The contraction problem may be described by considering a general contracted ERI of -type functions derived from the STO-3G basis set. Each basis function has degree of contraction . Thus, the ERI may be written
and requires 81 primitive integrals for the single ERI. The problem escalates dramatically for more highly contracted sets (STO-6G, 6-311G) and has been the motivation for the development of techniques for shell-pair modeling, in which a second shell-pair is constructed with fewer primitives that the first, but introduces no extra error relative to the integral threshold sought.
The Pople-Hehre axis-switch method
J. Comput. Phys.
(1978), 27, pp. 161. is excellent for high contraction low angular momentum integral classes.