Lack of orbital invariance in metrics such as Λ, ∆r, ∆σ, and Γ is problematic in applications, as shown by examples that are discussed in Section 4. As such, we propose alternative means to measure charge displacement that are based on proper expectation values and thus invariant to unitary transformations of the MOs. Some of these were introduced previously by Plasser, Dreuw, and co-workers, and can be defined also for correlated wave function models. Density matrices for the excited electron and the hole (eq. A3), constructed from the amplitudes x and y, are introduced in Appendix A. In position space, these density matrices correspond to the (unrelaxed) difference densities ∆ρ elec (r) and ∆ρ hole (r) that together afford the difference density with respect to the ground state: ∆ρ(r) = ∆ρ elec (r) + ∆ρ hole (r) .