Diffraction by single crystals electron density determination

9 Diffraction by single crystals electron density determination 

Experimental deformation density map for dimolybdenum tetra-ethanoate, assuming that all atoms are neutral. The map is for a section through a plane formed by one Mo atom and four O atoms bonded to it. Negative contours are dotted. Reprinted with permission from [39]. Copyright 1981 lUCr. 

The most usual way is effectively the same as is used for completion of crystal structures during structure solution (Section 10.7.6 andEq. 10.12). When a reasonable part of the structure has been described and some atoms positions have been defined, along with correct scattering factors and thermal parameters, a difference map can be calculated between this (incomplete) model and the Fourier transform of the experimental structure amplitudes. This map is a representation of the difference between the electron density of the model and that determined by the experiment. The biggest accumulations of electron density are assigned as new atoms until the structural model is complete. But even then there is residual electron density, which describes the difference between the true electron density and the model of a sum of independent spherical atom contributions, taking some simplified model of displacement into account There is also some random noise. 

Nowadays, this view of electron density has been refined and extended by more sophisticated topological analysis. Modem methods are based on accurate experimental (or calculated) electron density distributions. Hansen and Coppens developed the finite multipole expansion (multipole model, MM) [40], which partitions 

Residual electron density maps in the Cs ring plane of HP[CNS(C6H4)]2 when described by multipole models of different order (a) monopoles, (b) dipoles, (c) quadrupoles, (d) octapoles. Positive values are drawn as solid lines, negative as dashed, the zero contour is dotted, step size 0.1 Redrawn with permission from [41]. Copyright 2011 John Wiley Sons. 

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