**Hartree-Fock theory** Hartree-Fock is a mean field theory in which each electron has its own wavefunction (orbital), which in turn obeys an effective 1-electron Schrodinger equation.

The effective hamiltonian (Fock operator) contains the average field (Coulomb and exchange) of all other electrons in the system. In other words, the electron electron repulsion is treated in a mean field way.

The total electronic wavefunction for the molecule, ignoring complications introduced by the Pauli principle, is a simple product of the orbitals.

Following the Born interpretation of wavefunctions, this implies that if the probability density for finding electron 1 at position r1 is P(r1) and if the probability density for finding electron 2 at position r2 is P(r2), that the probability density for finding electron 1 at r1 and electron 2 at r2 is:

P(r1,r2) = P(r1)P(r2)

In other words, the probability density for a given electron is independent of the positions of all other electrons. In reality however the motions of electrons are more intimately correclated. Because of the direct Coulomb repulsion of electrons the instantaneous position of electron 2 forms a region in space that electron 1 will avoid. This avoidance is more than that caused by the mean field. So P(r1,r2) near r1=r2 is too high since electron 1 has no knowledge of the instantaneous position of electron 2. It only eperiences a field due to the average value of the position of electron 2.

This effect is also called

electron correlation. Hartree-Fock theory neglects electron correlation effects. The correlation energy is the difference between the Hartree-Fock limit and the exact energy. A certain amount of electron correlation is already considered within the HF approximation, found in the electron exchange term describing the correlation between electrons with parallel spin. This basic correlation prevents two parallel-spin electrons from being found at the same point in space and is often called Fermi correlation.

HF wavefunctions are not adequate for describing the formation and dissociation of covalent bonds. The problem is that the two electrons associated with a particular bond generally associate with different fragments (radicals) as the bond is broken. In HF wavefunctions a bond pair consists of one doubly occupied orbital and hence will not, in general, lead to the correct dissociated radical species.

__See also:__ HF band gap

http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1300859601/0#0 __Sources:__ AB INITIO METHODS FOR ELECTRON CORRELATION IN MOLECULES, Peter Knowles

http://www.fz-juelich.de/nic-series/Volume3/knowles.pdf __See also:__ http://www.eng.fsu.edu/~dommelen/quantum/style_a/hf.html