Fock expansion field correlations

As already noted, all the examples in the preceding section refer to SCF ab initio wave functions, which do not take into account electron correlation. It is well known, however, that the SCF approximation at the Hartree-Fock limit is good enough to give a reliable representation of a one-electron, first-order observable like the electronic potential, at least for closed-shell ground-state systems like those considered here. If we keep to the field of SCF ab initio wave functions, the differences in accuracy between several wave functions for the same molecule depend upon the adequacy of the expansion basis set / employed in the calculations. In the next paragraph, however, we will also treat the case of semiempirical SCF wave functions. 

Although orbital wave functions, such as Hartree-Fock, generalized valence bond, or valence-orbital complete active space self-consistent field wave functions, provide a semi-quantitative description of the electronic structure of molecules, accurate predictions of molecular properties cannot be made without explicit inclusion of the effects of dynamical electron correlation. The accuracy of correlated molecular wave functions is determined by two inter-related expansions the many-electron expansion in terms of antisymmetrized products of molecular orbitals that defines the form of the wave function, and the basis set used to expand the one-electron molecular orbitals. The error associated with the first expansion is the electronic structure method error the error associated with the second expansion is the basis set error. Only by eliminating the basis set error, i.e., by approaching the complete basis set (CBS) limit, can the intrinsic accuracy of the electronic structure method be determined. 

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