Within the HF method, Roothaan's equations allow to solve the problem in the AO basis. In this context, one needs to compute the O(N 4 orb ) two-electron integrals (µν|λσ) over the AO basis. anks to a large e ort in algorithmic development and implementation, these integrals can now be computed very fast on modern computers. However, with post-HF methods, the computation of the two-electron integrals is a potential bo leneck. Indeed, when computing matrix elements of the Hamiltonian in the basis of Slater determinants, ERIs over MOs are required. Using Eq. ( ), the cost of computing a single integral (pq|rs) scales as O(N 4 orb ). A naive computation of all integrals in the MO basis would cost O(N 8 orb ). Fortunately, computing all of them can be scaled down to O(N 5 orb ) by transforming the indices one by one. 78 is step is known as the four-index integral transformation. In addition to being very costly, this step is hard to parallelize in a distributed way, because it requires multiple collective communications. However, techniques such as density ing (also called the resolution of the identity), lowrank approximations, or the combination of both are now routinely employed to overcome the computational and storage bo lenecks.