Ab initio calculations on large molecules: The multiplicative integral approximation

Abstract In the multiplicative integral approximation (MIA), two‐electron integrals are evaluated using an expansion of a product of two Gaussians in terms of auxiliary functions. An estimator of the error introduced by the approximation is incorporated in the self‐consistent field (SCF) calculations and the integrals for which the error estimate is larger than a preset value are systematically corrected. In this way the results of a MIA‐assisted calculation have the same accuracy as a conventional calculation. The full exploitation of the expansion technique while constructing the Fock‐matrix allows important time savings. Results are presented for a number of test cases.