Chemistry Reference
In-Depth Information
This already makes clear that there is no strong correspondence between the quality
of a model and its
R
-values, because parameter changes affect different entities
such as intensities and structure factor moduli differently, resulting in different
“optimum models”.
To give an example: let us assume the experimenter decides to fit the density
model with respect to the agreement between measured and predicted structure
factor moduli. He finally gets a resulting
R
1
-value of
W
. Now he wants to compare
the quality of these results with other published data, however, these were given
as
R
2
-values. So he calculates what the
R
1
-value means, when translated to an
R
2
-value and gets a result
X
. After reexpressing his results, he has the idea to do the
refinement again, this time directly with respect to the intensities, instead of the
structure factor moduli and he gets a result
R
2
¼
Y
. We kindly ask the reader to stop
here for some 30 s and think about the following question: is this result
Y
greater,
equal or smaller than
X
? Please make an educated guess before you continue
reading.
Before we come back to this question, we briefly discuss another situation.
Suppose there is excellent high-resolution data and an independent atom model
(IAM) is fitted to the data. Let us assume the atoms move only harmonically. After
the model converged to its final values, anharmonic motion parameter refinement
is included for all heavy atoms, which are still considered to be spherically
symmetric. The
R
-values will fall further, however, the resulting density model
is not necessarily better, as anharmonic motion parameters will artificially
account partly for the aspheric electron density due to chemical bonding, to
compensate for the inadequate spherical static density model. In this case, a
smaller
R
-value just expresses that the experimentally and theoretically obtained
intensities are in better agreement; however, they are in
better
agreement for the
wrong
reasons. This kind of error, to obtain better agreement for the wrong
reason, is very important in charge-density studies. Although this last example
may be a bit trivial, however, it expresses one point very clearly:
R
-values do not
say anything about how physically or chemically reasonable a model is.
R
-values
do not
prove
a model to be better than another one, they just indicate agreement
but the agreement can be achieved by any combination of density- and thermal
motion parameters, which need not be physically and chemically meaningful.
This is of special importance in charge-density studies, with highly flexible
models, correlating model parameters, and small
R
-value differences between
competing models.
Now back to the other example. Did you make a guess? You still can, if you do
not read on. But now we have to go on and solve the riddle. The
R
2
-value
obtained for a refinement against structure factor moduli was
X
, while the
R
2
-value for a refinement against intensities was
Y
. Of course,
Y
will in general
be smaller than
X
. That is because it makes a difference when refining against |
F
|
or against
I
and an optimum for one case is not necessarily also an optimum for
the other case.
When the experimenter now decides to compute the
R
1
-value from
R
2
¼
Y
,he
will obtain a result
Z
that is in general larger than
W
.
