Chemistry Reference
In-Depth Information
applied nevertheless, there is a danger of obtaining too significant reflections by an
artificial reduction of the standard deviations.
Another example: in [
23
], a scaling scheme is given by iterative least-squares
fitting to minimize
0
1
2
D
E
X
Fj
meas
@
A
hi
=d
h
2
e
2
p
2
u
2
w
2
k
1
ΒΌ
w
h
2
;
(28)
DE
1
h
Fjj
where the denominator in the first term in brackets is evaluated by an application of
Wilson's statistics [
24
]. The scaling factor to be determined is
k
and the displace-
ment parameters are hidden in the exponent. When in a charge-density experiment,
the data has been scaled according to Equation (28) and there is no disorder and a
high quality of the model, then one could in a postprocessing step rescale the data
where Wilson's statistic is replaced by the statistics derived from the model. This
would lead to a correction and to a self-consistent procedure. The reader might
think that the scaling is then biased toward the model used and therefore the
proposed procedure should not be accepted. One can see it the other way round,
too: If scaling is performed according to (28), then the scaling is biased toward
Wilson's statistics, which implicitly assumes uniform random atoms at rest on no
special positions. Wilson's statistics might be a good starting point, when not much
is known about the structure. However, when the structure is known in great detail,
Wilson's statistics might not be a good assumption any more, in particular when
atomic numbers vary heavily or when heavy atoms are on special positions. Then
the known IAM structure is a better prior knowledge than Wilson's statistics. In any
case, the proposed procedure is applicable only as a postprocessing step for very
high quality data and very good density models in the absence of disorder.
The discussion of this section shows that there is a shift from the straightforward
application of (over?)-simplified scattering theories toward complex simulations
and deeper analysis of potential and actual sources of error. This effort might not be
necessary for every charge-density experiment. On the other hand, if it allows the
determination of the electron density more accurately also for weakly diffracting
compounds, it might well be worth the effort. As a by-product, there is much to
learn about the physics of the scattering process, machines and detectors, about the
statistics useful in data reduction processes and so forth.
4.3 A Common Effort
The most important question is that of learning together. As an individual one just
adds to the work, but being part of a larger community acting in concert means that
the individual efforts will be multiplied and the rewards will be for the individuals
contributing and for the charge-density community as a whole. This is the spirit of
