hence R in eq. 6 represents an index running over all the occupied spin-orbitals. The fermionic prefactor is Γ D i AI = (-1) n , where n is the number of occupied spin-orbitals between A and I in determinant |D i . Note also, that the indices for the single and double excitations have to be pairwise different (I = J, A = B, {I, J} ∩ {A, B} = ∅). We will write uppercase I for spin-orbitals, lowercase i for spatial orbitals, and i σ for the i-th spatial orbital with spin σ.