Chemistry Reference
In-Depth Information
A spatially well-localized error in the model may influence all other parameters due
to parameter restrictions and correlations. As an example, one may think of the
monopole parameters. These are interconnected by the restriction that they sum up
to the total number of electrons, which is constant during the refinement. If disorder
is present but not taken into account, the monopole values (and with high probability
other model parameters, too) of the disordered part are wrong. This also affects the
other monopole values
via
the above-mentioned constraint. If disorder is present, it
needs to be described. The problem may be to detect disorder in the first place.
1.4.3 Overfitting
The number of model parameters and observed data needs to be in balance. For
many parameters and few observations, there may be many parameter value
combinations, which fit the experimental data all very well. Not a single set of
parameter values out of these needs to be physically or chemically meaningful.
A problem of this kind would arise, for instance, when the diffraction data are not of
the resolution needed for a charge-density study, however, a multipole expansion is
performed. Despite this inappropriateness of the model, the
R
-values would of
course decrease. This may sound trivial, but it is not, because high-resolution
data may be sufficient for the refinement of dipoles of the heavy atoms, however,
for quadrupoles and higher moments, the data may not be sufficient. Where exactly
is this border between overfitting and appropriate parameterization? Also in these
cases, it would be helpful to analyze the residual density locally and globally. If the
local analysis does not indicate progress in the fitting, the atom is probably over-
fitted. Analysis tools may help in these cases also to mark the border between
predicted
density parameter values such as the ones obtained from an Invariom
refinement [
4
] and parameter values
derived
from the data.
1.4.4 Sharing Experiences
In the day-to-day work of charge-density refinements, the search for systematic
errors has to be done over and over again for each individual refinement. There are
individual errors, which will probably repeat and there are errors more specific to
the charge-density problem at hand. How much easier would it be, if there was an
indicator warning of certain mistakes or systematic errors. It would be helpful if one
could picture the effect of an error and would know immediately, what is going on,
because the characteristic imprint of this error was described earlier in the literature.
One would learn faster not only from own mistakes, but also from those made by
others. The refinement process would become more efficient. Moreover, one would
learn the more, the more mistakes are made. The word “mistake” should be taken
here without valuation, as a neutral word describing a probably unexpected mis-
match or discrepancy between predicted and measured values or between predicted
