Atomic orbital basis function incomplete

Unfortunately, even with an incomplete one-electron basis, a full Cl is computationally intractable for any but the smallest systems, due to the vast number of. V-electron basis functions required (the size of the Cl space is discussed in section 2.4.1). The Cl space must be reduced, hopefully in such a way that the approximate Cl wavefunction and energy are as close as possible to the exact values. By far the most common approximation is to begin with the Hartree-Fock procedure, which determines the best single-configuration approximation to the wavefunction that can be formed from a given basis set of one-electron orbitals (usually atom centered and hence called atomic orbitals, or AOs). This yields a set of molecular orbitals (MOs) which are linear combinations of the AOs ... 

Use of atomic orbitals as basis functions also goes a good deal of the way to satisfying the third condition. If the basis functions are well adapted to the expansion of the MOs, then the length of the expansions can be limited. In short, the mathematical completeness of the basis set is an impractical ideal and we shall have to be satisfied with a well-chosen (on physical grounds, that is) incomplete basis. 

Recent results within the context of a benchmark ab initio study of atomic electron affinities of first and second row atoms [35], confirmed the quality of these hybrid functionals. The study enabled us to compare DFT calculated EA values with what we considered to be the best non relativistic values available until now. They were obtained by adding valence and core correlation terms to basis set extrapolated SCF results, finally correcting for differences with full Cl and basis set incompleteness. Adding relativistic corrections (spin orbit, Darwin and mass velocity terms) one obtains what we called the "best calculated values" (vide supra) which show a mean absolute difference of only 9 10" eV with experiment. In Table 1 these reference values are given, together with the most recent and accurate experimental values. 

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