B AOInts

B.5 Shell-Quartets and Integral Classes

Given a sorted list of shell-pair data, it is possible to construct all potentially important shell-quartets by pairing of the shell-pairs with one another. Because the shell-pairs have been sorted, it is possible to deal with batches of integrals of the same type or class (e.g., (ss|ss), (sp|sp), (dd|dd), etc.) where an integral class is characterized by both angular momentum (L) and degree of contraction (K). Such an approach is advantageous for vector processors and for semi-direct integral algorithms where the most expensive (high K or L integral classes can be computed once, stored in memory (or disk) and only less expensive classes rebuilt on each iteration.

While the shell-pairs may have been carefully screened, it is possible for a pair of significant shell-pairs to form a shell-quartet which need not be computed directly. Three cases are:

  • The quartet is equivalent, by point group symmetry, to another quartet already treated.

  • The quartet can be ignored on the basis of cheaply computed ERI bounds297 on the largest quartet bra-ket.

  • On the basis of an incremental Fock matrix build, the largest density matrix element which will multiply any of the bra-kets associated with the quartet may be negligibly small.

Note:  Significance and negligibility is always based on the level of integral threshold set by the $rem variable THRESH.