Generalized pairwise correlation method

When we first introduced the "orbital approximation" and noted that, at least for electrons of opposite spin, it is an independent electron theory, we mentioned that the electrons are therefore not correlated. Hence, in the HF-SCF method each electron moves in a general field created by all the other electrons. In reality, however, the motions of electrons are pairwise correlated to keep the electrons apart when one electron "moves left", a nearby electron will move out of its way, because like charges repel. This correlation of electron motions is a stabilizing effect, and thus Escf is always too high, even at the so-called Hartree-Fock limit (the result you would get with a basis set of infinite size). The error associated with the Hartree-Fock limit is called the correlation energy (Eq. 14.36). 

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