where the values R Bondi,A are taken from Ref. 100 and differ from Bondi's original vdW radii 101 in that R Bondi,H is reduced from 1.2 Å to 1.1 Å. The use of eq. 23 is a standard cavity construction for PCM calculations. For a cavity consisting of a single sphere, however, we find that better agreement with the Born ion model is obtained using a switching function based on tanh(x) rather than erf(x). For a single sphere of radius R vdW , centered at R 0 , we take the permittivity function to be