ANHARMONIC MOTION VS CHEMICAL BONDING - ON THE INTERPRETATION OF ELECTRON-DENSITIES DETERMINED BY X-RAY-DIFFRACTION

Anharmonic and electron-density refinements against accurate X-ray dif fraction data are today almost routine. However, the unambiguous ident ification and separation of effects due to anharmonic atomic motion an d to chemical bonding is impossible with a single X-ray data set and d ifficult even with data measured at different temperatures, especially in heavy-atom compounds. For cubic site symmetry, analytical expressi ons are compared for the convolutions of: (i) the electron density of a spherical free atom with an anharmonic probability density distribut ion (p.d.f.); and (ii) an aspherical atom with a Gaussian p.d.f. If bo th the free atom and the deformation functions of the aspherical atom are represented by Gaussian-type functions, there exists for every set of anharmonic parameters an equivalent set of aspherical-atom paramet ers but the reverse is not necessarily true. Both models are usually s uitable for parametrizing anharmonicity also in the case of real atoms and exponential-type deformation functions. Contrary to widespread be lief, both models predict a qualitatively similar change of the aspher ical density with decreasing temperature: the extrema move towards the atom center and their heights increase except at low temperatures. Qu antitatively, however, the temperature dependence of the adjusted para meters should be different: in the case of anharmonicity, the second-, third- and fourth-order coefficients should be proportional to T, T-2 and T-3, respectively, while the population factors of the deformatio n functions should be independent of T. The theory is tested and verif ied with refinements on calculated and on measured X-ray structure amp litudes for K2PtCl6 at room temperature and at 100 K, and Si at room t emperature. Results for K2PtCl6 agree well with the anharmonic model. In Si at room temperature, the two effects overlap only slightly and c an be reasonably well identified; they cannot be distinguished with si mulated high-temperature data.