Chemistry Reference
In-Depth Information
1.2.2 Global and Local Measures
Despite the shortcomings of
R
-values already mentioned, there is yet another aspect
of quality measures that becomes increasingly important in charge-density studies.
This is the question of local and global measures.
In charge-density studies, typical questions are about the details of the electron
density: is there a positive or a negative charge at this atom? Are there VSCCs at a
given atom? And so on. Two different charge-density models may have more in
common than differences, e.g., when one model employs an Al
3
þ
scattering factor,
whereas in another model the Al atom is considered to be neutral. Or in one model
anharmonic motion of an atom is considered, and in the other not. Or two models
just differ in the set of radial screening parameters for the spherical core density
k
or
for the aspheric valence density
k
0
.
Because the changes in the models are so small, the
R
-values, which measure the
total or
global
agreement, also change only little. It would sometimes be helpful if
the
local
description also could be compared, i.e., if the local environment of an
atom or a group of atoms could be analyzed with respect to the influence of certain
parameters like those above mentioned.
Summary:
R
-values just measure global agreement, but there may be many different
density models, which all agree to the same degree with the data, even in the case of
vanishing
R
-values. In contrast to standard structure determination, in charge-density
studies
R
-values are also not able to establish the superiority of one model over another.
As a consequence, further quality criteria in addition to
R
-values are needed.
1.3 The Residual Density: Flat and Featureless?
What is known about the properties of the residual density? In the relevant litera-
ture, one finds the phrase that the residual density should be “flat and featureless”
[
3
] and that this is the most important single criterion. But what exactly does this
mean? “Flat” is easy to understand, it means that the absolute values of residual
density peaks and holes should be as small as possible. But how is the content of
features in the residual density assessed? How is it possible to prove the presence of
features in the residual density?
To show that the residual density does not contain features is of importance for
several reasons. First of all, it proves that the model is able to describe the experi-
mental findings in the whole unit cell and that the model parameter values have been
adjusted appropriately. Features in the residual density are a hint toward an incom-
plete or inappropriate model, wrong parameter values, or hidden sources of error.
Similar to the
R
-values, also the absence of features in the residual density does not
prove the model to be correct in a mathematical sense, but the opposite holds:
features in the residual density prove inappropriateness in the model-to-data rela-
tionship. The source may be in the experiment (data measurement, data processing)
or in the theoretical and modeling part (inappropriate density- or thermal motion
