A concept of nonredundant sets of primitive gaussian basis functions is described, which proved highly efficient for rapid computing all sets of electron-repulsion integrals. Combination of the RT parallel algorithm with the nonredundant method demonstrated performance faster than the GAMESS program by a margin greater than fivefold even with a single processor calculation, making it ideal for large-scale SCF calculations. Further performance gains require accelerating calculations of initial auxiliary integrals. (C) 2003 Elsevier B.V. All rights reserved.