[Big-Daddy]

In a small inorganic molecule of unknown structure, how do I work out which molecule to give a free radical? (We must assume structures need to be drawn without conjugated delocalization shown)
e.g. N always seems to have a free radical in structures with O, rather than the O itself.

e.g. What is the structure of ClO₂, and what is the bond angle? ClO₂^- and ClO₂⁺ are both easy - the first has Cl (less electronegative and therefore central) bonded by a single bond to one O atom, which has the negative charge, and by a double bond to another (2 lone pairs so the shape is bent/v-shaped), the second has Cl (we can assume it is the one with one less  outer electron, so it has 6, since the less electronegative atom is more likely to have the electron removed to form a positive ion, in terms of formal charge) simply double-bonded to 2 O atoms, with one lone pair. But ClO₂ has an odd number of electrons so we will not be able to prevent a free radical or complete the octet for each atom. Which atom must be incomplete (i.e. have a free radical and not be a complete set), and why? What about CO?

[Corribus]

There's no magic rule.  The best way is to draw a molecular orbital diagram and fill in the electrons according to Hund's rules.  This will usually give you an idea of what kind of oribital the long electron is in.  In most cases, it's going to be located in a bonding or antibonding orbital, which means its shared between more than one atom.  In NO, for instance, the lone electron is in an antibonding pi orbital, so in reality it's not localized on either N or O.  (Even then, realize that MO theory still makes assumptions; it is still an approximation and in strange situations, like radicals, it doesn't always give a prediction that makes sense.)

That said, in a formal charge or oxidation state formalism it is customary to assign electrons to specific atoms in a molecule as a means of bookkeeping.  Obviously where you put the lone electron is going to affect the formal charge or oxidation state of the atom it's put on.  In general when writing a Lewis structure and negative formal charge should be on a more electronegative element (and vice-versa), so look at the possible structures for the radical and place the lone electron appropriately.  A structure with formal charges of zero is most preferable.

For NO, for example, if the lone electron is on nitrogen, then formal charges of both oxygen and nitrogen are zero.  If the lone electron is on oxygen, the formal charge on oxygen is +1 and the formal charge on nitrogen is -1.  Not only is this incorrect because nitrogen is the less electronegative element, and therefore should have the most positive formal charge, but also becauase you have a negative formal charge right next to a positive formal charge.  Therefore having the electron on nitrogen is the appropriate answer.  (And this is predicted by the MO diagram as well - the antibonding pi orbital has more nitrogen character than oxygen character.)

For ClO₂, I think it's pretty obvious that the best place to put the lone electron (in a Lewis structure) is on the chlorine.  For one thing, doing so means that fewer atoms disobey the octet rule and all formal charges are zero.  Additionally, if the lone electron is placed on the oxygen, then we have the same situation with NO (positive formal charge next to a negative one).

That said, it's been postulated that ClO₂ features a 2-center-3-electron bond so again with these things there are no hard and fast rules.  Lewis structures and such are formulated for simple molecules.  When you start getting into free radicals and such, it doesn't always make sense to use them.

[opsomath]

In reality, many radicals have the unpaired electron in a delocalized orbital which is spread out over several atoms. ClO2 is one of these. As the Wiki says, there's no way to draw a single perfectly satisfactory Lewis structure for this thing.

You can draw a hypervalent structure with two double bonds to oxygen, one lone pair, and one unpaired electron on Cl. This is probably the best one. However, you can also take one of the bonds to oxygen and split it up so that the Cl gets two lone pairs, the oxygen is single bonded, and it has one unpaired electron. Obviously, if you can do this to one of the oxygens you can do it to the other, so the oxygens will be equivalent.

Calculations and electron paramagnetic resonance studies show that somewhere between 50-70% of the spin density (meaning the unpaired electron density) is present on that center chlorine. The rest must be on the oxygens. This confirms our idea that the one with the radical on chlorine is the best one. Source: http://pubs.acs.org/doi/pdf/10.1021/j100109a017

Why would this be? Well, if you don't have anything else to go on, I would use your rules-for-basicity to determine where to put the radical, since it is electron deficient. Put it on the atom that would make the weakest base. In other words, put it on the most polarizable and least electronegative atom you can find. In this case, that is chlorine by both criteria. If you have to choose, polarizability trumps electronegativity.

[Big-Daddy]

Thank you!

The two main rules, as far as Lewis structures are concerned, that I have gleaned from this are:

1) Ensure that, in a molecule with several different elements, a less electronegative one never bears a more negative formal charge than a more electronegative one (unless this is inevitable given that this is the only possible Lewis structure with that molecular formula, etc., in which case I suppose it would probably not exist).
2) Generally, unless superceded by the rule above, I can expect to place the lone electron on the less electronegative atom. That is why N must tolerate having the lone electron.

So in the structure of NS, knowing that N has a higher electronegativity than S, we will place the lone electron on S. So N will have its standard 5 outer electrons - let's put 3 into a triple bond, and once S matches this, S will have 3 outer non-bonding electrons, including the lone electron, left. Formal charges are all 0 which is fine. Is this the structure as I should have deduced it?

[Corribus]

I would say the most important factor is minimizing the number of atoms with nonzero formal charges.  If an atom MUST have a formal charge, negative formal charges preferably go on more electronegative atoms.  And if you have a formal positive charge right next to a formal negative charge, you've probably done something wrong.

[Big-Daddy]

I would say the most important factor is minimizing the number of atoms with nonzero formal charges.  If an atom MUST have a formal charge, negative formal charges preferably go on more electronegative atoms.  And if you have a formal positive charge right next to a formal negative charge, you've probably done something wrong.

Thanks. Is my structure for NS (see last post) the one I could reasonably be expected to come up with, without considering MO theory etc.?