**Electron correlation** __Definition:__ Electronic correlation refers to the interaction between electrons in a quantum system whose electronic structure is being considered. The adjustment of electron motion to the instantaneous (as opposed to time-averaged) positions of all the electrons in a molecular entity.

The term correlation stems from mathematical statistics and means that two distribution functions, f and g, are not independent of each other.

__Definition:__ Configuration Interaction (or electron correlation) adds to the single determinant of the Hartree-Fock wave function a linear combination of determinants. In terms of a specification of orbital occupation, interaction means the mixing (interaction) of different electronic configurations (states). CI calculations determine the weighting of each determinant to produce the lowest energy ground state.

__Definition:__ The dynamical interactions among electrons give rise to instantaneous spatial correlations that must be handled to arrive at an accurate picture of the atomic and molecular structure. The single-configuration picture provided by the mean-field model is a useful starting point, but it is incapable of describing electron correlations. Therefore, improvements are needed. The use of doubly-excited configurations is a mechanism by which we can place

electron pairs, which in the mean-field picture occupy the same orbital, into different regions of space thereby lowering their mutual Coulombic repulsions. Such electron correlation effects are referred to as dynamical electron correlation; they are extremely important to include if one expects to achieve chemically meaningful accuracy.

Source: Encyclopedia of Chemical Physics and Physical Chemistry

__Definition__ The SCF procedure accounts for electron-electorn repulsion by optimising the one-electron MOs in the presence of an average field of the other electrons. The result is that electrons in the same spatial MO are too close together. Their motion is actually correlated (as one moves, the other responds).

Although there is no clearcut partitioning electron correction can be divided into:

- Dynamic correlation:

Dynamic correlation is due to the interaction between two electrons at short distance.

- Static correlation (near degeneracy correlation):

Static correlation or near degeneracy correlation is due to the appearance an mixing of two or more electronic configurations having the same or nearly the same energy.

Electron correlation is in terms of various levels of theory of solutions for the Schrodinger equation the difference between (B) the

Hartree-Fock limit and (D) the exact solution of the nonrelativistic Schrodinger equation. The various levels of theory in order of decreasing energy are:

- A: Hartree-Fock energy

- B: Hartree-Fock limit

- C: Post Hartree-Fock methods

- D: Exact solution of the nonrelativistic Schrodinger equation

- E: Relativistic energy

Methods to recover dynamic corelation are:

- CI: Configuration Interaction

- PT: Perturbation Theory

- CC: Coupled Cluster theory

See also:

Configuration Interaction

http://en.wikipedia.org/wiki/Configuration_interaction