Dodecahedral Metal Coordination: Are There Two Distances to Coordinating Atoms?

[osskall]

Is it true that there should be two distances from a dodecahedrally coordinated cation to the two types of coordinating atoms?
When I calculate what the octahedron should look like assuming that all anion-anion distances are equal I will get two different cation-anion distances:
if all anion-anion distances equal 2R, the cation-anion distances will be 3.5R for four of the anions and only 1.8R (!) for the other four anions.

Does this make sense?
Or am I wrong in assuming that all the anion-anion distances should be equal?

What holds for capped trigonal prisms? There probably there will be a larger cation-anion distance for the capping anions, right? (Otherwise the anions would come too close! Or?)

 

[osskall]

What holds for capped trigonal prisms? There probably there will be a larger cation-anion distance for the capping anions, right? (Otherwise the anions would come too close! Or?)

OK, I just calculated for a triply capped trigonal prism that there is just one radius ratio: 0.73

For a dodecahedron I calculate 0.83 as the minimum radius ratio (for cation-anion interactions) but this leaves four out of eight coordinating atoms at almost twice the distance (as described above)...

 

[Blueshift5]

Yes, it is true that in a dodecahedral metal coordination, there should be two different distances from the cation to the coordinating atoms. This is because the dodecahedral structure has two different types of coordinating atoms, with different bonding strengths and distances from the cation.

In terms of the anion-anion distances, it is not necessarily true that they should all be equal. The exact distances will depend on the specific metal and anion being coordinated, as well as the bonding strengths between them. However, in general, the distances from the cation to the coordinating anions will vary, as seen in the example given.

For capped trigonal prisms, there will likely be a larger cation-anion distance for the capping anions, as they are not directly bonded to the cation and therefore have a weaker bonding interaction. This helps to prevent the anions from coming too close to each other, which could lead to repulsive forces in the structure. Again, the exact distances will depend on the specific metal and anion involved.