Chemistry Reference
In-Depth Information
To allow for a comparison of the experimental findings with idealized data, we
used the coordinates and anisotropic displacement parameters from the experiment
to generate a reflection file with the same resolution. Noise was added to the
structure factors until the experimental number of gross residual electrons was
approximately obtained. The reflection file was imported into XD and residual
density grids were calculated from IAM refinements of these data. The RDA-plot of
the experimental results with PDC (blue filled circles) and of the theoretical data
(green open circles) is shown in Fig.
9
.
Theoretical and experimental RDA-plots are in good agreement. Differences
occur for
Dr
0
and
d
f
(0): both are smaller for the theoretical data and the difference
in
d
f
(0) is very large. In MM, it was frequently observed that
d
f
(0) from the
experimental data was smaller than from theoretical data. A possible explanation
for these observations is that again the p.d.f. of the residual density is influenced by the
entropy maximization procedure such that it leads to this spiked distribution. A similar
behavior is observed for the entropy minimization of the modulus of the residual
density distribution further above. That the resulting p.d.f. is more spiked in this
case whereas it was broader in the above case need not be a contradiction as the
preferred p.d.f. from the entropy functional may well be a function of the total error.
Another possible explanation is that experimental noise was fitted by the MEM
procedure, which would also lead to a redistribution of the residual density and
possibly to a deviation from the Gaussian distribution. This example shows that an
RDA may be useful for an evaluation of the properties of the entropy functional
Fig. 9 RDA-plot of experimental MEM data (
blue filled circles
) and theoretical data (
green open
circles
) with approximately the same number of gross residual electrons (3.4 e)
