Chemistry Reference
In-Depth Information
The parameter
R
-values differ more and for the model excluding anharmonic
nuclear motion all individual parameter
R
-values but
R
hexa
are larger compared to
the full model. As the parameter
R
-values for the appropriate model (second row)
are solely determined by the noise, this may be a sign that the hexadecapoles fit
experimental noise efficiently in this case. May this be as it is, the total parameter
R
-
value is larger for the model lacking anharmonic nuclear motion. Introduction of
anharmonic nuclear motion parameters reduces
Dr
0
from 0.54 to 0.27 e
˚
3
.
The neglect of anharmonic nuclear motion may lead to artificial VSCCs in the electron
density. When the highest residual density peak and deepest hole are on a straight line
through a nucleus, this may be an indicator for the neglect of 3rd order GC coefficients.
A shashlik-like pattern in the residual density with alternating signs and with an atom in a
nodal plane may also indicate neglect of 3rd order GC coefficients.
4 Future Developments
The RDA is only a little step toward more transparency in the detection, classifica-
tion, and elimination of density model and thermal motion model inadequacies, in
data processing and data reduction inadequacies, and so forth. As a comparative
method, it cannot state that either the data or the model is wrong, but it can detect
systematic discrepancies between data and model. For the plausibility of the
resulting density and thermal motion models, other than purely statistical measures
of quality need to be used.
4.1 Physical Measures of Quality
The statistical measures only give a degree of agreement between the theoretically
and experimentally obtained values. Nothing is said about the physics. Therefore, a
model with very high agreement still could be “unphysical.”
For structure determination, the statistical measures are completely sufficient;
however, when describing the electron density distribution in great detail, it might
be helpful to have additional measures of quality and/or additional knowledge,
which could be used as extra observations in the refinement. Why not using
physical measures of quality?
For example, due to the thermal motion (and the Heisenberg uncertainty princi-
ple), the nuclei in the crystal change their place all the time slightly, however, on
macroscopic time scales they do not move (crystal damage is not considered here).
The forces acting on the atoms are such that they drive the atoms back to their mean
locations, which do not change with time. It is an equilibrium situation. An equilib-
rium situation is established when the macroscopic properties do not change with the
course of time. Microscopically, however, changes may occur all the time.
