Density fitting scheme for pseudo-potentials
Sambasiva Rao Chinnamsetty, Wolfgang Hackbusch,and Heinz-Jürgen Flad
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Submission date: 08. Oct. 2008
Keywords and phrases: Hartree-Fock method, Density functional theory, Gaussian-type orbital, Optimal tensor product approximation
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We present density fitting scheme for pseudo-potentials in electronic structure calculations. 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., . 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.