More importantly, we believe that the metrics used to characterize excited states should be robust and stable in any basis set, so that the user need not worry that the wrong basis set might afford nonsensical results. Orbitalinvariant metrics might be used to verify that amplitudes discarded in a low-cost, localized-orbital implementation of TD-DFT make negligible contributions to the tran- for the problematic Rydberg excitation. For n > 2 sets of diffuse functions, there is absolutely no change in either (∆r) NTO = 1.71 Å or (∆σ) NTO = 0.98 Å. The NTO basis also affords stable results for the S 0 → S 1 transition and for the Λ metric, as documented in Table . This stability originates in the fact that both transitions are dominated by a single pair of principal NTOs, with λ 2 1 ≥ 0.99 for S 0 → S 1 and λ 2 1 ≥ 0.94 for S 0 → S 3 , even when the basis set contains numerous diffuse shells. If λ 1 ≈ 1 then ∆ρ elec (r) and ∆ρ hole (r) in eq. 23 can be approximated using just a single term involving ψ elec 1 (r) or ψ hole 1 (r). Expressions for (∆r) NTO and (∆σ) NTO reduce to a single term under these conditions, and use of the NTO representation approximates an expectation value that is stable with respect to additional diffuse shells.