Electron Densities from Gas-Phase Electron Diffraction Intensities. I. Preliminary Considerations

The intensity of electrons and x rays scattered by a freely rotating molecule is determined, in the kinematic approximation, solely by the nuclear–nuclear, electron–nuclear, and electron–electron radial distribution functions of the molecule. Although these functions are one‐dimensional, the latter two contain some information about the three‐dimensional distribution of electrons in the molecule because the electrons are distributed relative to several nuclear reference positions and the spatial distribution of the nuclei is known. The purpose of this series of papers is to investigate the extent to which this information can be deciphered. Although published accounts have purported to show that the electron density $\mathrm{\rho (r)}$ can be determined uniquely from the scattered intensity, we demonstrate that, in fact, the transfomation is not unique. Nevertheless, if certain, not unreasonable, restrictions are imposed upon the form of $\mathrm{\rho (r)}$ , it becomes possible to make fairly detailed inferences about the three‐dimensional character of the density. We propose a procedure which, although not guaranteeing a unique transformation, provides a means for deriving chemically significant knowledge about the molecular electron density from experimental gas‐phase intensities.