Considerations on the SCF Scheme

An ab initio SCF calculation using a fixed set of m basis functions includes the following steps  

Evaluation of integrals over the basis of atomic orbitals. The computing time of this process for the two-electron integrals (J q rs) increases as m and is common to any ab initio calculation. 

Linear transformations of the integrals previously listed, in order to prepare for the determination of the effective Hamiltonian and take advantage of the symmetry properties of the molecule. The computing time needed for this increases at least as w even if the molecule has no symmetry at all, the presence of exchange terms in the Hartree-Fock theory makes a part of the transformation still necessary, namely the construction of the integral list. 

Iterative construction of the self-consistent field. Each iteration can be assumed to require the computing time of an eigenvalue problem, which varies as w, but the construction of the new Hartree-Fock operator goes as m and the number of iterations necessary to obtain convergence may considerably grow with the size of the molecule, especially if one uses non-minimal basis sets. 

Sometimes it happens that the process (3) diverges and the work in 

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