Thus, while Λ has proven to be successful as a diagnostic for TD-DFT errors, its numerical value does not provide much physical insight. Moreover, this metric may fail to detect problems when the excited state involves excitation from a relatively compact occupied MO into a much more delocalized virtual MO, since these two orbitals may share significant spatial proximity (in the sense of O ia ) yet the delocalized nature of the final state might still engender an erroneously low TD-DFT excitation energy. One relevant class of examples is that large density rearrangements upon excitation of certain PAH molecules can lead to anomalously low TD-DFT excitation energies, especially in larger aromatic systems. This problem can be rectified through the use of asymptotically-correct LRC functionals, yet such states do not exhibit what might be understood as CT in intuitive chemical or functional-group terms, and values of Λ do not portend any problems in such cases. Other metrics that were introduced in Section 5.3 may do better job of providing physical insight, as they connect more directly on the physical separation between electron and hole. A straightforward measure is d - e-h [Eq. (5.13)], which is the distance between the centroids of ∆ρ elec (r) and hole density ∆ρ hole (r). As discussed in Section 5.3, the quantity d - e-h has sometimes been called simply a "CT metric", and denoted D CT or d CT , but this obscures its readily-interpretable physical origin. That d - e-h is simply the electron-hole separation is evident both from the nomenclature and from the definition, either Eq. (5.13) or (5.21). On the other hand, d - e-h measures center-to-center electron-hole distance but takes no account of the size of the distributions ∆ρ elec (r) and ∆ρ hole (r). That information is included in the charge-displacement distance, d CD [Eq. (5.22)], which reduces d - e-h by the average size of electron and hole as measured by their second moments.