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In this case, bielectronic and monoelectronic integrals are evaluated once and for all at the beginning of the calculation, and then used at each cycle of the SCF procedure. The problem of the "calculation and manipulation of horrendous numbers of many center integrals" (Monkhorst 1979) can be drastically simplified by point symmetry: one can obtain a saving factor as large as h (h is the order of the point group) in the number of bielectronic integrals to be computed and as large as h 2 in the number of those to be stored for the SCF part of the calculation.
Density functionals developed in the framework of DF theories can therefore also be utilized with reference to HF densities. The correlation-only functional proposed by Perdew and Yue (Perdew and Yue 1986, Perdew 1986) and obtained from a generalized gradient expansion appears particularly promising in this respect. Its application to atoms and ions, using HF densities as input data, gives impressively good results from hydrogen to argon. The non-local DF formulated by Colle and Salvetti (CSF) for evaluating the correlation 32 energy of molecular systems (Colle and Salvetti 1915, 1919, 1983) has many features in common with the Perdew functional, but has been derived in a different theoretical framework, that is, starting from an ansatz concerning the expression of the correlated wavefunction.
The material presented is meant to be self-contained; all working equations are derived and all technical solutions are accurately explained, so that the reader can follow the whole line of argument, from a basic knowledge of quantum chemistry. The sequence is as follows: The type and properties of basis functions are first described (section 2 and appendix A) and the fundamental equations are given in section 3, still in a general form, unsuitable for applications. Efficient and accurate means for truncating the Coulomb and exchange series are presented in section 4 and 5; the treatment of the Coulomb problem, in particular, requires sophisticated computational techniques and subtle algebraic manipulations (see also appendix C).