Chemistry Reference
In-Depth Information
A conventional multipole refinement of the dominant domain and a multipole
refinement taking the disorder into account have been performed and residual
density grids have been calculated and analyzed.
A 100
60 grid was used for the plane with edge lengths 10 and 6
˚
in Fig.
12a
and a 56
176 grid was used for the RDA-plot in Fig.
12b
. Both graphics
clearly indicate that the residual density is far from being flat and featureless.
The unmodeled disorder is clearly visible as positive residual density between
the atomic positions of the model and as negative residual density (red dashed lines)
around the atomic positions. The positive residual density at the atomic positions of
the first domain stems from too large anisotropic displacement parameters, which
artificially increased during the refinement to account for the other (unmodeled)
domain. Too large values for the
U
ij
generate circular areas of negative residual
density around the atomic positions. These are also seen in Fig.
12a
. A study on how
unphysical values of anisotropic displacement parameters affect the whole residual
density distribution and planes through the molecule can be found in [
1
]. The
unmodeled domain of PP contributes to the positive residual density shoulder in
Fig.
12b
, whereas the too large occupation factor (1.0 instead of 0.9) contributes
most to the negative residual density shoulder.
After taking the statistical disorder into account, the residual density distribution
changes drastically. In Fig.
13
, again a plane through the molecule is depicted as
well as the RDA-plot taking into account the residual density in the whole unit cell.
The fractal dimension
d
f
(
r
0
¼
76
0) increases from 2.5770 to 2.6286, which, in view
of the logarithmic scale involved in the definition of the fractal dimension of the
residual density, is interpreted as a rather large change. The total error decreases
from 16.08 to 6.74 gross residual electrons. Finally, the difference between maxi-
mum peak and deepest hole decreases from 0.98 to 0.27 e
˚
3
. The additional
refinement of the second domain describes the total electron density in the whole
unit cell to a very good degree. A good description, i.e., a description that fits the
experimental observations, is a necessary condition for an acceptable model.
Whether or not this model is physically acceptable (and chemically meaningful)
is out of the scope of the residual density analysis, for questions of this kind clearly
physical, and not only statistical, measures of quality need to be developed and
applied and the resulting density is to be analyzed with respect to information about
electrostatic forces (Tables
7
and
8
).
3.8
...
to an Anharmonic Motion Problem
One main application of the RDA(-plot) is to prove absence of features in the
residual density distribution to show that the density and thermal motion model is
among the acceptable models. This was also the way the RDA was applied in the
preceding section about static statistical molecular disorder.
Here, we describe in detail a case where the thermal nuclear motion model was
crucial. The experimental results are already discussed in a chapter of Electron
