Hartrees Self-Consistent Field SCF Method

Hartree set forth to calculate wave functions for atoms with many electrons soon after the discovery of the SE of the hydrogen atom. His idea was to write down the repulsive average potential for the electrons, which is easily done using electrostatic 

The problem is that the screening potential can only be calculated if the orbitals are already known. Therefore, Hartree had to find an iterative solution. He made an initial guess as to the extension of the orbitals in space and thus calculated a screening potential. The SE for the orbitals was solved and the screening potential npdated. The procedure was repeated and new orbitals were calculated, until the orbitals no longer changed from one iteration to the next. The final result was said to be self-consistent. The screening potential now corresponds exactly equal to the repulsion between the electrons of the occupied orbitals. 

Hartree did not have access to computers, of course, but he constructed the so-called differential analyzer with the help of a Meccano kit. He managed to calculate accurate AOs already in 1928. 

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The procedure for calcuiating the g, s was introduced by Hartree in 1928 and is called the Hartree self-consistent-field (SCF) method. Hartree arrived at the SCF procedure by intuitive physical arguments. The proof that Hartree s procedure gives the best possible variation function of the form (11.4) was given by Slater and by R)ck in 1930. [For the proof and a review of the SCF method, see S. M. Blinder, Am. J. Phys., 33,431 (1965).]... 

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