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Observing electron density

A reply to Spackman, Howard and Destro

I am grateful to Spackman et al for their spirited response (IUCr Newsletter, Vol 8, 1, 2000) to my Nature News and Views article (Nature 401, 21, 1999) which commented on the work by Zuo et al (Nature 401, 49, 1999) and for this opportunity to clarify the situation.

Zuo et al used a combination of electron diffraction (to measure low order diffracted intensities) and x-ray diffraction (for higher orders) to determine the charge density in the inorganic material Cu2O, and my Nature News and Views article commented on this work and on the potential application of the combined electron and x-ray diffraction techniques (as suggested in ref 1) to determine the charge density in cuprate superconductors, also inorganic materials of course. The whole thrust of my article was therefore about inorganic materials and for these materials I totally stand by my statement that x-ray diffraction 'is normally unable to give details about the shape of the charge distribution, in particular the shape of the bonds'. I also stand by the reason I gave for this, that the x-ray scattering from dislocations and defects in inorganic materials is normally 'greater than the scattering from the bonding electrons'. It is of interest to note that despite a considerable amount of x-ray diffraction work on cuprate superconductors, which has revealed the atomic positions in these materials, there has been no x-ray determination of charge densities in any cuprate superconductor despite the intense interest in knowing this. If the remarks of Spackman et al were correct, that 'extraction of detailed electron density distributions of organic, organometallic, inorganic, ionic metallic and mineral crystalline systems from x-ray diffraction data is now a mature and highly productive field' then surely x-ray diffraction would have determined the charge density in at least one cuprate superconductor by now! The situation is that although x-ray diffraction is a superb technique for determining electron densities in organic, etc., crystals, that is not yet the case for most inorganic crystals. Why is this?

In inorganic materials, the dislocation density is usually at least 106cm-2 and this can cause x-ray measurements of low order atomic scattering factors to be in error by at least 100%. Accurate measurements of low order scattering factors are essential for determining charge densities since it is the low order reflections which are most sensitive to the degree of ionicity of atoms. Despite the statement of Spackman et al, the true situation is that no totally successful scheme for correcting x-ray diffracted intensities has yet been devised for crystals with moderate to high densities of dislocations. Hence x-ray diffraction is normally unable to give details of the charge density for inorganic materials. For electron diffraction, on the other hand, an electron beam focussed to only 1 nm across can be used to select regions of relatively strain free perfect crystal between dislocations in a wide variety of inorganic materials and accurate low order scattering factors can be measured by interpreting diffracted intensities using the dynamical theory of electron diffraction. The only inorganic crystals for which x-ray diffraction can be used to give accurate charge densities are crystals which can be grown, or occur in nature, with very low dislocation densities, for example silicon and diamond.

However, although Spackman et al are in error concerning most inorganic materials, I gladly agree that for most organic and molecular crystals, x-ray diffraction is a superb technique for measuring charge densities. Why are inorganic and organic materials so different as regards x-ray diffraction measurements of charge densities? The answer lies in the defects. Organic and molecular crystals normally have much larger unit cells than inorganic crystals, and hence dislocations in these materials have much larger Burgers vectors, b, than in inorganic crystals. Since the energy of a dislocation is proportional to b2, dislocations have a very high energy in organic and molecular crystals, hence they are energetically unfavourable and the dislocation density in these materials is normally many orders of magnitude lower than for inorganic crystals. Thus x-ray diffraction is an excellent technique for measuring charge distributions in organic and molecular crystals, but for most inorganic materials, the low order reflections (which are the most sensitive to the ionicities of the atoms) are best measured using electron diffraction.

Colin J Humphreys, FREng
Goldsmiths Prof. of Materials Science


1. D. J. Smart and C. J. Humphreys, The application of electron diffraction to determining bonding charge densities in crystals. Inst. Phys. Conf. Ser. 52, 211- 214, 1980.


Dear Bill

Thank you for providing us the opportunity to comment on Humphreys' response to our letter (IUCr Newsletter 8, 2, 2000). We are disinclined to enter into a prolonged scientific argument on this matter, and believe that the substance of the points raised in his response, some of which seem most peculiar to us, will be best judged by the readers.

However, two points deserve emphasis:

  • Humphreys mocks our viewpoint thus: 'If the remarks of Spackman et al. were correct, that "extraction of detailed electron density distributions of organic, organometallic, inorganic, ionic, metallic and mineral crystalline systems from x-ray diffraction data is now a mature and highly productive field", then surely x-ray diffraction would have determined the charge density in at least one cuprate superconductor by now!'. Our letter cited two review articles which comprehensively summarized the experimental charge density work for the period 1992 - 1997, listing published x-ray diffraction results on almost one hundred different inorganic materials. Included were studies on several cuprate superconductors and related materials.
  • A detailed scientific critique on the original Nature article and commentary has been published: 'On Closed-Shell Interactions, Polar Covalences, d Shell Holes, and Direct Images of Orbitals: The Case of Cuprite', S.-G. Wang & W.H.E. Schwarz, Angew. Chem. Int. Ed. 2000, 39, 1757-1762.

M.A. Spackman, R. Destro and J.A.K. Howard

Dear Bill

In a recent letter to the IUCr Newsletter (Vol. 8, 1, 2000) Spackman, Howard and Destro made a welcome rebuttal of the statement that 'X-ray diffraction is normally unable to give details about the shape of the charge distribution' (Nature 401, 21; 1999). The comments published in Nature state that 'while electron diffraction can image electrons, X-ray diffraction is inherently incapable of doing so, as X-rays are scattered by defects in crystals'. Unfortunately, Nature did not permit a rebuttal of the statements made, and ignored the Spackman et al. letter as well as others, including one by me, sent in response to what appeared in print.

Quite apart from the nature of X-ray scattering (doesn't the widely used kinematic theory assume an imperfect crystal? Isn't extinction, which is the likely cause of the inaccuracy of the low-order X-ray structure factors for the crystals discussed, a result of the crystal being too close to perfect?), and whether or not Cu-Cu bonding has been observed in cuprite, the dramatic announcement 'Orbitals observed' on the cover of the issue of Nature (September 2, 1999) is astonishing, to say the least.

Fortunately, there are now several excellent publications that give hope that Science is still self-correcting. To paraphrase Wang and Schwartz in their comment in Angewandte Chemie, in nature (though not in Nature), orbitals are mathematical concepts that are not uniquely defined. In a definitive in-depth analysis (Angew. Chemie, Int. Edition, 2000, 39, 1757-1762,), they point out that although a shift in electron density may appear to have the same features as a text book orbital, the density corresponding to such an orbital is everywhere positive in three-dimensional space, and does not have negative and positive regions.

The Nature issue and resulting comments in journals such as Scientific American (see for example and Chemical & Engineering News (1999, 77, 38), raise the danger that such misconceptions will pervade the teaching curriculum. This issue is addressed most effectively in a timely article by Scerri entitled 'Have Orbitals Really Been Observed?', to appear this fall in the Journal of Chemical Education. Scerri notes that 'it is essential that claims of having arrived at a new understanding of such a crucial concept should be subjected to close scrutiny'. The issue has again demonstrated how important it is that the IUCr maintain its own Newsletter. The current tendency for dramatic publicity can only be counteracted when more restrained media are available for open discussion.

Philip Coppens
Buffalo, NY, September 2000