What is the Electron Correlation

Electrons in molecules and crystals repel each other according to Coulomb s law, with the repulsion energy depending on the interelectron distance as This interaction creates a correlation hole around any electron, i.e. the probabihty to find any pair of electrons at the same point of spin-coordinate space is zero. Prom this point of view only the Hartree product of molecular or crystalline spin-orbitals 

As considered in Chap. 4 the Hartree-Fock (SCF) method replaces the instantar neous electron-electron repulsion with the repulsion of each electron with an average electron charge cloud. The HF method assumes that the many-electron wavefunction can be written as one Slater determinant (4.9). The Hartree-Fock method is usually defined as uncorrelated . However, the electron motions are no longer completely independent. 

V2) = 0. No two electrons with the same spin can be at the same place. This is called the Fermi hole. Thus, same-spin electrons are correlated in Hartree Pock, different-spin electrons are not. Sometimes, it is said that HF methods take into account the so-called spin correlation. 

The HF methods are also called by the independent electrons approximation [5] but this independence is restricted by the Pauli principle. 

The exact solntion of Hartree-Fock-Roothaan equations (4.33) for molecular systems means use of a complete set of basis functions (such a solution corresponds to the Hartree-Fock hmit and in practice can be achieved mainly for the simple molecules). 

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