Given a n -electron wave function Ψ Ψ , one wants to compute the second moment cumulant of it. A cumulant is a linear combination of moments so we have: Λ Λ = ⟨ Ψ Ψ | S a b | Ψ Ψ ⟩ c = ⟨ Ψ Ψ | S a b | Ψ Ψ ⟩ − − ⟨ Ψ Ψ | a ^ ^ | Ψ Ψ ⟩ ⟨ Ψ Ψ | b ^ ^ | Ψ Ψ ⟩