Residual Density Analysis - Electron Density and Chemical Bonding - page 171

indeed from the IAM to the MM refinement from 69,564 to 30,574, indicating
that the residual density distribution after the MM refinement is flatter than that
after IAM refinement. In the MM refinement against theoretical data, however
S increases again. Obviously, the definition of flatness from the RDA, which just
uses

Dr 0 and from an entropy functional S , which takes into account the whole
distribution, have a different meaning: the p.d.f. corresponding to Fig. 6e is more
peaked than the broad p.d.f. corresponding to Fig. 6c . This leads to the increase in
the entropy for Fig. 6e . Please note that both have the same wR 1 | w ¼ 1 value as they
have the same number of gross residual electrons. It must be concluded that the
above functional prefers a non-Gaussian distribution of the residuals to minimize
the entropy for a given, small, fixed total amount of errors.

3.4

... to a Multipole Refinement

To monitor the effect on the residual density distribution of a multipole model
refinement against experimental data of S(N t Bu) 3 [ 8 ], a 50

50 residual
density grid of the whole unit cell was calculated with XDFOUR and analyzed after
each individual refinement step with jnk2RDA. The distributions of the residual
densities viewed through the glasses of the Residual Density Analysis approach are
shown in Fig. 7 and the corresponding residual density descriptors in Table 4 .
The scale factor was refined in each step. The multipole model started with the
refinement of a scale factor and coordinates of all atoms, anisotropic displacement

50

Fig. 7 Fractal dimension distribution for the individual steps of a multipole refinement on S(N t Bu) 3