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Hi O Silver

Roald Hoffmann

Those Charges are Real, Aren't They?

Iron is not only ferrous or ferric, but also comes in oxidation states ranging from +6 (in BaFeO4) to –2 (in Fe(CO)42–, a good organometallic reagent).

Is there really a charge of +6 on the iron in the first compound and a –2 charge in the carbonylate? Of course not, as Linus Pauling told us in one of his many correct (among some incorrect) intuitions. Such large charge separation in a molecule is unnatural. Those iron ions aren't bare—the metal center is surrounded by more or less tightly bound "ligands" of other simple ions (Cl for instance) or molecular groupings (CN, H2O, PH3, CO). The surrounding ligands act as sources or sinks of electrons, partly neutralizing the formal charge of the central metal atom. At the end, the net charge on a metal ion, regardless of its oxidation state, rarely lies outside the limits of +1 to –1.

Actually, my question should have been countered critically by another: How do you define the charge on an atom? A problem indeed. A Socratic dialogue on the concept would bring us to the unreality of dividing up electrons so they are all assigned to atoms and not partly to bonds. A kind of tortured pushing of quantum mechanical, delocalized reality into a classical, localized, electrostatic frame. In the course of that discussion it would become clear that the idea of a charge on an atom is a theoretical one, that it necessitates definition of regions of space and algorithms for divvying up electron density. And that discussion would devolve, no doubt acrimoniously, into a fight over the merits of uniquely defined but arbitrary protocols for assigning that density. People in the trade will recognize that I'm talking about "Mulliken population analysis" or "natural bond analysis" or Richard Bader's beautifully worked out scheme for dividing up space in a molecule.

What about experiment? Is there an observable that might gauge a charge on an atom? I think photoelectron spectroscopies (ESCA or Auger) come the closest. Here one measures the energy necessary to promote an inner-core electron to a higher level or to ionize it. Atoms in different oxidation states do tend to group themselves at certain energies. But the theoretical framework that relates these spectra to charges depends on the same assumptions that bedevil the definition of a charge on an atom.

An oxidation state bears little relation to the actual charge on the atom (except in the interior of the sun, where ligands are gone, there is plenty of energy, and you can have iron in oxidation states up to +26). This doesn't stop the occasional theoretician today from making a heap of a story when the copper in a formal Cu(III) complex comes out of a calculation bearing a charge of, say, +0.51.

Nor does it stop oxidation states from being just plain useful. Many chemical reactions involve electron transfer, with an attendant complex of changes in chemical, physical and biological properties. Oxidation state, a formalism and not a representation of the actual electron density at a metal center, is a wonderful way to "bookkeep" electrons in the course of a reaction. Even if that electron, whether added or removed, spends a good part of its time on the ligands.

But enough theory, or, as some of my colleagues would sigh, anthropomorphic platitudes. Let's look at some beautiful chemistry of extreme oxidation states.

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