Bonding and the X-ray Scattering Formalism

For anisotropic motions the expressions we have just discussed become more complicated. Note also that while these equations refer to positions and displacements of atoms (i.e. nuclei), the X-rays themselves are actually scattered by electrons. This is a potential problem, because the nature of chemical bonding means that the distribution of electrons is not a simple superposition of spherical atoms. And yet the assumption of exactly spherical atoms, also known as the independent atom model, is the basis of these equations. A more rigorous treatment relates the structure factors to electron density, i.e. the three-dimensional distribution of electrons in space represented by the function p x) with x representing space in three-dimensional coordinates x, y, z. Within this formalism the structure amplitude can then be expressed as... 

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