Theoretical calculation of the time-averaged electron density distribution for vibrating ethyne molecules in a model crystal structure

Calculations have been made on an ethyne model structure to investigate the influence of internal and external thermal motions of the molecules in a crystal on the time-averaged electron density distribution as obtained by X-ray diffraction. The density distributions in the chemical bonds have been studied from D(r) = Q(mol, r)-Q(at, r) difference maps, where Q(at, r) is the density of the free-atom structure. Vibrations expected to occur at low temperatures reduce the difference densities at the centres of the C-C and C-H bonds by 12 and 23% respectively. Reliable time-averaged difference density distributions can be calculated from the static distributions obtained by theory by use of the root-mean-square deviations (u²)^1/2 of the atoms which can be determined by X-ray diffraction. Only negligibly small errors occur in the theoretical difference density maps if librations are accounted for by linear vibrations. In the experimental [F_o-F_c] difference densities errors due to treating librations as linear vibrations are largely, but not completely, compensated by shifts of the atoms.