Chemistry Reference
In-Depth Information
r
0
Residual density, difference density. Synonyms for the density obtained
from a Fourier synthesis with Fourier absolute coefficients from the
difference of the absolute structure factors and phases from the model
Extinction coefficient; also weighted residual sum (
w
2
) for least
squares fitting
w
1 Motivation
1.1 Special Needs in Charge-Density Studies
It is an easy task to give the bee-line distance between G¨ ttingen and Berlin to an
accuracy of several 10 km; it is a harder task to give the distance between the
“G¨nseliesl” in G¨ ttingen and the “Brandenburger Tor” in Berlin to the accuracy of
several meters, and it is almost impossible to give the distance between the bill of
the goose and a detail of the “Brandenburger Tor” like the tip of the nose of Viktoria
to the accuracy of a few millimeters.
Also, the possible sources of error are very different for these tasks. While in
the first case not even the curvature of earth's surface has to be taken into
account, nor differences in altitude, in the second case both will have to be
considered. In the third case, one might find that this distance is not even well
defined and changes with time due to tidal forces or local oscillations caused by
heavy traffic.
A similar situation arises when comparing standard structure determination for
small molecules to charge-density studies and finally to the topological analysis
with the typical discussion of the second derivatives of the electron density: while
standard structure determinations are rather robust and still give chemically mean-
ingful results also when structure parameters are affected by measurement errors
and parameter correlation, this need not be the case for charge-density studies, and
for the Laplacian it might even be questioned whether this is a well-defined
quantity, when static densities are constructed by deconvolution from a time- and
space average, the dynamic density.
When aiming at the highest accuracy, the emphasis shifts from avoiding coarse
mistakes to measurement, assessment, and control of all possible sources of error.
Also, instruments are needed to discriminate between true “measured” properties
of the electron density and artifacts from random- or systematic errors. The
quotation marks are used, because in reality the electron density is not measured,
but reconstructed from the diffraction data. Reconstruction implies use of diffrac-
tion-, density-, and thermal motion-models, all of which may contain several
simplifications. In the end, there may be chemically and physically different
solutions to the density reconstruction problem, which fit the diffraction data
equally well.
These considerations are made a bit more explicit in the following paragraphs.
