e determinants are built using the following order: i) spin-up (↑) spinorbitals are placed before spin-down (↓) spinorbitals, as in the Waller-Hartree double determinant representation 104 Ô |I = Î| = Î↑ Î↓ | , and ii) within each operator Î↑ and Î↓ , the creation operators are sorted by increasing indices. For instance, let us consider the determinant