The reduced multiplication scheme of the Rys-Gauss quadrature for 1st order integral derivatives

Abstract

An implementation of the reduced multiplication scheme of the Rys-Gauss 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 the so-called intermediate products is also demonstrated to further reduce the floating point operation count. Two prescreening techniques based on the 2nd order density matrix in the basis of the uncontracted Gaussian functions is proposed and investigated in the paper. This investigation gives on hand that it is not necessary to employ the Cauchy-Schwarz inequality to achieve efficient prescreening. All the features mentioned above were demonstrated by their implementation into the gradient programalaska. The paper offers a theoretical and practical assessment 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 to symmetry, basis set quality, molecular size, and prescreening threshold.