Editing Hartree–Fock method (section)

===Hartree method===
{{main|Hartree equation}}
In 1927, [[Douglas Hartree|D. R. Hartree]] introduced a procedure, which he called the self-consistent field method, to calculate approximate wave functions and energies for atoms and ions.<ref name="Hartree1928">{{cite journal |first1=D. R. |last1=Hartree |authorlink1=Douglas Hartree |title=The Wave Mechanics of an Atom with a Non-Coulomb Central Field |journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]] |volume=24 |issue=1 |pages=111 |year=1928 |doi=10.1017/S0305004100011920 |bibcode=1928PCPS...24..111H |s2cid=121520012 }}</ref> Hartree sought to do away with empirical parameters and solve the many-body time-independent Schrödinger equation from fundamental physical principles, i.e., [[ab initio quantum chemistry methods|ab initio]]. His first proposed method of solution became known as the ''Hartree method'', or ''[[Hartree product]]''. However, many of Hartree's contemporaries did not understand the physical reasoning behind the Hartree method: it appeared to many people to contain empirical elements, and its connection to the solution of the many-body Schrödinger equation was unclear. However, in 1928 [[John C. Slater|J. C. Slater]] and J. A. Gaunt independently showed that the Hartree method could be couched on a sounder theoretical basis by applying the [[variational principle]] to an [[ansatz]] (trial wave function) as a product of single-particle functions.<ref name="Slater1928">{{cite journal |first=J. C. |last=Slater |title=The Self Consistent Field and the Structure of Atoms |journal=[[Physical Review]] |volume=32 |issue=3 |pages=339–348 |year=1928 |doi=10.1103/PhysRev.32.339 |bibcode=1928PhRv...32..339S }}</ref><ref name="Gaunt1928">{{cite journal |first=J. A. |last=Gaunt |title=A Theory of Hartree's Atomic Fields |journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]] |volume=24 |issue=2 |pages=328–342 |year=1928 |doi=10.1017/S0305004100015851 |bibcode=1928PCPS...24..328G |s2cid=119685329 }}</ref>

In 1930, Slater and [[Vladimir Fock|V. A. Fock]] independently pointed out that the Hartree method did not respect the principle of [[exchange symmetry|antisymmetry]] of the wave function.<ref name="Slater1930">{{cite journal |first=J. C. |last=Slater |title=Note on Hartree's Method |journal=[[Physical Review]] |volume=35 |issue=2 |pages=210–211 |year=1930 |doi=10.1103/PhysRev.35.210.2 |bibcode=1930PhRv...35..210S }}</ref>
<ref name="Fock1930">{{cite journal |first=V. A. |last=Fock |title=Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems |language=de |journal=[[Zeitschrift für Physik]] |volume=61 |issue=1 |pages=126–148 |year=1930 |doi=10.1007/BF01340294 |bibcode=1930ZPhy...61..126F |s2cid=125419115 }} {{cite journal |first=V. A. |last=Fock |title="Selfconsistent field" mit Austausch für Natrium |language=de |journal=[[Zeitschrift für Physik]] |volume=62 |issue=11 |pages=795–805 |year=1930 |doi=10.1007/BF01330439 |bibcode=1930ZPhy...62..795F |s2cid=120921212 }}</ref> The Hartree method used the [[Pauli exclusion principle]] in its older formulation, forbidding the presence of two electrons in the same quantum state. However, this was shown to be fundamentally incomplete in its neglect of [[quantum statistics]].