Editing Hartree–Fock method (section)

===Early semi-empirical methods===
The origin of the Hartree–Fock method dates back to the end of the 1920s, soon after the discovery of the [[Schrödinger equation]] in 1926. Douglas Hartree's methods were guided by some earlier, semi-empirical methods of the early 1920s (by E. Fues, [[Robert Bruce Lindsay|R. B. Lindsay]], and himself) set in the [[old quantum theory]] of Bohr.

In the [[Bohr model]] of the atom, the energy of a state with [[principal quantum number]] ''n'' is given in atomic units as <math>E = -1 / n^2</math>. It was observed from atomic spectra that the energy levels of many-electron atoms are well described by applying a modified version of Bohr's formula. By introducing the [[quantum defect]] ''d'' as an empirical parameter, the energy levels of a generic atom were well approximated by the formula <math>E = -1 / (n + d)^2</math>, in the sense that one could reproduce fairly well the observed transitions levels observed in the [[X-ray]] region (for example, see the empirical discussion and derivation in [[Moseley's law]]). The existence of a non-zero quantum defect was attributed to electron–electron repulsion, which clearly does not exist in the isolated hydrogen atom. This repulsion resulted in partial [[screening effect|screening]] of the bare nuclear charge. These early researchers later introduced other potentials containing additional empirical parameters with the hope of better reproducing the experimental data.