with a + cs c /a cs c creation/annihilation operator of an electron in the spin-orbital ψ c , with spatial part φ c and spin η c . Within all the CI methods, the molecular orbitals are partitioned in two main groups: (i) one set collecting the N i orbitals that are doubly occupied in all the configurations, called inactive orbitals, (ii) the second set collecting the N a orbitals which allow for an occupation number from 0 to 2, called active orbitals. Pointing out that the operator T ab can not connect two doubly occupied orbitals, the Hamiltonian in eq. ( ) can be re-written making explicit the non-null terms as: