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Three professors argue it is non-polar.

My professor argues that it is a monopole, like most ions.

The structure of the triiodide ion places a negative formal charge on the central iodine atom. The molecular geometry is also linear (at least according to VSEPR), and its electronic geometry is trigonal bipyramidal. Given the high amount of symmetry, shouldn't triiodide be non-polar? Sure, it might have a charged central atom, but so does carbon dioxide.

What's the answer?

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    $\begingroup$ $D_{\infty\mathrm{h}}$ molecules like the triiodide ion cannot be polar. Polarity in the context of chemistry would mean having a dipole moment so imo the monopole is irrelevant $\endgroup$ – orthocresol Dec 9 '15 at 22:49
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    $\begingroup$ @orthocresol You should know better than to describe polarity only with dipole of molecule. $\endgroup$ – Mithoron Dec 9 '15 at 22:55
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    $\begingroup$ @Mithoron this is going into semantics already - if you consider triiodide polar because each individual I-I bond is polar, then you must also consider CO2, BF3 and CCl4 to be polar. In all cases there is a partial positive charge on the central atom. $\endgroup$ – orthocresol Dec 9 '15 at 22:59
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    $\begingroup$ Yes, polarity isn't well defined and I'm not even sure if it makes sense to ask about polarity of anion. $\endgroup$ – Mithoron Dec 9 '15 at 23:08
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    $\begingroup$ goldbook.iupac.org/P04710.html - IUPAC definition says nothing about any dipoles, and it's rather macroscopic property not microscopic, seems "polar" was simply convenient adjective for describing molecules, but isn't necessarily proper for it. $\endgroup$ – Mithoron Dec 10 '15 at 21:44
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The structure of the triiodide ion places a negative formal charge on the central iodine atom.

No it doesn’t. The two resonance structures that describe the four-electron three-centre bond put the negative formal charge on the outer iodines ($\ce{1/2-}$ each).

That said, polarity is usually defined as having a non-zero dipole moment. The dipole moment’s vector must display the same symmetry as the entire molecule. Since the molecule is linear and both $\ce{I\bond{...}I}$ distances are equal, its point group is $D_{\infty \mathrm{h}}$ which includes $i$ which means the overall dipole moment must be zero.

The charge it carries does not matter. Any single-atom ion also has zero dipole moment and would thus be called non-polar. ‘Non-polar’ does not mean ‘free of electrostatic interaction’.

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    $\begingroup$ Can you include the resonance structures you are talking about? I have a hard time seeing the formal charge being on the terminal iodine. $\endgroup$ – Martin - マーチン Dec 11 '15 at 4:13
  • $\begingroup$ @Martin-マーチン I can’t draw it atm, but it is: $\ce{I-I}~\ce{I-}$ $\endgroup$ – Jan Dec 18 '15 at 22:54
  • $\begingroup$ I see. I did not think about this. So the resonance you are talking about would be $$\ce{I-I\bond{<-}I- <=> {}^{-}I\bond{->}I-I}?$$ But I think we shall not forget about other resonance structures, too. $$\ce{{}^{-}I\bond{->}\overset{+}{I}\bond{<-}I- <=> I-{I- }-I}$$ $\endgroup$ – Martin - マーチン Dec 22 '15 at 4:25
  • $\begingroup$ @Martin-マーチン And I disagree with the last one because it creates a dectet on the central iodione. $\endgroup$ – Jan Dec 23 '15 at 0:51
  • $\begingroup$ You realize that all those resonance contributors violate the octet rule, at least when you want to describe their bonding as covalent. $\endgroup$ – Martin - マーチン Dec 24 '15 at 6:15
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If you accept the Atkins Physical Chemistry definition of polar:

A polar molecule has a permanent electric dipole moment arising from the partial charges on its atoms

Then the answer turns upon whether triiodide is actually linear.

Isolated Triiodide and Pentaiodide Anions in the Crystal Structure of [Rb(Dibenzopyridino-18-Crown-6)2]2(I3)(I5) Zeitschrift für anorganische und allgemeine Chemie Volume 634, pages 1247–1248, says it is bent with an angle of 174.8 degrees.

Theoretical Study of the Solvent Effect on Triiodide Ion in Solutions J. Phys. Chem. A 1998, 102, 2065-2071, says that triiodide is linear in the gas phase, but "The free-energy surface of the same ion in aqueous solution is distinctly different and indicates a drastically enhanced probability for structures with lower symmetry."

So in the gas phase it would be non-polar by the Atkins definition of polar, while in other situations it can be slightly bent and therefore slightly polar.

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    $\begingroup$ According to the IUPAC: A molecule is an electrically neutral entity, which would exclude the $\ce{I3-}$, even in Atkin's definition. I made the same mistake though. For the rest of your statements I am happy to give you a thumbs up. $\endgroup$ – Martin - マーチン Dec 22 '15 at 4:08
  • $\begingroup$ @Martin-マーチン I wouldn't say Atkins is limiting the word "polar" to molecules. Instead, he is only defining the term "polar molecular" rather than "polar". The journal Inorganic Chemistry seems to think it's ok to refer to polar ions, "The Polar [WO2F4]2- Anion in the Solid State", chemgroups.northwestern.edu/poeppelmeier/pubs/HT/… . $\endgroup$ – DavePhD Dec 31 '15 at 12:10
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I would argue it is a polar molecular ion. In the comments to this question there has been already pointed out that the term "polarity" is quite ill-defined.
Many chemists understand that if a molecule has a vanishing dipole moment, the molecule itself is non-polar; at least this is true since molecules are neutral by definition. If you actually can extend that definition to charged species is open for debate. I personally dislike this definition - molecule or not.

In this framework carbon dioxide is non-polar, but it reacts with polar substrates, like Grignard agents. The reason for this is its quadrupole moment.
A much more general definition of the term polarity hence should include any molecule that has a multipole of any kind. We can then even include ions.

A polar molecular entity is a molecule that possesses a multipole.

Since the triiodide anion has a non-zero quadrupole moment, I would consider it polar. This point has been and will always be open for debate.

A quick DF-BP86/def2-SVP calculation determines the natural atomic charges as $q(\ce{I_{\mu}})=-0.11$ (the atom in the middle) and $q(\ce{I_{term}})=-0.44$ (the terminal two; deviations from $1.00$ due to rounding). The same calculation finds:

 Traceless Quadrupole moment (field-independent basis, Debye-Ang):
   XX=             10.9525   YY=             10.9525   ZZ=            -21.9050
   XY=              0.0000   XZ=              0.0000   YZ=              0.0000

‡: It is not a molecule, since it is not neutral, which is a prerequisite from the IUPAC goldbook definition.

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  • $\begingroup$ ♦ - just to make sure, your calculations show that the central iodide ion has a -0.11 charge, correct? $\endgroup$ – Dissenter Dec 18 '15 at 11:35
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    $\begingroup$ @Martin if you define "polar" as having any multipole, you have to consider H-H, N-N, and every molecule as polar. "It is true, that for H2, N2 etc., wave mechanics, too, gives at least quadrupoles." Fritz London pubs.rsc.org/en/content/articlepdf/1937/tf/tf937330008b $\endgroup$ – DavePhD Dec 18 '15 at 13:04
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    $\begingroup$ @DavePhD I would not dismiss that thought. But what does that add to the specification of the molecule any way. $\endgroup$ – Martin - マーチン Dec 18 '15 at 13:09
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    $\begingroup$ @Martin-マーチン Well, if you define polar as having a permanent electric dipole moment, it specifies some subset of molecules. On another note, is triiodide really linear? "Isolated Triiodide and Pentaiodide Anions..." is saying bent 174.8 degrees onlinelibrary.wiley.com/doi/10.1002/zaac.200800115/abstract $\endgroup$ – DavePhD Dec 18 '15 at 13:20
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    $\begingroup$ @DavePhD All I am trying to say is that looking at the dipole moment for clarification is not enough. And I am saying that that classification does not add anything to the discussion anyway. It's too simple. Also, we might not want to have this discussion in the comment section. Maybe chat, but I am on the road tonight.... $\endgroup$ – Martin - マーチン Dec 18 '15 at 13:30

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