Simplifications in the Generation and Transformation of Two-Electron Integrals in Molecular Calculations

Approximate numerical linear dependence among the columns of the two-electron integral matrix and the positiveness of the Coulomb operator are exploited in order to reduce the number of integrals that need to be calculated when a numerical accuracy is given by the machine in use or by the choice of the investigator. Numerical results presented indicate that the method leads to an algorithm for carrying out the two-electron integral four-index transformation which in practice can be achieved in a small fraction (similar to 1/5-1/3)) of the time required to generate the integrals by one of the fastest available Gaussian integral programs, Almlof's MOLECULE. This effectively removes one of the major bottlenecks of computational quantum chemistry.