Chemistry Reference
In-Depth Information
compensate for some reflections with the presence of TDS, which peaks under the
Bragg signals. In this case of
error compensation
, the effective deletion of one
source of error may deteriorate the situation as long as the counteracting source of
systematic errors is not deleted, too.
May this be as it is, the validity of the experimental results is limited by the
systematic errors. This situation is in charge-density studies much more demanding
than in conventional crystallography.
Any one of the above-mentioned possible sources of error has the potential to
completely spoil a charge-density study. This might not even be obvious, as small
R
-values and good fitting statistics may give the impression that everything is fine.
It is therefore of increasing importance to assess, control, and quantify these
errors as the wind needs to be tempered to the shorn lamb.
1.6 The “Traditional” Approach for Evaluating the Quality
of a Refinement
Until recently, it was common to “prove” that the residual density is flat and
featureless by showing difference density plots in selected planes, often chosen in
a way as to contain the heaviest atoms. Sometimes, these plots were calculated for a
resolution well below of the experimental one, insinuating explicitly, or, more
frequently, implicitly, that features appearing at higher resolutions are pure artifacts
from experimental noise - which is not the case. The selection of the planes and the
step width of the contour lines were chosen freely. If the plane containing the
highest difference peak and the deepest hole, which also often appear in the vicinity
of the heaviest atom, was not shown, usually nobody would ask for it.
This situation has come about since there was a common understanding that
difference densities need to be featureless, but no generally accepted standard
procedure how to prove that a difference density is without features was known.
There were just no general standards available. It is, however, well known that the
largest peak and deepest hole need not appear in a molecular plane, and that features
tend to accumulate at special positions or symmetry axes in the unit cell. For this
reason alone, it is important to analyze the whole unit cell and not only subjectively
selected planes. Furthermore, there should be a criterion available, which tells
whether features in the residual density are of truly statistical random error. If
they are not, this means that the model is inadequate and all properties derived from
the model may be spoiled. It is even more problematic that it is impossible to tell
which of the model-derived properties are not affected. But as indicated in the
introduction, as a rule of thumb one can regard standard structure parameters as
being relatively robust, whereas the second derivatives of the charge-density and
the Laplacian are regarded as most sensitive. The Laplacian, however, is most
important when the electron density is interpreted chemically, as it is connected to
the valence shell charge concentrations (VSCCs).
