The Fock matrix is formed by contracting the ERIs with the density matrix. At the Hartree-Fock and hybrid DFT levels of theory, the two-electron part of the Fock matrix consists of two contributions with different contracting patterns namely the Coulomb and the exchange contributions, which are denoted as J and K, respectively. To reduce the computational cost of the Fock matrix formation, which formally scales as O(N 4 ) with N being the number of basis functions, it is essential to make use of efficient screening of integrals based on the Schwarz upper bound 43