The most diffuse exponent in the 6-31(9+,9+)G* ba-sis set is ζ ≈ 2.44 × 10 -6 a -2 0 , corresponding to a half width at half maximum of 533 Å. This means that much of the probability density for the aforementioned ultra-diffuse Boys orbital lies near the edges of the basis set, which may impair our ability to numerically integrate the functions in question even though we have used dense grids for these calculations as described in Section 3 .1. However, there is good consistency in (∆r) Boys and (∆σ) Boys up to n = 8 (Table ), which might be considered more reliable. Even for n = 8, the S 0 → S 3 excitation has significant contributions from amplitudes x ia with R ia (Boys) = 49 Å and σ ia (Boys) = 76 Å. In a proper expectation value, such long-distance chargeseparation would cancel in a coherent superposition of i → a excitations with different phases, but this does not occur in the κ 2 ia R ia and κ 2 ia σ ia terms that appear in the definitions of ∆r and ∆σ.