The current thesis deals with the bonding situation of low valent tetrels. More precisely an experimental charge density study of the silylone (cAACcy)2Si[16,32,212] was carried out in order to investigate whether the bonding in this new type of molecule is best described by the dual donor-acceptor bond or if silylones should be considered silicon congeners of allenes, showing cumulated double bonds. Furthermore, this work focuses on the improvement of the precision, reliability and validity of charge density studies of such complex organometallic molecules. In the following the results of the work and possible implications for prospective studies will briefly be revised.
In the effort to improve the accuracy of charge density studies TDS was proven to be one of the most important unsolved problems in modern charge density investigations responsible for distorting the results. Since TDS is dependent on the hardness of a material, problems arising from TDS can especially show up for relatively soft organometallic molecular crystals. Therefore, a multi-temperature study was performed on di-(tris(3,5-dimethylpyrazolyl)methane)-magnesium(II) (1)[126-127] and 9-diphenylthio-phosphinoylanthracene (2)[68,128-130]. It was confirmed that TDS introduces errors to the modelled valence density[124], although the low-order reflections are not directly affected by TDS. It could be shown that the distortion of the scaling factor by the high order reflection introduces a change of the valence density. Furthermore, it could be demonstrated that the refinement of resolution-dependent scaling can be used as a validation tool to check whether a correction of TDS induced errors is needed. Typical signs for problems arising from TDS were found to be positive residual density close to or even at the atomic position as well as a u-shaped course of the scale factor with resolution.
The model was found to benefit from data integration with a drastically reduced size of the integration box. This improvement in outcome can be attributed to the peak broadening caused by the TDS contribution to the Bragg peak. However, the best way to reduce the errors introduced by TDS turned out to be the correction of the hkl-file with a correction factor 𝛼=𝑎 ∙(sin(𝜃)/𝜆)2+𝑏 ∙(sin(𝜃)/𝜆)3. An automatized routine was developed to deduce the parameters a and b from a refinement with resolution dependent scaling.
Unfortunately, no physical meaning could be attributed to the derived correction factors, which can be explained by the strong correlation between the scaling factor and the atomic displacement parameters. Therefore, a correction for other resolution dependent errors
Summary and Outlook
could not be excluded completely. Nonetheless, the temperature dependence of the correction could clearly prove that the errors in the datasets are at least partly arising from TDS.
Future studies are needed to verify TDS to be the main reason for the resolution dependent error. However, as reported in the literature the knowledge of the elastic constants is not sufficient for a proper TDS correction as the experimental setting seems to be even more important.[113,117] Therefore a data collection on a crystal with known elastic constants would not help in validating the correction factor. In order to treat TDS in a physically more meaningful way an implementation of a TDS correction as it was used for point detector data by Zavodnik et al.[80,122] would be most helpful. By analysing the peak profile of the low-order reflections, it might be possible to derive a learned profile that could be used to evaluate the peak broadening of the high order reflections. From this a correction could be calculated. However, such a correction necessarily has to be incorporated in the integration programs. Meanwhile the presented empirical corretion seems to be the best way of reducing the errors arising from TDS.[125]
The importance of a TDS correction also became apparent in the investigation of the silylone (cAAC)2Si (3). Typical signs for TDS introduced errors were found after the MM refinement.
However, using the empirical correction developed in this work the errors arising from TDS could be reduced to an acceptable level. An additional systematic error was found in the scaling of the automatically attenuated frames, which otherwise would exceed the dynamic range of the CCD detector. This error was eliminated using the program SUMMARY in the APEX II software suit[216] and a manual identification of reflections showing unusually large differences between equivalent reflections and large standard deviations. Because this procedure is very time consuming, the automatic attenuation should not be used for future charge density data collections.
Yet, especially for molecule crystals showing strong thermal motion it can be difficult to find a crystal of good size that allows the measurement of reflection up to high resolution and at the same time allows a measurement of the intense reflection within the counting rate of the detector. Suitable alternatives to circumvent these problems could be the collection of ‘fast’
scans, in which the scan interval per frame is increased or the reduction of the incident beam for complete runs. Future studies will be necessary to test the suitability of these strategies. Additionally, concerning this question further studies using the new single-photon counting hybrid pixel area detector might lead to data of outstanding quality.[145,147]
Summary and Outlook
However, using the additional corrections developed within this work the model obtained for the silylone shows an excellent quality and the topological analysis of the EDD was able to give detailed insights into its bonding situation. The two carbene carbon atoms in 3 revealed a Laplacian distribution typically found for Fischer-type carbenes. Additionally, two non-bonding VSCCs were found at the central silicon atom, indicating the presents of two non-bonding lone pairs. The indicative role of the bonding geometry of the nitrogen for the electronic state of the cAAC ligand suggested from earlier IAM studies could be confirmed by the EDD obtained from the more detailed MM. Thus the bonding situation in 3 was considered to be best described as two donor-acceptor bonds between two singlet cAAC ligands and a singlet silicon central atom of formally oxidation state zero. Thus it could be demonstrated that widening of bonding models of the main group chemistry by those originating from coordination chemistry certainly is justified, since it gives a chance to describe the untypical bonding features found in a silylone.
A comparison of the two Si–C bonds revealed a different amount of π-backdonation in the two Si–C bonds, reflected in slightly different bond length. In cooperation with the working group of Prof. Gernot Frenking it was possible to reproduce this different bonding situation via periodic solid state quantum chemical calculation at least partly. The calculations suggested that it is most likely that weak intermolecular interactions force the different π-backdonation via a different coordination angle of the two cAACs. However, further quanti-tative studies of the intermolecular interactions especially in comparison with the dimethyl substituted cAACs, which do not show this behaviour,[212] are needed in order to completely understand this effect.
A future target for further investigations of the difference between covalent and donor-acceptor Si–C bonds certainly would be the dichloride biradical precursor (cAAC)2SiCl2. However, since the crystals of this compound were found to crystallise with two slightly different polymorphs within the same crystal, an investigation by high-resolution X-ray crystallography is impossible.[195] Therefore the four-coordinate silaimine (PhC(NtBu)2)(N(Ad)SiMe3)SiN(SiMe3)[250] might be a better target molecule for the investigation of the difference of covalent and donor-acceptor bonds in silicon compounds.
A charge density investigation of this molecule would allow the comparison of covalent single and double bonds with donor acceptor bonds not only within the same molecule but at the same silicon centre.
The germanium cluster [Ge8{N(SiMe3)2}6][233] should be investigated within this work as a representative of a heavier low valent tetrel. However, it could be shown from the high-resolution data that the germanium core of the cluster shows a small disorder, while the
Summary and Outlook
ligand periphery stays in place. Therefore, a meaningful experimental charge density investigation is prevented and new insights into the bonding situation could not be drawn.
The last section of this thesis deals with the limitations of the models that can be obtained via refinement against high-resolution X-ray data. Cross-validation[31] was used as a statistical method to detect overfitting. A program was written to facilitate cross-validation for refinements performed with XD2006.[29] Two examples of the applicability of cross-validation have been carried out. Firstly, it was possible to prove that the refinement of the valence electrons of a magnesium atom in 1 is not an overfitting. Secondly, it was investi-gated for the refinement of 3, whether it is reasonable to refine a model without chemical any chemical constraint atoms and without local symmetry restrictions for the multipole parameters. Moreover, the reasonability of the refinement of the Gram-Charlier coefficients for the atoms showing signs of anharmonic motion was tested. The results indicated that a refinement of Gram-Charlier coefficients up to third order is possible without overfitting the data. However, the refinement without symmetry restriction of the multipole parameters an overfitting for most of the atoms. However, it is not for the silicon atom. Moreover, for the chemical constraints it could be shown that the refinement of individual multipole parameters for the two carbene ligands is not advisable. Yet, it was also proven that the different π-backdonation in the Si–C bonds is independent from the chemical constraints.
Further studies are needed in order to find out whether these implications concerning the local symmetry restrictions and the chemical constraints are valid for MM refinements in general. Cross-validation will give interesting insights into this topic.
Crystal Structure Determination in Collaboration