Cations as Trikisoctahedra

The inner sphere of relatively small ions is generally accepted to have 4 or 6 dipoles in symmetrical tetrahedral or octahedral coordination, depending on the ion size and charge. In principle, these might respectively accommodate 4 and 8 other oriented intercalated dipoles as a second shell. In the tetrahedral case, the second dipole group would be at (180 - ( )0 from the first, where is the tetrahedral angle, i.e., at 70.53°. In the octahedral arrangement, the second set are 

If the ion-dipole center distance is 2.75 A and the overall packing corresponds to the closest approach distance for water (taken as 2.76 A), then the second set of dipoles are 15% further away than the first, whereas if it is 2.5 A, the second group are 31% further away. The concept of a tightly bound inner shell and a more loosely bound second shell offers a good explanation for the coordination number (c) and hydration number (n). 154,155 

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