A TOPOLOGICAL ANALYSIS OF CHARGE-DENSITIES IN DIAMOND, SILICON AND GERMANIUM-CRYSTALS

The Hansen-Coppens multipole model of charge density has been fitted t o highly accurate published experimental and theoretical structure fac tors for diamond, silicon and germanium crystals. Analysis of both mod el experimental and theoretical charge densities using the resulting m odel parameters was performed in terms of Bader's topological theory. The general topology of the charge density appeared to be identical fo r 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 val ues of charge density and its Laplacian show quantitative and semiquan titative agreement, respectively, at the critical points of model char ge densities. For Ge crystals, such agreement is worse at the ring cri tical point. These results suggest the possibility of semiquantitative (within 10-30%) study of the topological characteristics of highly ac curate X-ray charge densities of crystals displaying shared interatomi c interactions. Comparative topological analysis of the chemical bond in this series of crystals is discussed in terms of the quantum topolo gical theory.