THE REDUCED MULTIPLICATION SCHEME OF THE RYS-GAUSS QUADRATURE FOR 1ST-ORDER INTEGRAL DERIVATIVES

An implementation of the reduced multiplication scheme of the Rys-Gaus s quadrature to compute the gradients of electron repulsion integrals is discussed. The study demonstrates that the Rys-Gauss quadrature is very suitable for efficient utilization of simplifications as offered by the direct computation of symmetry adapted gradients and the use of the translational invariance of the integrals. The introduction of th e so-called intermediate products is also demonstrated to further redu ce the floating point operation count. Two prescreening techniques bas ed on the 2nd order density matrix in the basis of the uncontracted Ga ussian functions is proposed and investigated in the paper. This inves tigation gives on hand that it is not necessary to employ the Cauchy-S chwarz inequality to achieve efficient prescreening. All the features mentioned above were demonstrated by their implementation into the gra dient program ALASKA. The paper offers a theoretical and practical ass essment of the modified Rys-Gauss quadrature in comparison with other methods and implementations and a detailed analysis of the behavior of the method as suggested above as a function of changes with respect t o symmetry, basis set quality, molecular size, and prescreening thresh old.