Douglas Rayner Hartree (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree–Fock equations of atomic physics and the construction of a differential analyser using Meccano.
Douglas Hartree was born in Cambridge, England. His father, William, was a lecturer in engineering at the University of Cambridge. His mother, Eva Rayner, was president of the National Council of Women of Great Britain and first woman to be mayor of the city of Cambridge. One of his great-grandfathers was Samuel Smiles; another was the marine engineer William Hartree, partner of John Penn. Douglas Hartree was the oldest of three sons who survived infancy. A brother and sister died in infancy when he was still a child, but his two brothers would later also die. Hartree's 7-year-old brother John Edwin died when Hartree was 17, and Hartree's 22-year-old brother Colin William died from meningitis in February 1920 when Hartree was 23. His maternal cousin was the geologist Dorothy Helen Rayner.
Hartree attended St Faith's School in Cambridge, then Bedales School, returning to Cambridge for his degree studies at St John's College, Cambridge, which the first World War interrupted. He (and his father and brother) joined a group working on anti-aircraft ballistics under A. V. Hill, where he gained considerable skill and an abiding interest in practical calculation and numerical methods for differential equations, executing most of his own work with pencil and paper. According to Hill, writing in Hartree's obituary, ‘Quietly one day he improvised a long-base height-finder out of some wires, posts, and a steel tape’. This became known as the Hartree height-finder and was used extensively by British Anti-Aircraft troops until better optical height-finders were introduced. Its advantage was said to be that the height can be calculated from the observed quantities ‘very rapidly by the use of nothing but simple arithmetic’. It was also cheap to manufacture and easy to use.
After the end of World War I, Hartree returned to Cambridge graduating in 1922 with a Second Class degree in natural sciences.
In 1921, a visit by Niels Bohr to Cambridge inspired Hartree to apply his numerical skills to Bohr's theory of the atom, for which he obtained his PhD in 1926 – his advisor was Ernest Rutherford. With the publication of Schrödinger's equation in the same year, Hartree was able to apply his knowledge
of differential equations and numerical analysis to the new quantum theory.
He derived the Hartree equations for the distribution of electrons in an atom and proposed the self-consistent field method for their solution. The wavefunctions from this theory did not satisfy the Pauli exclusion principle for which Slater showed that determinantal functions are required. V. Fock published the "equations with exchange" now known as Hartree–Fock equations. These are considerably more demanding computationally even with the efficient methods Hartree proposed for the calculation of exchange contributions. Today, the Hartree-Fock equations are of great importance to the field of computational chemistry, and are applied and solved numerically within most of the density functional theory programs used for electronic structure calculations of molecules and condensed phase systems.
In 1929, Hartree was appointed to the Beyer Chair of Applied Mathematics at the University of Manchester. and was elected to membership of the Manchester Literary and Philosophical Society in 1929.
In 1933, he visited Vannevar Bush at the Massachusetts Institute of Technology and learned first hand about his differential analyser. Immediately on his return to Manchester, he set about building his own analyser from Meccano. Seeing the potential for further exploiting his numerical methods using the machine, he persuaded Sir Robert McDougall to fund a more robust machine, which was built in collaboration with Metropolitan-Vickers.
The first application of the machine, reflecting Hartree's enthusiasm for railways, was calculating timetables for the London, Midland and Scottish Railway. He spent the rest of the decade applying the differential analyser to find solutions of differential equations arising in physics, including control theory and laminar boundary layer theory in fluid dynamics, making significant contributions to each of the fields.
The differential analyser was not suitable for the solution of equations with exchange. When Fock's publication pre-empted Hartree's work on equations with exchange, Hartree turned his research to radio-wave propagation that led to the Appleton–Hartree equation. In 1935, his father, William Hartree, offered to do calculations for him. Results with exchange soon followed. Douglas recognised the importance of configuration interaction that he referred to as "superposition of configurations".
The first multiconfiguration Hartree–Fock results were published by father, son, and Bertha Swirles (later Lady Jeffreys) in 1939.
At Hartree's suggestion, Bertha Swirles proceeded to derive equations with exchange for atoms using the Dirac equation in 1935. With Hartree's advice, the first relativistic calculations (without exchange) were reported in 1940 by A. O. Williams, a student of R. B. Lindsay.
During the Second World War Hartree supervised two computing groups. The first group, for the Ministry of Supply, has been described by Jack Howlett as a "job shop" for the solution of differential equations. At the outbreak of World War II, the differential analyser at the University
of Manchester was the only full-size (eight integrator)
differential analyser in the country. Arrangements were made to have the machine available
for work in support of the national war effort. In time, the group consisted of four members (Jack Howlett, Nicholas R. Eyres, J. G. L. Michel, Douglas Hartree, and Phyllis Lockett Nicolson). Problems were submitted to the group without information about the source but included the automatic tracking of targets, radio propagation, underwater explosions, heat flow in steel, and the diffusion equation later found to be for isotope separation. The second group was the magnetron research group of
Phyllis Lockett Nicolson, David Copely, and Oscar Buneman.