Fig. 5. (drawn to scale) The oxygen (O) and two hydrogen (H) atoms of water are shown as circles with covalent radii, d(O) and d(H). The circles on the right represent ions with aqueous ionic radii, d(i), aq = kd(A). The length of the hydration bond, d(–O) is the distance between the center of O(water) and P(i/w) (shown as dotted lines in Figs. I–V): (I) Li+, cdots, three dots, centered, Cs+: k = 0.81 = phi/2, d(–O) = 0.64 (±) 0.03 Å. d(i), aq (in Å): 1.42 (Li+) < 1.65 (Ag+ circle with dashes) < 1.74 (Na+) < 2.16 (K+) < 2.26 (Rb+) < 2.49 (Cs+). (II) F−, cdots, three dots, centered, I−: k = 1.57 = 2/phi1/2, d(–O) = 1.60 (±) 0.04 Å. d(i), aq (in Å): 1.11 (F−) < 1.48 (Cl−) < 1.74 (Br−) < 2.08 (I−). The ‘hydrogen bond’ length d(–H) = d(–O) − d(OH) = 0.63 Å. (III): Ni+2, cdots, three dots, centered, Ba+2: k = 0.80 not, vert, similar phi/2 = 0.81, d(–O) = 1.06 (±) 0.08 Å. d(i), aq (in Å) (only some are shown to avoid overcrowding): 0.98 (Ni+2) < 1.19 (Hg+2) < 1.32 (Mg+2) < 2.06 (Ba+2). (IV): Al+3, cdots, three dots, centered, Eu+3: k = 0.47 = (2/phi3), d(–O) = 1.40 (±) 0.06 Å. d(i), aq (in Å) (only some are shown): 0.55 (Al+3) < 0.63 (Rh+3) < 0.81 (Tl+3) < 0.91 (Yb+3, dashed line) < 1.08 (Eu+3, dash and dot line). (V) Lu+3, cdots, three dots, centered, La+3: k = 0.62 = phi/2, d(–O) = 1.37 (±) 0.05 Å. d(i), aq in increasing order (in Å) (only some are shown): 0.97 (Lu+3) < 1.01 (Y+3, dashed line) < 1.13 (Sm+3) < 1.17 (La+3).
