RIGOROUS FORMULA FOR THE FAST CALCULATION OF THE ELECTRON REPULSION INTEGRAL OVER THE SOLID HARMONIC GAUSSIAN-TYPE ORBITALS

A rigorous general formula for calculating the electron repulsion inte gral (ERI) over the solid harmonic (SH) Gaussian-type orbitals (GTOs) can be derived, A general algorithm can be obtained from this formula named as: accompanying coordinate expansion (ACE) b3k3. This algorithm is capable of computing very fast SH-ERIs, especially for SH contract ed GTOs. Numerical assessment is shown for the (LL\LL) class of SH-ERI s (L=2-5). It is found that the present ACE-b3k3 algorithm is the fast est among all algorithms in the literature in the floating-point-oprat ion (FLOP) count assessment when the degree of contraction is large. ( C) 1998 American Institute of Physics.