Determinant-based sCI algorithms generate wave functions expressed in a truncated space of determinants. Obviously, the selection presented in the previous section does not enforce that Ĥ commutes with Ŝ2 in the truncated space. Hence, the eigenstates of Ĥ are usually not eigenvectors of Ŝ2 , although the situation improves when the size of the internal space tends to be complete. A natural way to circumvent this problem is to work in the basis of con guration state functions (CSFs), but this representation makes the direct computation of the Hamiltonian less straightforward during the Davidson diagonalization.