Integral direct algorithm.

In the iterative method outlined above, the super-matrices $A$ and $B$ never need to be set up explicitly; only the products of $A$ and $B$ with some suitable basis vectors are required. These matrix-vector-products are evaluated very efficiently in the AO basis, because the required four-index integrals can be computed ``on the fly'' and need not be transformed or stored on disk. In addition, prescreening techniques based on rigorous bounds are straightforward to apply. This leads to a low-order scaling $O(N^2)-O(N)$ for the time-determining steps. Due to the similarity to ground state fock matrix construction, the same keywords are used to control these steps as in semi-direct SCF, namely $thime, $thize, $scfintunit, see Chapter 4. The same is true for DFT and RI keywords such as $dft, $ridft, $ricore.