Chemistry Reference
In-Depth Information
2 Basic Ideas and Aims of the RDA
It would go much too far to state that the RDA is able to solve all the above-
mentioned problems, but it is true that the RDA touches these in one way or the
other. For example, the RDA allows for an assessment of the whole residual density
in the unit cell. The RDA plots allow for an estimate to which degree maximum
peak and deepest hole fit naturally in the residual density distribution. How “flat”
and “featureless” the residual density is can be seen from an RDA plot. The
difference between an MM or a MEM refinement and an IAM refinement can be
quantified in terms of “gross residual electrons” or in “percentage of features”
(POF). The influence of data processing such as extinction correction can be
translated to a number of gross residual electrons. This number may be compared
to the difference in gross residual electrons from IAM and MM or IAM and MEM,
thereby giving an impression of how sensitive the output of an MM or MEM
refinement is with respect to extinction correction procedures. In summary, the
RDA is a first step toward unifying and standardizing the description of experimen-
tal (and data processing) sources of error.
The basic idea is that the residual density contains extremely valuable informa-
tion about modeling errors and modeling inadequacies. Modeling in this context
comprises also data collection and reduction as well as the scattering theory, the
density- and the thermal motion models, and all theories, assumptions, approaches,
and simplifications entering at any stage, e.g., assumptions about the background
signals or spot profiles. Why is data collection and reduction a part of modeling?
Because the data collected is supposed to be Bragg data corresponding to mono-
chromatic X-rays deflected from a crystal with perfect periodicity.
The basis idea is further to extract this information from the residual density,
i.e., to analyze the residual density, hence Residual Density Analysis. In the
second step, the information gain should be used to improve the modeling, if
necessary.
A very important aim is also to give the term “featureless” a meaning, i.e., to
derive a quality criterion that tells whether or not the residual density distribution in
the whole unit cell can be considered featureless. The development of these ideas
was continuously accompanied by the question how things would be in an ideal
world. This sharpens the expectations and makes it easy to differentiate between the
general and the special cases. So, for deriving the residual density descriptors, we
just follow this line and start with answering the question:
How would the residual density look like after a refinement in an ideal world?
In a very ideal world without noise and background signals and with a perfect
diffractometer, with a perfect detector and a perfect scattering theory, a perfect
imperfect crystal and unlimited resolution, there are no residuals at all and
correspondingly no peaks and holes in the residual density. If you try to picture
this residual density distribution in the unit cell in your mind, you will see a
completely flat “distribution” with only one value, which is zero and which
completely fills the unit cell. Mathematically, this situation can be described
