Abstract
In this chapter, the models for the electron charge and spin density derived from X-ray and polarized neutron diffraction experiments are presented. The pitfalls of the spherical atom model are depicted and the advantage of more sophisticated models like the multipolar atom model are discussed.
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Notes
- 1.
For a given electronic configuration of an atom, there are different possible distributions of the electrons in the atomic orbitals, which implies several possible total angular (orbital) and spin momentums. For each pair of orbital and spin momentums, we obtain a state and the one with lowest energy is the ground state. However, each state may be produced by several microstates, depending on the exact distribution of electrons in each orbital type. A calculation normally refers to one such microstates and therefore may return a non-spherical electron distribution around an atom, whereas an average among microstates necessarily returns a spherical electron density.
- 2.
Noteworthy, sometime the quantity \(\mathbf{H}\) is used to indicate the vector in the reciprocal space which satisfies diffraction conditions, where \(\left|\mathbf{H}\right|=1/{d}_{\mathbf{H}}=\left|{\mathbf{k}}_{\mathrm{diffracted}}-{\mathbf{k}}_{\mathrm{incident}}\right|/2 \pi =2sin\vartheta / \lambda\), while \(\mathbf{k} \,or\, \mathbf{S}\, ({\text{with}} \,\mathbf{k}=2\mathrm{\pi }\mathbf{S}\)) are used to address a generic point in the reciprocal space. Therefore, the coordinates of \(\mathbf{H}\) in the reciprocal space are integer numbers h, k, l, those emerging from the Laue conditions.
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Macchi, P. (2022). Beyond the Semi-classical View of Atoms and Molecules in Crystals. In: Quantum Crystallography: Expectations vs Reality. SpringerBriefs in Crystallography. Springer, Cham. https://doi.org/10.1007/978-3-030-95641-7_3
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DOI: https://doi.org/10.1007/978-3-030-95641-7_3
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