Recently we developed a new algorithm for a fast and accurate numerical evaluation of three-centre nuclear attraction integrals over Slater-type functions, the results obtained were very satisfactory. Now, it is shown that this new algorithm can also be applied to hybrid and three-centre two-electron Coulomb integrals over Slater-type functions. These integrals, which are numerous, are very difficult to evaluate to a high accuracy, because of the presence of spherical Bessel functions and hypergeometric series in the integrands. We have proved that the integrands that occur in the analytic expressions of the integrals under consideration satisfy all the conditions to apply the S(d) over bar approach. The hypergeometric functions which occur in the semi-infinite integrals can be expressed as a finite expansion and the semi-infinite integrals involving the spherical Bessel functions can be transformed into semi-infinite integrals involving the simple sine function. The numerical results obtained with linear and non-linear systems illustrate clearly a further improvement of accuracy and a substantial reduction in calculation times. Comparisons with existing codes, STOP developed by Bouferguene et al (1996 Int. J. Quantum Chem. 57 80 1) and ADGGSTNGINT developed by Rico et al (1997 Comp. Phys. Commun. 105 216), are listed.
