# Lennard-Jones, John Edward

# Lennard-Jones, John Edward

(*b*. Leigh, Lancashire, England, 27 October 1894;*d*. Stoke-on-Trent, England, 1 November 1954)

*theoretical physics, theoretical chemistry*.

As one of the first scientists to make a career of theoretical physics and theoretical chemistry, Lennard Jones was an outstanding example of a type that has now become familiar in the physical sciences. His genius was not to make fundamental discoveries or to conduct crucial experiments but to realize quickly the potentialities of new theories proposed by other scientists and, by ingenious and painstaking calculations, to develop them to the stage where they could be applied quantitatively to a wide range of experimental data. His major contributions were in three closely related areas: the determination of interatomic and intermolecular forces; the quantum theory of molecular structure; and the statistical mechanics of liquids, gases, and surfaces.

Until the age of thirty-one his name was John Edward Jones. He studied mathematics at Manchester University, where he began his research career under the direction of Sir Horace Lamb, with work on the theory of sound. After serving in the Royal Flying Corps during World War I, he returned to Manchester as lecturer in mathematics. Jones became interested in the kinetic theory of gases through his contact with Sydney Chapman, who was then the professor of mathematics and natural philosophy at the university. In 1916 Chapman had published a new method for calculating the transport coefficients of a gas (viscosity, thermal conductivity, and diffusion) for various kinds of molecular force laws. In 1922 Jones extended this work to rarefied gases. He then went to Cambridge University, where he received his Ph.D. in 1924, and worked with R. H. Fowler, who was at that time developing quantum statistical mechanics. In 1925 he married Kathleen Mary Lennard and changed his own name to Lennard-Jones. In the same year he was elected reader in mathematical physics at the University of Bristol; he was later the first occupant of the chair of theoretical physics there.

The work for which Lennard-Jones is now best known—his determination of a semiempirical interatomic force law—was based on Chapman’s gas theory and the Heisenberg-Schrödinger quantum mechanics, together with an analysis of experimental data on the properties of gases and solids. In 1924 he proposed to represent interatomic forces by the general formula

where *r* is the distance between the centers of two atoms. (Negative values of the function correspond to an attractive force, positive values to a repulsive force.) He attempted to determine the constants *a*, *b*, *n*, and *m* for various gases by comparing theoretical and experimental values of transport coefficients and virial coefficients (the latter being obtained from the pressure-volume-temperature relationships). In addition X-ray diffraction data on the equilibrium interatomic distances in the solid state were used.

Lennard-Jones’s first results led to values of about 5 for *n* and 14 or 15 for *m,* for the noble gases. Quantum-mechanical calculations by S. C. Wang, J. C. Slater, R. Eisenschitz, and F. London (1927-1930) indicated that *n,* the exponent for the longrange attractive force, should be 7 rather than 5. As a result Lennard-Jones adopted the value *n* = 7 and then, primarily for reasons of mathematical convenience, chose *m* = 13; the experimental data could be fitted equally well by several values of *m.* The potential energy function corresponding to this force law is

and this function, first proposed in 1931, is now generally known as the Lennard-Jones potential, or sometimes more specifically as the Lennard-Jones (6,12) potential, to distinguish it from the general form proposed earlier.

It was already evident by 1931 that quantummechanical calculations led to an exponential form for the short-range repulsive force; thus an alternative potential function, *V*(*r*) =—*Ar*^{-6} + *Be*^{-kr}, was advocated by J. C. Slater and later by R. A. Buckingham; it is generally known as the (exp, 6) potential. Extensive calculations of transport coefficients and virial coefficients of gases for these two potential functions led to the conclusion, by 1955, that both were about equally satisfactory. More recent research has shown that neither is really adequate for describing molecular and atomic interactions at very short or very long distances. Nevertheless, the Lennard-Jones potential continues to be used in many statistical mechanical calculations.

In 1932 Lennard-Jones was appointed to the new Plummer chair of theoretical chemistry at Cambridge University. As the first officially recognized “theoretical chemist” in England (or perhaps in the world), he quickly established himself as a leader in applying quantum mechanics to numerous aspects of the structure and properties of molecules. Many of his students are still actively pursuing research in this area, and Lennard-Jones must therefore be given much of the credit for introducing the discipline of quantum chemistry into Britain. His own research papers, in the 1930’s and in the early 1950’s dealt with the molecular orbital method, in which calculations are based on trial wave functions chosen to reflect the structure and symmetry of the molecule as a whole, in contrast with the “valence bond” method, advocated by Linus Pauling and others, in which atomic wave functions are taken as the starting point. Lennard-Jones also pioneered the use of mechanical computers in quantum-mechanical calculations as early as 1939.

In 1937-1939 Lennard-Jones and A. F. Devonshire published a series of papers on critical phenomena and the equation of state of liquids and dense gases. Their theory was based on a “cell model” in which each molecule is assumed to move only within a small volume, where it is acted on by a force field determined by the average positions of its neighbors. While this model would seem to attribute a solidlike structure to the system, it was found to give approximately correct results for the behavior of gases and liquids near the critical point and thus stimulated considerable work by other theorists who attempted to improve the model.

Lennard-Jones used his considerable administrative talents not only in his academic positions but also as chief superintendent of armament research for the Ministry of Supply during World War II. In 1953 he accepted the position of principal at the newly founded University College of North Staffordshire, Keele, but he was prevented from carrying out his plans for that institution by his death in 1954.

## BIBLIOGRAPHY

I. Original Works. A partial list of Lennard-Jones’s publications is given in the memoir by N. F. Mott (cited below). The following corrections should be made in the list:

1926. “The Forces Between Atoms and Ions.” Pt. II of this paper has B. M. Dent as coauthor.

1927. “The Equation of State of a Gaseous Mixture.” W. R. Cook is coauthor.

1934. “Energy Distribution in Molecules in Relation to Chemical Reactions.” The discussion remark by Lennard Jones begins on p. 242, not 239.

1936. “The Interaction of Atoms and Molecules With Solid Surfaces.” Pts. III and IV have A. F. Devonshire as coauthor; pt. V is by Devonshire alone and therefore should not be listed here.

1937. (Same title). Pts. VI and VII have A. F. Devonshire as coauthor.

The following papers should be added to Mott’s list: “Calculation of Surface-Tension From Intermolecular Forces,” in *Transactions of the Faraday Society,***36** (1940), 1156-1162, written with J. Corner; “Critical and Co-operative Phenomena. VI. The Neighbour Distribution Function in Monatomic Liquids and Dense Gases,” in *Proceedings of the Royal Society,***178A** (1941), 401-414, written with J. Corner; “The Education of the Man of Science (Discussion Remarks),” in *Advancement of Science,***4** (1948), 318-319; “Implications of the Barlow Report (Discussion Remarks),” *ibid.,***5,** no. 17 (1948), 7-8; “The Molecular Orbital Theory of Chemical Valency.XIV. Paired Electrons in the Presence of Two Unlike Attracting Centers, “in *Proceedings of the Royal Society,***218A** (1953) 327-333, written with A. C. Hurley; and “New Ideas in Chemistry,” in *Advancement of Science*, **11** (1954), 136-148, repr. in *Scientific Monthly,***80** (Mar. 1955), 1757-184.

II Secondary Literature. Short obituary notices on Lennard-Jones were published by C. A. Coulson in *Nature***174** (1954), 994-995; and by A. M.Tyndall in *Proceedings of the Physical Society of London*, **67A** (1954), 1128-1129, **67B** (1954), 916-917. An article by N.F. Mott with bibliography and portrait, appeared in *Biographical Memoirs of Fellows of the Royal Society*, **1** (1955), 175-184. His work on interatomic forces and statistical mechanics is discussed by S. G. Brush, “Interatomic Forces and Gas Theory From Newton to Lennard-Jones,” in Archive for *Rational Mechanics and Analysis*, **39** (1970), 1-29; and by J. O. Hirschfelder, C. F. Curtiss, and R. B. Bid, *Molecular Theory of Gases and Liquids* (New York, 1954).

Stephen G. Brush

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