a more robust procedure in the present context is the "global density-dependent" (GDD) or "ω GDD " procedure . This approach, which adjusts ω based on the size of the exchange hole, mitigates the strong dependence on system size that is observed when using IE tuning , and which might otherwise be a problem when studying water clusters of varying size . For water, we use ω = 0.277 a -1 0 , which represents an average over several cluster geometries. For the ions, we tune ω individually at the optimized gas-phase geometry of each, resulting in a range of values from ω = 0.248 a -1 0 for iodide and ω = 0.261 a -1 0 for bromide, where the tails of the anion's density are most diffuse, up to ω = 0.398 a -1 0 for cyanate and ω = 0.405 a -1 0 for cyanide, where the density is most compact. (Recall that LRC functionals switch from semilocal to HF exchange on a length scale of ∼ 1/ω.)