Quantumbiochemistry.org

The weakness of the Hartree-Fock method is that it allows electrons of unparallel spin to move independent on one another. This is wrong so any solution to the Hartee-Fock equations has a build-in error.

Perturbation theory and configuration interaction are methods to obtain a correction to the Hartree–Fock equations. These methods are based on the principle that a molecular wave function can be represented by a linear combination of several Slater determinants.

The Hartee-Fock procedure produces a set of occupied spin orbitals it also produces a set of unoccupied spin orbitals. These unoccupied spin orbitals can then be used to formulate more Slater determinants. Any molecular wave function can also be represented by a series of Slater determinants. Interaction terms between the one electron orbitals of these distinct Slater determinants are corrections to the solutions of the Hartree-Fock equations.