Residual Density Analysis - Electron Density and Chemical Bonding - page 149

l Errors in Lorentz and polarization corrections
l Errors in the error model
l Thermal diffuse scattering
l Limited flexibility of the density model
l Disorder and libration
l Anharmonic motion
l Signal overflow at the detector
l Electric noise in the detector, dark currents
l Radiation damage of the crystal
l Wrong scattering factors, e.g., nonrelativistic for heavy atoms
l Beam impurities such as l /2 scattering, diverging beam, nonflat beam profile
or spectral truncation
l Higher order diffraction
l Crystal not bathing in the beam, not adequately centered, moving during mea-
surement, chemically instable, etc.
l Wrong, missing or inappropriate incident beam correction
l Inappropriate conversion factors for the detector
l Data scaling
l Additional diffraction by ice, the pin holding the crystal, oil, air, the beam stop,
or the monochromator
l Data integration errors

Admittedly, some effects have been mentioned several times now, however, it is
also obvious that the list is not complete. Some of the systematic errors should be
attributed to the theory. As an example, let us take again the Renninger reflections.
Their appearance is a natural consequence of a very high crystal quality and strong
intensities and is expected. However, the simplified theory used does not include
the description of Renninger reflections, therefore the standard theory applied,
which provides the connection between the electron density distribution in the
unit cell and the diffraction pattern, should be extended to include these effects.
This, however, is not accomplished on the fly.
One may optimistically assume that extinction corrections are small for small
extinction coefficients w << 1 (for a definition of w , see Equation (26)). It has been

shown, however, that this is not true [ 1 ]. For an extinction coefficient of w ¼

0.049,
the “correction” is much larger than all changes induced by employing a multipole
model instead of the spherical IAM. As a consequence, little errors or only a little
imprecision in the correction method might have a large effect on the density
model. We will come back to this example later.
If one tries to minimize a systematic error by changing the experimental con-
ditions, one almost always reinforces another error. For example, the lower the
experimental temperature, the better rotation disorder of methyl groups is pre-
vented; however, at the same time the probability for extinction effects rises due
to the lower thermal motion and accordingly better diffraction.
Also, some of the systematic errors will compensate each other at least partly.
A hypothetical example: when the background signal is measured too strong, it may