Mathematik in den Naturwissenschaften Leipzig Density fitting scheme for pseudo - potentials

The computational complexity of ab initio electronic structure methods can be decreased through the so-called density fitting scheme. The density fitting scheme is also known as resolution of identity (RI). Density fitting schemes became a popular approach to approximate the four-centre two-electron integrals which appear in the computation of the Fock matrix in the Hartree-Fock (HF) method. In the HF method, the computational effort to compute the Fock matrix scales with the fourth power of the number of basis functions, i.e., N4 BF . Therefore, we need to compute a huge number of integrals for large molecules. This cost can be reduced by using density fitting schemes. In recent years, density fitting schemes became a popular approach not only in the HF method, but also in almost all post-HF methods, where the computation of the two-electron integrals provides a major bottleneck. Traditionally quantum chemists consider the tensor product approximation in terms of Gaussians. We propose a new look at the subject of density fitting from the point of view of optimal tensor product approximation to handle the two-electron integrals more efficiently. In order to improve the approximation quality near the nuclei, we apply the density fitting scheme for pseudo-potentials. Using pseudo-potentials not only improves the quality of approximation in the immediate neighbourhoods of the nuclei but also reduces the computational costs. This article is dedicated to Prof. Dr. Dr. h.c. Wolfgang Hackbusch in honour of his sixtieth birthday. 1 Density fitting schemes in electronic structure calculations Gaussian-type orbital (GTO) basis functions are the most popular choice to deal with oneand two-electron integrals that appear in HF and post-HF methods, where the computation of the two-electron integrals (μν|σλ) = ∫