Let us begin by considering a molecule with N electrons in its neutral state. The Hamiltonian operator governing this molecular is denoted as Ĥ : L 2 R 3N -→ L 2 R 3N , that we assume to be self-adjoint. The ground state energy, represented by the smallest eigenvalue of Ĥ, is denoted as ε 0 ∈ R. The degeneracy of the ground state is denoted as K, and let the wave functions ψ 1 , . . . , ψ K ∈ L 2 R 3N collectively form an orthonormal basis for the lowest energy eigenspace of Ĥ. We define the eigendensity, denoted as ρ ε 0 ∈ L 1 R 3 , for this eigenspace as the following integral: