Using B(α)LYP+D3, we observe a consistent trend towards larger interaction energies (i.e., larger values of |∆E|) as α increases. In Fig. , we have included data for functionals with α = 5 and α = 15 that were not considered above, in order to emphasize that this trend is quite systematic. In contrast to thermochemical properties, where there was often little variation in accuracy over the range 30 ≤ α ≤ 50, here there are systematic shifts in that range. An essentially linear shift in the mean value of |∆E|, as α increases, reflects delocalization of the ion's density into frontier molecular orbitals (MOs) of the neighboring water molecules, and the GGA functional BLYP+D3 underestimates |∆E| by about 3.4 kcal/mol. The B(20)LYP+D3 errors are not dissimilar from the B3LYP+D3 errors albeit shifted slightly so that the mean error is nearly zero. For α ≥ 30, the ion is increasingly overbound as α increases. For BH&H-LYP, the mean error is 4.2 kcal/mol (towards overbinding). In percentage terms, however, the mean BH&H-LYP+D3 error is < 10% because |∆E| is quite large. for second-row elements, which are considered in Section 3 .4 .1, whereas valence excitation energies are discussed in Section 3 .4 .2. In Section 3 .4 .3 we consider the absorption spectrum of the hydrated electron, e -(aq).