Badania rozkładu gęstości elektronowej w kryształach, czyli jak zobaczyć szczegóły struktury elektronowej cząsteczek

X-ray structural analysis might be regarded as a method of visualizing molecules as they appear in the crystals. The model, which is conventionally and universally used in this method, the Independent Atom Model (IAM) assumes that the electron density distribution, which scatters the X-rays is built of the spherically-symmetrical, neutral atoms. This model is responsible for the unprecedented success of X-ray structural analysis, which reflects in about one million crystal structures (i.e. the sets coordinates of the atoms constituting the molecules) deposited in the various databanks (cf. Fig. 1), and in the speed and accuracy which the method has reached. In principle, in few hours one can get the complete information about the crystal structure. But this success is accompanied by negligence of the scientific virtue hidden beyond the IAM. In fact, it was known from the very beginning of the X-ray diffraction studies by von Laue and Braggs, that some fine details of the electron density distribution should be available. The technological advance (four-circle diffractometers, powerful X-ray sources, fast computers etc.) caused that in 1960’s the time was ripe for the development of the experimental studies of details of electron density distribution in the crystals, beyond the IAM. The early experiments by Coppens and co-workers proved that this information – about the electron density transferred to the covalent bonds, lone pairs, even intermolecular interactions – can actually be obtained and analyzed (Fig. 2). The need for the model which could be used in the least-squares procedure led to the formulation of so-called pseudoatom models, including the most popular till now, Hansen-Coppens model (eq. 2) in which the aspherical part is described in terms of real spherical harmonics. In this paper, the basics of the electron density studies is described in some detail, including the step-by-step description of a typical procedure from the experiment to the final steps of refinement. An example of the analysis of the high-resolution structure of 1,2-dimethyl-4-nitro-5-morpholine-imidazole hydrate is used to show an application of this method in studying the intermolecular interactions, including weak C-H···O and C-H···N hydrogen bonds. It is shown that the multipolar model is able to deliver more informations than the promolecular model with spherically symmetrical electron distributions.