Editing Hartree–Fock method (section)

=== Approximations ===
The Hartree–Fock method makes five major simplifications to deal with this task:
* The [[Born–Oppenheimer approximation]] is inherently assumed.  The full molecular wave function is actually a function of the coordinates of each of the nuclei, in addition to those of the electrons.
* Typically, [[Special relativity|relativistic]] effects are completely neglected.  The [[momentum]] operator is assumed to be completely non-relativistic.
* The variational solution is assumed to be a [[linear combination]] of a finite number of [[basis set (chemistry)|basis functions]], which are usually (but not always) chosen to be [[orthogonal]]. The finite basis set is assumed to be approximately [[Orthonormal basis#Incomplete orthogonal sets|complete]].
* Each [[energy eigenfunction]] is assumed to be describable by a single [[Slater determinant]], an antisymmetrized product of one-electron wave functions (i.e., [[Molecular orbital|orbitals]]).
* The [[mean field theory|mean-field approximation]] is implied. Effects arising from deviations from this assumption are neglected. These effects are often collectively used as a definition of the term [[electron correlation]]. However, the label "electron correlation" strictly spoken encompasses both the Coulomb correlation and Fermi correlation, and the latter is an effect of electron exchange, which is fully accounted for in the Hartree–Fock method.<ref>{{cite book |title=Modelling Molecular Structures |last=Hinchliffe |first=Alan |edition=2nd |year=2000 |publisher=John Wiley & Sons Ltd |location=Baffins Lane, Chichester, West Sussex PO19 1UD, England |isbn=0-471-48993-X |page=186 }}</ref><ref name="Szabo">{{cite book
  | last1 = Szabo
  | first1 = A.
  | last2= Ostlund| first2= N. S.
  | title = Modern Quantum Chemistry
  | publisher = Dover Publishing | year = 1996 | location = Mineola, New York
  | isbn = 0-486-69186-1}}</ref> Stated in this terminology, the method only neglects the Coulomb correlation. However, this is an important flaw, accounting for (among others) Hartree–Fock's inability to capture [[London dispersion]].<ref>{{Citation |author=A. J. Stone |title=The Theory of Intermolecular Forces |year=1996 |publisher=Clarendon Press |location=Oxford}}.</ref>

Relaxation of the last two approximations give rise to many so-called [[post-Hartree–Fock]] methods.