Charge density analysis

Clearly the CCD data is adequate for a charge density analysis. It is also possible that the weak data, contrary to popular wisdom, is actually better than that from point... 

Least-Squares Methods and Their Use in Charge Density Analysis... 

In addition to the positional and thermal parameters of the atoms, least-squares procedures are used to determine the scale of the data, and parameters such as mosaic spread or particle size, which influence the intensities through multiple-beam effects (Becker and Coppens 1974a, b, 1975). It is not an exaggeration to say that modern crystallography is, to a large extent, made possible by the use of least-squares methods. Similarly, least-squares techniques play a central role in the charge density analysis with the scattering formalisms described in the previous chapter. 

Least-Squares Methods in Charge Density Analysis 73 each of which is known to depend linearly on a set of m parameters... 

Least-Squares Methods in Charge Density Analysis 75... 

Diamond (1966) has applied a filtering procedure in the refinement of protein structures, in which poorly determined linear combinations are not varied. In charge density analysis, the principal component analysis has been tested in a refinement of theoretical structure factors on diborane, B2H6, with a formalism including both one-center and two-center overlap terms (Jones et al. 1972). Not unexpectedly, it was found that the sum of the populations of the 2s and spherically averaged 2p shells on the boron atoms constitutes a well-determined eigenparameter, while the difference is very poorly determined. Correlation between one- and two-center terms was also evident in the analysis. 

Octahedral and distorted octahedral complexes of first-row transition metal atoms were subjected to X-ray charge density analysis in the pioneering studies of Iwata and Saito in the early 1970s (Iwata and Saito 1973). 

The bonding features in the charge density are pronounced in crystals with extended covalent networks. The availability of perfect silicon crystals has allowed the measurement of uncommonly accurate structure factors, of millielectron accuracy. The data have served as a test of experimental formalisms for charge density analysis, and at the same time have provided a stringent criterion for quantum-mechanical methods. 

The suitability of light-atom crystals for charge density analysis can be understood in terms of the relative importance of core electron scattering. As the perturbation of the core electrons by the chemical environment is beyond the reach of practically all experimental studies, the frozen-core approximation is routinely used. It assumes the intensity of the core electron scattering to be invariable, while the valence scattering is affected by the chemical environment, as discussed in chapter... 

Gatti C, Macchi P (eds) (2011) Modem charge density analysis. Springer... 

Charge density analysis has been carried out for three reaction paths involving intramolecular hydrogen transfer the keto-enol tautomerism of acetaldehyde, the pinacol rearrangement of protonated ethane-1,2-diol, and the unimolecular decomposition of methanediol, reactions involving H-transfer between C O, C C, and O O atoms.288... 

T.S. Koritsanszky and P. Coppens, Chemical Applications of X-ray Charge-Density Analysis, Chem. Rev. 

A preliminary knowledge of the crystal structure is important prior to a detailed charge density analysis. Direct methods are commonly used to solve structures in the spherical atom approximation. The most popular code is the Shelx from Sheldrick [26] which provides excellent graphical tools for visualization. The refinement of the atom positional parameters and anisotropic temperature factors are carried out by applying the full-matrix least-squares method on a data corrected if found necessary, for absorption and diffuse scattering. Hydrogen atoms are either fixed at idealized positions or located using the difference Fourier technique. 

A charge density analysis reveals that the carbene carbon atom of the unsaturated carbene has a higher absolute and relative pTt(C ) occupancy than the saturated counterpart... 

Thus, while the X-ray method of charge density analysis does not suffer from some of the ambiguities of the theoretical calculations, the measurements give information on a molecule in a particular environment and not on the isolated state commonly treated in theoretical work. Nevertheless the absence of strong interactions in the FeTPP crystal leads to the conclusion that the ground state of this molecule in its isolated state is close to the 3 ... 

Smith, V. H., Jr. Concepts of charge density analysis the theoretical approach. In Electron Distributions and the Chemical Bond. (Eds., Coppens, P., and Hall, M. B.) pp. 3-59. Plenum New York, London (1982). 

---