Interpretation of Experimental Charge Densities. The study of chemical bonding

Abstract

The first question to be discussed here is what kind of diffraction theory is applicable to the sample under study. The range between kinematical and dynamical theory is so wide that the problem has to be considered very seriously. It is necessary to consider the relative influence of thermal diffuse scattering versus Bragg scattering, in order to obtain the average of the structure factors over the lattice modes. A limit of resolution results from the series termination error: the neglect of core polarisation and the necessity to define a deformation density; obtained by subtracting isolated vibrating atoms. Various sources of error are discussed, and especially the problems related to the scale factor. The experiments are concluded to be more reliable than most calculations at a distance larger than 0.3 Å from the nuclei. The analysis can be done either in real or reciprocal space. A qualitative description of the possible types of bonding has been undertaken few years ago and a systematisation is now becoming possible. The "chemical bonds" are described in different terms depending whether one looks at the total or deformation density. To go towards a quantitative description, two major problems have to be solved: the influence of thermal motion on the density or the molecular properties, and the definition of proper molecular regions in the solid. It should be kept in mind that intermolecular effects are now in the domain of observability and therefore a combination of theoretical and experimental work should become very fruitful for the study of crystalline forces. In reciprocal space, the problem is to find models that represent the structure factor. It is possible to think in terms of an orbital expansion: one has to deal with the very complicated two center form factors, and an attribution of a temperature factor to these factors is impossible. Better models are based in a functional partitioning of the density in terms of deformation functions around each nucleus. A careful study of correlation between different functions leads to a multipolar expansion. But, in order to deduce unbiased properties, the influence of internal modes of vibration has to be considered carefully. An interplay with other techniques is necessary if one wants to get precise information on the density near atomic positions.