Conventional stored-integral method

A compromise between the direct method, which recomputes all integrals as needed, and the conventional stored-integral method, is the widely used semidirect method, which stores some integrals (those most time-consuming to calculate) and recomputes others. 

Since the first formulation of the MO-LCAO finite basis approach to molecular Ilartree-Pock calculations, computer applications of the method have conventionally been implemented as a two-step process. In the first of these steps a (large) number of integrals — mostly two-electron integrals — arc calculated and stored on external storage. Th e second step then con sists of the iterative solution of the Roothaan equations, where the integrals from the first step arc read once for every iteration. 

In the Direct SCF method, we do. not store the two-electron integrals over the basis functions, we recalculate them on demand every cycle of the HF procedure At first sight, this may seem wasteful, but Conventional methods rely on disk input/output transfer rates whilst Direct methods rely on processor power. There is obviously a balance between processor speed and disk I/O. Just for the record my calculation on aspirin (73 basis functions) took 363 s using the Direct method and 567 s using the Conventional method. 

The testbench in the last section was an implementation of conventional SCF the one-electron and repulsion integrals were computed once and stored for use during the iterations of the SCF procedure. It is just as easy to set up a testbench to demonstrate the other extreme the calculation of the energy integrals as they are required during the SCF iterations the so-called direct SCF method. 

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