An Effective Algorithm of the Hartree–Fock Approach with the Storing of Two-Electron Integrals in the Resolution of Identity Approximation

The authors obtain the standard version of the restricted Hartree–Fock approach with the storing of two-electron integrals in the resolution of identity approximation or Cholesky expansion. The most labor-intensive stages of the algorithm are formulated as matrix-vector operations, allowing efficient use of modern linear algebra libraries. The algorithm is shown to have high performance and good parallelism. It is compared to a direct version, based on the repeated recalculation of two-electron integrals without storing them in the computer’s memory. It is shown that the developed algorithm is more efficient for calculations using large basis sets. With small basis sets, this algorithm is more efficient than the direct one for small and medium-sized molecules.