ere is, however, a computational downside to sCI methods. In conventional CI methods, the rule by which determinants are selected is known a priori, and therefore, one can map a particular determinant to some row or column indices. As a consequence, it can be systematically determined to which matrix element of Ĥ a two-electron integral contributes. is allows for the implementation of so-called integral-driven methods that work essentially by iterating over integrals. On the contrary, in (most) sCI methods, the determinants are selected a posteriori, and an explicit list has to be maintained as there is no immediate way to know whether or not a determinant has been selected. Consequently, we must rely on the so-called determinant-driven approach in which iterations are performed over determinants rather than integrals. is can be a lot more expensive, since the number of determinants N det is typically much larger than the number of integrals. e number of determinants scales as O(N orb !) while the number of integrals scales (formally) as O(N 4 orb ). What makes sCI calculations possible in practice is that sCI methods generate relatively compact wave functions, i.e. wave functions where N det is much smaller (by orders of magnitude) than the size of the FCI space. Furthermore, determinant-driven methods require an e ective way to compare determinants in order to extract the corresponding excitation operators, and a way to rapidly fetch the associated integrals involved, as described in Sec. III A.