Here, ψ r |r 2 |ψ r is the second moment of orbital ψ r , so σ ia is a measure of the disparity between the size of the excited electron and the size of the hole, for the excitation ψ i → ψ a . Again, these size measures are summed incoherently rather than constructing a transition density for the excited state in question. As such, the quantities ∆σ and Γ also fail to preserve orbital invariance. Nevertheless, Γ has been used to define a critical threshold or "trust radius" for TD-DFT excitation energies, which is similar to the manner in which Λ has been used but with an ostensibly more direct physical interpretation, since Γ has units of length. It was observed in Ref. 11 that Γ has a different numerical value in the CMO basis as compared to the basis of natural transition orbitals (NTOs), although no explanation was provided. (See Appendix B for a brief overview of NTOs and Ref. 2 for more complete discussion.) Furthermore, ∆r was seen to be sensitive to the presence of diffuse basis functions. The present work provides a physical and mathematical explanation for these observations.