Slaters Xa Model

I have dealt at length with the Hartree and the Hartree-Foek models. The father of this field, Sir Wilham Hartree, was eoneemed with the atomie problem where it is routinely possible to integrate numerieally the HF integro-differential equations in order to produee (numerieal) wavefunetions that eorrespond to the Hartree-Foek limit. For moleeular applieations the LCAO variant of HF theory assumes a dominant role beeause of the redueed symmetry of the problem. 

Briefly, we write the atomie orbitals for a one-electron atom as 

In order to retain the orbital model for a many-electron atom, Hartree assumed that each electron came under the influence of the nuclear charge and an average potential due to the remaining electrons. He therefore retained the form of the radial equation for a one-electron atom, equation 12.2, but assumed that the mutual potential energy U was the sum of 

Sir William Hartree developed ingenious ways of solving the radial equation, and they are documented in Douglas R. Hartree s book (1957). By the time this book was published, the SCF method had been well developed, and its connection with the variation principle was finally understood. It is interesting to note that Chapter 2 of Douglas R. Hartree s book deals with the variation principle. 

if we consider a closed-shell singlet state with m electron pairs and electronic configuration 

R(r) is called the radial function, and Y mi (8, f ) is a spherical harmonic. U(r) is the mutual potential energy of the nucleus and the electron. 

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