Efficient and Accurate Approximations for Two-Electron Integrals

Our group also works on improving algorithms for computing two-electron integrals efficiently and accurately. Computing and processing two-electron integrals in Fock-matrix calculations is usually the most time-consuming step of Hartree-Fock (HF), DFT, and CASSCF calculations. The Coulomb (direct) and exchange part of the Fock matrix are well approximated with the resolution-of-the-identity approximation and semi-numerical chain-of-spheres (COSX) approach, respectively. In a recent project together with Prof. Frank Neese, Dr. Robert Izsak (Middlebury College), and Dr. Bernardo de Souza (FAccTs GmbH), we were able to make COSX calculations much faster by re-engineering the analytic electrostatic potential integrals. The errors of the numerical integration were also substantially reduced with newly developed grids where we have used machine learning. Our third generation COSX implementation allows us now to simulate UV/Vis spectra of large molecules using hybrid TDDFT and to compute binding energies of inter-molecular complexes using large basis sets of quadruple-zeta quality. Future work will be devoted to nuclear-displacement dependent properties like gradients and harmonic vibrational frequencies.