The utility of oxidation states

Chemistry students discover soon enough the difficulties of building a description of chemistry from quantum-mechanical first principles. We learn that there is no unique quantum theory of chemical bonding: instead, one must grapple with the relative merits of the molecular-orbital and valence-bond approaches.  

The arguments that raged over which system was best were never really resolved but merely ended when the key protagonists (Linus Pauling and Robert Mulliken) died. Pauling’s clear advocacy helped to ensure that molecular-orbital theory emerged as the most popular and useful description, even if it is not always the most intuitive. 

In June 2008, Hannes Raebiger and colleagues at the National Renewable Energy Laboratory in Colorado, US, described ab initio quantum calculations of oxidation states of transition metals in various solid-state materials.¹ Their aim was to investigate what, if anything, the concept of oxidation state means at the quantum level.

Obviously, oxidation state is a convenient fiction so far as absolute numbers are concerned: no one claims that it reflects the true charge on the atoms concerned. This is clearly the case for predominantly covalent compounds such as SF₆ and SO₂, where the sulfur atoms have formal oxidation states (+6 and +4) that bear no relation to their charge.

Yet the concept of oxidation state is far from meaningless. Atoms ascribed different oxidation states can display markedly different properties - witness the colour changes of transition metals, such as pink Mn(ii), black-brown Mn(iv) and purple Mn(vii). Different oxidation states also exhibit differences in coordination geometry, effective radii and x-ray spectra. And from a heuristic point of view, oxidation states are invaluable for creating balanced chemical equations. Even if they don’t describe charge states, they do seem to refer to something real. 

A heretical conclusion 

Raebiger and colleagues calculated how the charge changes on transition metals located in host crystals as the materials are doped with electrons. They considered hosts that were predominantly ionic (MgO), predominantly covalent (GaAs), and intermediate (Cu₂O). The expectation might be that the transition metals (Co, Fe, Mn, Cr), having relatively labile oxidation states, would ‘soak up’ the extra charge and thereby alter their own local charge, reflecting the way that their formal oxidation state must be considered to alter. But the results showed quite the contrary: the actual charge on the transition-metal atoms barely changed at all. The researchers found a kind of homeostatic feedback mechanism that maintains the charge at a constant value. As an electron is added, the nature of the bonding between the transition metal and the surrounding ligands shifts in such a way as to displace the extra negative charge away from the metal and spread it out elsewhere. An accompanying commentary to the paper² by Raffaele Resta of the University of Trieste, Italy, stated that this implies a ‘heretical conclusion - those variable charge states are a myth.’ 

To Martin Jansen and Ulrich Wedig at the Max Planck Institute for Solid State Research in Stuttgart, Germany, this is tantamount to saying that ‘the usefulness of the term "oxidation state" is called into question’. In a recent critique of the work³, they say not only that ‘informed chemists will rub their eyes in astonishment’, but that they would be right to do so. They argue that Raebiger and colleagues have been lured into the error of thinking that quantum-mechanical wavefunctions can be compared with heuristic chemical concepts. At the level of the wavefunction, they say, ‘chemistry becomes structureless’. To recover any of the familiar entities of chemistry, such as localised bonds, atomic radii, charge states and so forth, the quantum continuum must be carved up in more or less arbitrary ways. In the present case, Jansen and Wedig question the way that Raebiger and colleagues calculate charges by integrating electron density over a sphere with the arbitrary radius of 1.3Å. It isn’t clear, they say, that this ‘size’ of the transition metal must be considered constant. More crucially, ‘oxidation state depends on all the atoms in a system’ - it is not a property of an atom, but a property of an atom in relation to others. 

No doubt this won’t be the last word on the matter. Whatever the merits of Jansen and Wedig’s case they are surely right to point out that, not only does chemistry need its heuristics, but these can’t necessarily be expected to fall out of a more fundamental quantum description of chemical phenomena.