Computer Time Saving in Evaluation of Integrals

Discussion in this section is focussed on the computation of integrals with contracted Gaussian basis sets, though many approaches noted here are of general importance and may be applied also to STO 

Another way of reducing the time of integral evaluation is based 

The efficiency of the use of symmetry may be demonstrated with a-cetylene. For a OZ basis it is necessary to compute 45150 two-electron integrals. If use is made of the 0 symmetry, which is the highest symmetry of acetylene in the representation of Cartesian GTF s, their number reduces to 6558, 

Assume next for the sake of simplicity that are of s-type, so that s = t B u = 0 and the normalized primitives in eqn, (3,25) become 

The direct calculation of (-(ivlXff) over the summation (3,27) is ineffective because it involves redundant recalculation of many partial terms. This may be best seen if eqn. (3.27) is rewritten in the following form (compare (3.23) and take into account normalization of primitives (3.20))  

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