The Hartree-Fock method is an iterative procedure that optimises an approximate asymmetric wavefunction using the variational principle, in the attempt to estimate the eigenvalues of a modified form of the non-relativistic multi-electron Hamiltonian.

One of the deficiencies of the Hartree self-consistent field method is that it does not consider exchange forces due to electron spin interactions. This is because the derivation of the Hartree equations uses eq3, which does not satisfy the Pauli exclusion principle. In 1930, Vladimir Fock developed an improved procedure called the Hartree-Fock method. It replaces the product of orbitals in eq3 with a Slater determinant of spin-orbitals to represent the wavefunction of an atom.

Similar to the Hartree self-consistent field method, the computation of the energy of an atom via the Hartree-Fock method involves simultaneously solving a set of equations called the * Hartree-Fock equations*:

where .

The derivation of the Hartree-Fock equations is shown in the next article.