A topological analysis of charge densities in diamond, silicon and germanium crystals

The Hansen-Coppens multipole model of charge density has been fitted to highly accurate published experimental and theoretical structure factors for diamond, silicon and germanium crystals. Analysis of both model experimental and theoretical charge densities using the resulting model parameters was performed in terms of Bader's topological theory. The general topology of the charge density appeared to be identical for all crystals, containing the four possible types of critical points of rank three, and no non-nuclear attractors between neighboring atoms were found within achieved accuracy. Theoretical and experimental values of charge density and its Laplacian show quantitative and semiquantitative agreement, respectively, at the critical points of model charge densities. For Ge crystals, such agreement is worse at the ring critical point. These results suggest the possibility of semiquantitative (within 10-30%) study of the topological characteristics of highly accurate X-ray charge densities of crystals displaying shared interatomic interactions. Comparative topological analysis of the chemical bond in this series of crystals is discussed in terms of the quantum topological theory.