. According to John Ellement in the Boston Globe, the Nobel laureate once explained his field of research as a way to "get at what is the truth of things. The more we know about the universe, the better off we are."

Born on March 13, 1899, in Middletown, Connecticut, Van Vleck hailed from an esteemed family with origins that dated back to some of the first European families to settle in New Jersey. Intellectual achievements were already commonplace in his family by the time he arrived: his grandfather was a professor of astronomy at Wesleyan College in Middletown, Connecticut, and the college's observatory is named in his honor. Van Vleck's father, Edward Burr Van Vleck, was professor of mathematics, also at Wesleyan. It was a stimulating environment for a boy, but Van Vleck claimed he grew up an extremely shy child. Fascinated by railroads, he pored over train time tables for hours on end in order to commit them to memory. Later in his life, he usually traveled without referring to a printed train schedule.

The Van Vleck family relocated to Madison, Wisconsin when Edward Van Vleck was hired by the University of Wisconsin. Summers were sometimes spent in Europe on lengthy family vacations, but back in Madison Van Vleck attended public schools. He then entered the University of Wisconsin, and majored in physics. After graduating in 1920, he was determined to forge his own path in life. Because both his father and grandfather had undertaken active and prominent careers in academia, Van Vleck himself "vowed as a child that I would not be a college professor," as he later wrote in an autobiography posted on the Nobel Prize Website. "But after a semester of graduate work at Harvard, I outgrew my childish prejudices, and realized that the life work for which I was best qualified was that of a physicist, not of the experimental variety, but in an academic environment."

Delved into Theoretical and Quantum Physics

Van Vleck earned his doctorate in physics from Harvard University, and while there he turned toward theoretical physics, which was a new field at the time. In fact, his 1922 doctoral thesis is thought to have been the first American paper based on a purely theoretical subject, in his case the ionization energy of a particular model of the helium atom. Theoretical physics differs from standard physics in that it seeks to predict outcomes by using a model of reality, only part of which may be observable or proven by scientific experiment. Van Vleck's work showed such early promise that job offers came easily: his first postgraduate post came as an instructor in physics at Harvard, and a year later, in 1923, he was hired by the University of Minnesota.

Van Vleck would spend the next five years in Minnesota, and his relatively light teaching load allowed him ample time to devote to research. He began investigating the application of quantum mechanical theory to a variety of physical phenomena, and wrote his first book, Quantum Principles and Line Spectra, in 1926. The work sold unexpectedly well for its subject matter, though its audience was most likely a purely academic one. Quantum science was also a new and exciting field at the time, which certainly accounts for some of the book's appeal.

In 1927 Van Vleck made a breakthrough discovery involving the general theory of magnetic and electric susceptibilities in gases. He also made his first forays into the field that would mark his name in the annals of science: the quantum explanation of magnetic effects. His 1932 book, The Theory of Electric and Magnetic Susceptibilities, featured new ideas regarding the crystal field theory. His research efforts sought to describe paramagnetic salts, especially salts that contained rare-earth ions. It was for this work that Van Vleck earned the 1977 Nobel Prize, as well as the moniker the "father of modern magnetism."

Hired at Harvard

In 1928 Van Vleck returned to his first alma mater, the University of Wisconsin, to become a professor of physics. He rejoined the staff at Harvard University six years later and spent the remainder of his career there. During World War II, he served on a government-appointed committee of scientists charged with evaluating the feasibility of building an atomic bomb; their recommendations spurred the creation of the Manhattan Project, the joint effort that helped bring to fruition the world's first nuclear weapon in 1945. Later into the war Van Vleck became involved in radar work at the Radio Research Laboratory of Cambridge, Massachusetts.

Only later in his career did the work Van Vleck had carried out on crystal field theory, ferromagnetics, and magnetic resonance find practical applications. Some of these include lasers, transistors, and even the copper spirals used in certain birth-control devices. When he was awarded the 1977 Nobel Prize for, in the words of the Nobel committee, his "fundamental theoretical investigations of the electronic structure of magnetic and disordered systems," it was nearly 50 years after he had first launched his research projects. He shared his award with Philip W. Anderson, who had also once been his student, and Sir Nevill Mott. Van Vleck was pleased by the honor, despite the passage of years. "So often the prizes go to younger men," Ellement quoted him as saying in the Boston Globe. "Anybody couldn't help feeling that it is a culmination when you're 78 years old."

In the late 1940s, Van Vleck served as chair of Harvard's physics department, and in the following decade helped create the interdisciplinary Division of Engineering and Applied Physics; he also served as that division's first dean. In 1951 he became the Hollis Professor of Mathematical and Natural Philosophy, the oldest endowed science chair in North America, which he held until his retirement in 1969. He died in Cambridge, Massachusetts, on October 27, 1980, survived by his wife Abigail Pearson Van Vleck, whom he had wed in June of 1927. For much of his life, his friends and colleagues knew him simply as "Van," and though his childhood shyness had endured, he had been known for generously sharing credit on his research projects. As a writer noted in the London Times in announcing his death, Van Vleck "had a warm, outgoing and unassuming personality, always eager to help, be it in personal or professional matters, always generous in his praise of the achievements of his students and colleagues and, relying on his vast fund of knowledge, ever ready to help in solving knotty scientific problems."


Dictionary of American Biography, Supplement 10: 1976-1980, Charles Scribner's Sons, 1995.

World of Physics, edited by Kimberly A. McGrath, Gale, 2001.


Boston Globe, October 28, 1980.

Times (London, England), November 1, 1980.


"John H. Van Vleck," Nobel Prize Website, (December 19, 2004).