Chemistry Reference
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same factors (1)-(4) given above. The dependency on these factors is discussed in
detail in [
10
]. Additionally, this value
d
f
(
r
0
) is related to the features in the residual
density, as has been shown in Sect. 2.1.8.
The RDA-plot shows the formerly separated properties “flatness” and “features”
of the residual density in one graphic. Under ideal circumstances, when no system-
atic errors are present, this distribution is parabolic in shape.
Table
1
shows an increasing number of gross residual electrons and an increasing
difference between maximum peak and deepest hole for increasing noise, whereas
the fractal dimension at the residual density value zero simultaneously decreases
a little bit, which is expected under the assumption that strong noise also tends
to spread spatially wider than weak noise. Even for no noise,
p
1
¼
0.000,
e
gross
remains finite, although one would of course expect it to approach zero. This
difference is explained by the observation that in XD the structure factor calculation
does not yield identical results between input structure factors and output structure
factors, when no refinement is performed, despite using the correct input file for the
model parameters. Instead, changes in the last digit occur for a number of structure
factors. These little differences add up to a nonzero value for
e
gross
.
3.2
...
to Experimental Resolution Truncation
As already mentioned above, the experimental resolution is sometimes truncated
for the difference density plots. For the determination of the parameters from a
least-squares fit, however, the whole data is used. It has also been mentioned
that this procedure is not advisable, as there exists valuable information about
the adequateness of the model to the data in the high-frequency data. It is indeed
that this data reveals best otherwise hidden sources of error. To demonstrate
the effect of experimental resolution truncation, again the S(N
t
Bu)
3
data is used.
The fully refined model is used for the calculation of 50
50 residual
density grids, however, the resolution is truncated from 1.14 to 1.00 and
0.80
˚
1
, respectively. The same model parameters are used throughout. Figure
5
shows the RDA-plots for the whole unit cell and contour plots in the molecular plane.
The more the resolution is truncated the smoother and more acceptable the residual
density appears. The model, however, has not been changed and the valuable infor-
mation in the high-frequency data that indicates a nonperfect model and systematic
differences between model and data is suppressed by the cutoff.
50
3.3
...
to Quantify Features in a Model Refined Against
Experimental Data
In this example, POFs of an IAM refinement and of an MM refinement against
experimental data of S(N
t
Bu)
3
are calculated. These data have been used for the
histograms in Figs.
1
and
2
.
