Although d - e-h and d CD provide the most direct physical interpretation of the CT character, several alternatives have been proposed in the spirit of the Λ metric, as attempts to find a diagnostic that is also physically meaningful. One of these is a charge-separation metric ∆r, defined as ∆r = ia κ 2 ia R ia jb κ 2 jb (6.5) where R ia = ψ i |r|ψ i -ψ a |r|ψ a (6.6) is the relative position vector of the centroids of orbitals ψ i (r) and ψ a (r). The quantity ∆r measures the change in the orbital centroids upon ψ i → ψ a excitation, weighted by κ 2 ia . Although the definition in Eq. (6.5) seems like an intuitive way to measure charge separation, the utility of ∆r as a separate metric is questionable. Within the TDA, this quantity is precisely equal to the electronhole separation d - e-h defined in eq. (5.13), whereas for full TD-DFT the definition of ∆r employs the same curious choice of normalization that was used to define Λ, namely, use of κ 2 ia in the denominator of Eq. (6.5). Perhaps more damningly, ∆r is not orbitally invariant so that its numerical value depends upon the choice of MOs that are used in Eq. (6.6). It has been suggested to evaluate ∆r in NTO basis, as this seems to afford good correlation between ∆r and D CT , but the need to make such a choice is a bothersome manifestation of having broken orbital invariance. Moreover, for a different data set of intramolecular CT energies, reasonable correlations are found between ∆r regardless of whether canonical MOs or NTOs are used, but those values also correlate well with d exc . The latter quantity, along with expectation values such as r elec and r hole , and also d - e-h that is defined from them, are invariant to unitary transformations of MOs. Quantities such as d - e-h , d exc , and d CD are thus fundamental properties of the exciton, independent of its representation, and should therefore be preferred as measures of its properties.