Efficient computation of the product of orbitals in Daubechies wavelet bases

The computation of two-electron integrals, i.e., Coulomb integrals and exchange integrals is a major bottleneck in Hartree-Fock, density functional theory and post-Hartree-Fock methods. For large systems, one has to compute a huge number of two-electron integrals for these methods. This leads to very high computational costs. To break this complexity, we need efficient algorithms to handle these two-electron integrals. The representation of product of orbitals in wavelet bases provides an efficient treatment for two-electron integrals. We discuss the efficiency of the algorithm for the product of orbitals in Daubechies wavelet bases and then the computation of two-electron integrals. For this, we use the novel approach of Beylkin which is based on uncoupling the interaction between resolution levels. We provide a detailed procedure and analysis which lead to the further improvements of the algorithm to compute two-electron integrals more efficiently.