From Table 13 in Chapter 4 it can be seen that only multipoles for the atoms C1, C2, B1, F1, O1, H1 and H2 are refined. Therefore, meaningful standard deviations can only be obtained for bonds involving these atoms. In Figure 73 plots of the electron density in dependence of the error model option used are shown. In
general, it can be seen that all the values show no significant deviation. When only considering the absolute values of at the bond critical points it can be seen that
Figure 73: Plots of the electron density ρ vs the error model option used including 3 times the standard deviation.
a) b)
c) d)
e)
seem to form two groups. The agreement within the groups seems to better than between the groups. However, it needs to be noted that within a 3σ range these values are the same.
In contrast to the Laplacian of the electron density does show significant deviations (Figure 74). Except for the oxygen –hydrogen bonding O1 – H1 of the
water molecule the absolute values of the Laplacian shows a narrow distribution (≈
±1 eÅ-5). In contrast to that the oxygen hydrogen bond shows a difference between
Figure 74: Plots of the Laplacian of the electron density∇ vs the error model option used including standard deviation.
a) b)
c) d)
e)
minimum and maximum value of approximately 14 eÅ-5. From Figure 74 a) to d) no clear trend as for compound 1 is visible. In addition, the grouping observed for the model quality indicators is not resembled within the values of the Laplacian, as for compound 1. It can be seen that there is no obvious trend. This is also true for potassium fluorine interactions which represent regions of shallow electron density.
In Figure 75, plots of the electron density and the Laplacian for selected potassium fluorine contacts are shown. It can be seen that the electron density at the BCP does hardly vary even for this type of interaction. The Laplacian shows some variations but the distribution of the values is quite flat.
5.7 Conclusion
In conclusion it could be confirmed that asJørgensen et al stated the influence of the error model on the refined model within a multipolar model refinement is in fact minimal.[135]. If the model quality indicators are considered it seems favourable to use error model options 0 to 2. For these error model options, in both cases tested,
Figure 75: Plots of the value ofρ (right) and the Laplacian (left) at the BCP in dependence of the error model used for selected potassium fluorine contacts.
distribution of the squared differences of the experimental and calculated structure factors is more normal for these error model options. It could be shown that the model parameters are hardly deviating in dependence of the error model.
The influence on the derived properties of the electron densities has also been examined. The electron density itself has proven to be quite stable. Significant deviations have only been observed for the lithium – nitrogen bonds in compound 1. As well as the potassium – fluorine interactions they are characterised by low electron densities at the bond critical points. Therefore, it is not unexpected that these interactions show the highest deviation for the values at the BCP. However, even the distribution of the absolute values of the lithium – nitrogen and potassium fluorine interactions shows a narrow range. From the lithium – nitrogen interactions it could be shown that the relation between the electron densities for the Li2N2 ring in compound1 is preserved for all error model options.
The Laplacian, which reveals the subtle features of the electron density, shows significant deviations for the examined compounds. At least for compound 1 the deviations show a similar behaviour as the model quality indicators. However, the calculation of the estimated standard deviations (esd) within XDPROP is in the current version of the program severely limited. First of all the calculation of esds is only possible for dipole moments, and ∇ . The calculation of the esds for and∇ does at the moment only take contributions from the multipole populations into account. This means neither coordinates or thermal vibration nor the expansion contractions parameters do have an effect on the standard uncertainties.
Additionally, symmetry generated atoms are not taken into account. Furthermore, the standard deviations for atoms chemically constraint to another atom do not appear in the variance-covariance matrix on which the estimated standard uncertainties are calculated. This means meaningful esds are only calculated for atoms that are not chemically constraint to any other atom. Kaminski et al and Krause et al already addressed this topic in two different ways.Kaminski et al used a large number of measurements of α-oxalic acid dihydrate which is used for diffractometer calibration to calculate standard deviations.[145] They could thereby
show that the standard deviation of the electron density as calculated by XD2006 is in good agreement with those calculated from multiple measurements. However, their study showed that the standard deviations of the Laplacian of the electron density is underestimated by XD2006 (> 1 eÅ-5) compared to the one obtained from multiple measurements (several eÅ-5). To estimate standard deviations of the propertiesKrause et al use the refinements obtained from their implementation of Rfree.[30] Using their method, the authors showed that the standard deviation of∇ is underestimated by a factor of ten by XD2006. Bearing this in mind, even the deviations in the Laplacian can be considered insignificant.
To further confirm or falsify these results more and as different as possible compounds should be tested. Hilke Wolf already showed that for crystal structures containing only light atoms the influence on the derived parameters can be considered negligible.[146] However she did not comment on the thereupon derived properties. Especially compounds where open shell interactions with values of the Laplacian at the BCP very close to zero exist. It would be interesting to see if the value of the Laplacian changes sign from positive to negative. This would be in contrast to the definition of an open shell interaction according to Baders quantum theory of atoms in molecules. If only a singular error model option is evaluated this may be misleading.
In summary, the error model options 0 to 2 should be used to ensure the best model quality even if the model parameters and the derived properties are barely influenced.
Modern high resolution X-ray crystallography requires sufficiently brilliant sources. With the increase in brilliance it is possible to get complete datasets in less time. Furthermore, macromolecular crystallography which is usually carried out at synchrotron facilities can be achieved in house.[147] However, with increasing source intensities by using for example excillums MetalJet or new high brilliance rotating anodes the demands for the detector also rise.Howard et al elaborated on the desirable properties and characteristics an X-ray detector should have.[148] The characteristics they list are:
• detection efficiency
• linearity of response
• proportionality
• sensitivity
• dynamic range
• spectral sensitivity
• energy resolution
• spatial resolution
• stability in time
• resistance against radiation damage
From these some are of bigger importance when it comes to high resolution data measurements with high-brilliance sources. AsJakob Hey already concluded in his PhD thesis thedynamic range (which is in general defined by the ratio of the highest and smallest detectable value) is of high interest especially when using high energy X-rays (synchrotron radiation, silver or indium sources). In this case, due to the compressed reciprocal space reflections with a broad variety of intensities occur in one frame. Furthermore, the stability in time is of importance. In principle, as defined byAslanov et al this translates to the precision of the detector. This point is of great importance for modern area detectors because reflections are measured numerous times and later on used for example for computational methods like semi-empirical absorption correction.
X-Ray detectors have come a long way from Laue cameras through point detectors and charge-coupled devices (CCD) and complementary metal-oxide-semiconductor (CMOS) sensors to the most recent hybrid pixel counting and charge-integrating pixel array detectors (HPC, CPAD respectively).[149,150] During the work on this thesis the acquisition of a new specialised high resolution diffractometer for the work group was envisaged. Therefore, several tests regarding the source as well as the most suitable detector were carried out by different members of the work group. In this thesis 3 different detectors (APEXII, PHOTON
100, PILATUS3 X CdTe) from 2 manufacturers (BRUKER and DECTRIS) have been tested for their stability in time.