Hartree-Fock Self-Consistent Field Method

The Hartree-Fock Self-Consistent Field Method is similar to the Hartree SCF Method, but takes the antisymmetry property into account by writing the trial wave function as a Slater determinant of variational spin-orbitals,

$$\Phi = \frac{1}{\sqrt{n!}} \left \vert \begin{matrix}1S(1)\alpha(... ...... & ... \\ 1S(n)\alpha(n) & 1S(n)\beta(n) & ... \\ \end{matrix} \right \vert,$$

where typical basis functions for the spatial orbitals 1S, 2S, ..., etc., are linear combinations of Gaussians, or Slater type orbitals $r^{n-1} e^{-\xi r/a_0} Y_l^m$.

Configuration Interaction

Improvement over the one-determinant trial wave function can be achieved by using a trial wave function that involves a linear combination of Slater determinants. This method is known as configuration interaction. The energy correction over the Hartree-Fock energy,

$$E_{cor} = E - E_{HF},$$

is known as correlation energy.