Henry Rzepa's Blog

X-ray crystallography is the technique of using the diffraction of x-rays by the electrons in a molecule to determine the positions of all the atoms in that molecule. Quantum theory teaches us that the electrons are to be found in shells around the atomic nuclei. There are two broad types, the outermost shell (also called the valence shell) and all the inner or core shells. The density of the core electrons is much higher (more compact) than the more diffuse valence shell for all but the hydrogen atom, which only has valence electrons. How does this relate to x-ray diffraction by electrons? Well, core electrons, because of their relative compactness, diffract X-rays more strongly than the valence electrons. This compactness of the core also means that its electron density distribution can be well (but not exactly) approximated by a sphere, with the nucleus at the centre of that sphere. And from this it follows that the density for each atom can be treated independently, the so-called IAM or independent atom model. For example all the carbon atoms in a molecule are approximated as having the same value for the electron density of their core shell. But the IAM approximation is much less good for hydrogen atoms, especially when they are attached to very polar atoms (Li, O, F, etc) and even atoms such as carbon or oxygen have noticeable deviations as illustrated in  figure 1 below. [1]

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References

1. F. Kleemiss, O.V. Dolomanov, M. Bodensteiner, N. Peyerimhoff, L. Midgley, L.J. Bourhis, A. Genoni, L.A. Malaspina, D. Jayatilaka, J.L. Spencer, F. White, B. Grundkötter-Stock, S. Steinhauer, D. Lentz, H. Puschmann, and S. Grabowsky, "Accurate crystal structures and chemical properties from NoSpherA2", Chemical Science, vol. 12, pp. 1675-1692, 2021. https://doi.org/10.1039/d0sc05526c