- Maximum-Entropie-Methode (1) (remove)
- Accurate charge densities of amino acids and peptides by the Maximum Entropy Method (2008)
- In the present thesis accurate charge densities of several amino acids and peptides have been reconstructed by the Maximum Entropy Method (MEM) to study chemical bonds. The MEM model-independently determines the most probable electron density, which simultaneously maximizes the information entropy and fits the X-ray diffraction data. The quality of the MEM densities is enhanced by several extensions to the MEM such as the use of a non-uniform prior-density, the employment of the method of prior-derived F-constraint, static weighting and the choice of the optimal stopping criterion for the MEM iterations. The latter is achieved by inspection of difference Fourier maps and dynamic deformation maps. The reconstructed electron densities have been analyzed according to Baders Atoms in Molecules (AIM) theory to derive information about chemical bonds, in particular covalent bonds and hydrogen bonds. Local maxima of the densities, their associated atomic basins and charges, bond critical points (BCPs) and their densities and second derivatives, i.e. the eigenvalues and the Laplacians, have been determined according to the AIM theory. For all studied compounds it is shown that, providing the employment of the extensions to the MEM, the densities obtained from the MEM exhibit similar properties as those obtained from the multipole method. However, it is demonstrated that the features of hydrogen bonds are described more convincingly by the MEM than by the multipole method. By comparison of densities at BCPs from the MEM with the corresponding values from multipole refinement and from quantum chemical calculations it is shown that each method produces similar densities at BCPs. For all studied compounds it is demonstrated that for MEM densities, densities at BCPs of hydrogen bonds possess a larger magnitude than corresponding values from densities by the multipole method, while the opposite is true for covalent bonds. The values of the Laplacians at BCPs, especially of C–O bonds, show larger discrepancies between values from the MEM and from multipole refinement. These differences are caused by thermal motion which is present in dynamic MEM densities, but absent in static densities produced by the multipole method. The results of the extensive study of electron densities of amino acids and tripeptides show that densities and energetic properties at BCPs of covalent bonds and hydrogen bonds depend exponentially on their bond lengths. The functions of the dependencies of the densities on the bond lengths differ from the corresponding functions fitted to values from the multipole method. It is demonstrated that the ratio of the potential and kinetic energy densities at BCPs of hydrogen bonds reveals the possibility to classify them according to the distance between hydrogen atom and acceptor atom. Short hydrogen bonds possess covalent character, hydrogen bonds with intermediate distance have a mixed covalent-ionic character and long hydrogen bonds are ionic. This classification coincides with the usual classification of strong, intermediate and weak hydrogen bonds as proposed in the literature. The studied hydrogen bonds are classified as possessing mainly a mixed covalent-ionic character. However, for covalent bonds a classification according to the bond lengths does not suffice to characterize them. The results of the amino acids and tripeptides indicate that the prior density contributes a large part to the densities at BCPs. However, for the Laplacians and the energy densities at BCPs the differences between MEM and prior densities are larger than for the densities at BCPs. Densities at BCPs of hydrogen bonds from MEM densities show a different trend in their dependence on the bond distance than corresponding trends from prior densities. Thus, it is demonstrated that the analysis of the true density instead of the prior or procrystal density is recommended in order to extract information about chemical bonding. It is concluded from the results of the Accurate Charge Density studies reported in the present thesis, that the MEM allows a good characterization of chemical bonds and describes the electron density of hydrogen bonds more realistic than the multipole model. Chapter 3 of the present thesis has been published in Acta Crystallogr. B, 63, 285–295 (2007) and is reproduced with permission of the International Union of Crystallography (http://journals.iucr.org). Chapter 4 of the present thesis has been published in CrystEngComm, 10, 335–343 (2008) and is reproduced with permission of The Royal Society of Chemistry (RSC) (http://www.rsc.org).