Once all the integrals needed are calculated, the SCF calculation can be started. A trial density matrix is constructed; this is a diagonal matrix with the diagonal terms chosen so that every atom starts off electrically neutral (except for ions, when each atom is given an equal charge).

Using this trial density matrix, the one-electron matrix, and the two-electron integrals, a trial Fock matrix is constructed.

Diagonalization produces a set of eigenvectors, from which a better density matrix can be made.

This sequence (constructing the density matrix--constructing the Fock matrix--diagonalizing the Fock to get new eigenvectors) is repeated until the density matrix has become self-consistent to within a pre-set limit (SELCON).