Fortunately, invariant metrics such as d e-h (mean electron-hole separation), d exc (RMS exciton size), and d CD1 (charge displacement) are no more complicated or expensive to evaluate as compared to non-invariant metrics such as ∆r, ∆σ, and Γ. The invariant metrics never lose their physical interpretability. For that reason, they should be used exclusively when characterizing excitedstate wave functions and transition densities. y = 0 as in the TDA (see below). The values λ 2 i are also connected to the natural occupation numbers of the excited-state density matrix. NTOs for the excited electron (ψ elec i ) are defined by a unitary transformation U v of the virtual MOs that diagonalizes the positive semidefinite matrix ∆P elec . The values λ 2 1 ≥ λ 2 2 ≥ λ 2 3 ≥ • • • in eq. B1 are precisely the nonzero eigenvalues of ∆P elec , so the transformation of the virtual space can be expressed as 78