1. Hartree-Fock method

The Hartree-Fock equations have historically paved the way for so-called self-consistent field (SCF) methods. In the context of a Slater determinant representation of the polyelectronic wave function, the Hartree-Fock method enables the Schrödinger equation to be solved by replacing the search for eigenvalues and eigenfunctions of the Hamiltonian operator with those of a "pseudo" monoelectronic operator, i.e. representing the interaction of an electron with the nuclei on the one hand, and a local repulsive mean field taking into account the presence of other electrons on the other. The solution must, however, be sought by convergence following an iterative (self-coherent) procedure, as the new operator applying to any single-electron spinorbit depends functionally on all the others.

If we represent the ground state of an n-electron system by the normalized determinant...