The electron density : experimental determination and theoretical analysis
Two related lines of research in experimental electron density determination are reported in this thesis. In the first case, the well-proven and popular multipole modeling technique is applied to three high resolution, single-crystal X-ray diffraction data sets. The preliminary part of this thesis (Chapters 2-5) deals with the theoretical aspects of the multipole model, and also some of the theoretical and practical aspects of data collection and reduction. Chapter 6 reports an experimental charge density determination of a nitrogen ylide. Chapter 7 contains details of the treatment of data from a large, pendant-arm macrocyclic complex of nickel, while Chapter 8 reports the characteristics of the experimentally determined charge density for a substituted acetylene molecule which exhibits interesting intramolecular interactions. The charge densities for all three cases are analysed using Bader's Theory of Atoms in Molecules. The latter part of this thesis deals with more novel ways of treating experimental data. Chapter 9 gives a thorough review of the literature on the application of Maximum Entropy techniques to image reconstruction in general and charge density determination in particular, followed in Chapter 10 by an application to diffraction data from the cubic phase of acetylene. The novel approach of removing core scattering from the data is developed and gives improved results. Chapter 11 reviews some aspects of fermion density matrices and their relationship to electron density functions and X-ray scattering, followed in Chapter 12 by results from the density matrix refinement method applied to diffraction data from formamide. Particular emphasis is placed upon basis set effects, idempotency and various N-representable approximations to the experimentally determined density matrix.