[Rutherford]

Is it possible to deduct the structure of the polyiodide ions below just from their formulas? I think not, but I need a second opinion and a possible explanation. For example, why is octaiodide ion z-shaped?

[mkurek]

well this is mostly speculation but I would say

I^(-1) - obviously a lone molecule
I^(-2) - just draw the lewis structure, its a straight line because its electrons distribute evenly
I^(-3) - straight again
I^(-5) - draw it out, it'll have a couple extra pairs of electrons, much like a water molecule, giving it a bent shape

and the rest got me beat

[Rutherford]

I am interested in the higher ones.

[AWK]

some examples from literature

[Big-Daddy]

I think it can be explained. So far I have looked through all and the only thing I cannot explain is the 45 degree angle on the third I from right in I₉^-. I can't treat this in my method so I'm going to consider that to be a 90 degree caused by 2 lone pairs.

If you think of the I₃^- chain, the middle I has negative formal charge. It has 3 lone pairs so the shape it keeps it pretty much linear. If we want the chain to have another I, we would then have two I atoms with negative formal charge. If we want a 5-I chain, this will incur -3 negative formal charge in total, and so on.

Then we have bridges. So here the angle changes by 90 degrees because there are 2 lone pairs, or 45 degrees because there is 1 lone pair. So we deduce that I atoms which link 2 chains (chains described above as linear) are +1 and those linking 3 chains are +2 etc.

Given this and the coefficients on the species, we can write the following general statements:

(Symbolism: v[I] is the coefficient of I in the species; v[C,x] is the number of chains of length x I atoms in the species; v[B,y] is the number of bridging I atoms which connect y chains; z is the valency of the species)
v[I] = 3*v[C,3]+4*v[C,4]-v[B,2]-2*v[B,3]-3*v[B,4]
z=-v[C,3]-2*v[C,4]+v[B,2]+2*v[B,3]+3*v[B,4]

Now obviously this is not a perfectly determined system, but you can use it to make good headway towards the solutions, particularly keeping in mind that for Lewis structures it is better to have less formal charges, so the v[C,4] and v[B,4] will be minimized as much as possible in favour of v[C,3] and v[B,2] or v[B,3] respectively.

[Rutherford]

Why isn't the triodide fragment connected through its central iodine atom with other fragments?

[Big-Daddy]

Because that is not conducive to the negative formal charges you are looking for. Take I₅^- for instance. If the branch came off from the central I atom then that atom would have +2 formal charge (as it would have 3 bonds) and there would be one atom with a negative -1 formal charge, so we'd have I₅⁺. The reason such a species doesn't exist is probably that the +2 formal charge on one atom is unfavourable for such a small species.

[Rutherford]

I see it this way: The triodide ion is produced when a dative bond is formed between I^- and I-I. The iodide ion is the donor and a iodine atom from the molecule is the acceptor, so the iodide loses the negative charge which is passed a iodine atom (which is central): I I^- - I. This central atom isn't positive, but negative. This works for I₈^2- but not for I₅^-. Why  ?

[Big-Daddy]

I see. That's an interesting idea. We can deduce that such a mechanism is not all there is to it, from the fact that as you say it gives the wrong structures. It is a little bit odd that the bridging (previously neutral) I atom should act as a ligand rather than the I atom with a negative formal charge. But I'm sure the answer still resides in the pattern I found before being correct, even if I can't explain much of that pattern in terms of stability.

It's similar to nitrogen - why is it that whenever N has 2 bonds we tend to allocate it 2 lone pairs and call it negative? Barely ever does it have 2 bonds yet be positive, and whenever it does, the resonance forms in question are always less stable than others. I find this, with I, a similar case, as explained in Reply #4.

[Rutherford]

Okay, if it is a four-electron-three-center bond, your pattern can apply. I₉^- I still don't understand,  how I₂ coordinates with I₂.