Chemical Education Today
Letters Have Orbitals Really Been Observed? In a recent note (1), E. Scerri correctly points out that atomic orbitals are not directly observable, contrary to the claim he believes we make in the text of our recent paper (2). In fact, our paper describes a new technique for the mapping of charge densities in crystals, free of the usual extinction errors that have made the observation of details due to the formation of chemical bonds so difficult. The aim of our work, as in all our preceding publications on this topic, is the study of charge densities (these words occur 18 times) to elucidate bonding effects, not the observation of orbitals (mentioned four times). The increased accuracy of our measurements reveals a charge density difference map for copper atoms in cuprous oxide strikingly similar to textbook images of a dz orbital, which we comment on in passing. We entirely agree with Scerri that orbital wave functions are unobservable and that all the indistinguishable electrons in a crystal define a single quantum state. (The separation of atoms to infinite separation does raise fundamental issues in quantum mechanics concerning distinguishability, of which educators should be aware.) We also agree with him that “the orbital model remains enormously useful … and lies at the heart of much of computational chemistry; but it is just that, a model, as computational chemists and physicists are well aware.” Aware of this ourselves, we use many-electron theory in all the calculations reported in our paper. However, it would be perverse not to mention the undoubted resemblance of our final result to the simple one-electron model of a d-orbital charge-density distribution. This similarity merely indicates that the one-electron model retains some validity, even in a transition metal oxide, and that one particular choice of basis functions (hydrogenic orbitals) converges more efficiently than others. We should not mix pedantry with our pedagogy. Words can and are used in more than one sense as long as there is no danger of confusion. The New Shorter Oxford English Dictionary defines “orbital” in part as “An actual or potential 2
pattern of electron density”. A parallel example to the (mis)use of orbital is the use of “lattice”, which, sensu stricto, is also a mathematical construct, to mean “crystal structure”, as in terms such as “lattice dynamics”, “lattice image”, and “lattice defects”. “Meaning is use”, said the great philosopher Wittgenstein. The expulsion of all one-electron language from chemistry (apparently advocated by Scerri) would be entirely foolish. Terms and concepts such as “d-electron”, “molecular orbital diagram”, “orbital degeneracy”, “orbital angular momentum”, “anti-bonding orbital”, “d-orbital hole”, etc. could never be used or applied to crystals or molecules. Two successive papers in a recent issue of Physica have titles beginning “Direct Observation of Orbital Ordering”, describing work in one of the hottest areas of condensed matter science. Thus the device of metonym is common throughout chemistry. The continued use of one-electron terms by all authorities in the field simply indicates that this theory is too useful an approximation to be abandoned. Yes, it is important to know when approximations are made, but success in a science like chemistry is largely a matter of finding useful approximations: this is what students should be taught. Literature Cited 1. Scerri, E. R. J. Chem. Educ. 2000, 77, 1492. 2. Zuo, J.; Kim, M.; O’Keeffe, M.; Spence, J. Nature 1999, 401, 49. J. C. H. Spence Department of Physics, Arizona State University, Tempe, AZ 85287;
[email protected] M. O’Keeffe Department of Chemistry, Arizona State University, Tempe, AZ 85287 J. M. Zuo Department of Materials Science, University of Illinois, Champagne–Urbana, IL 61801;
[email protected] JChemEd.chem.wisc.edu • Vol. 78 No. 7 July 2001 • Journal of Chemical Education
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