Topological Characterization of the Electron Density Laplacian in Crystals. The Case of the Group IV Elements

We discuss the rigorous characterization of the electron density Laplacian of crystals in terms of its topological properties: critical points (CPs), zero flux surfaces, and accumulation and depletion basins. Comparison with the atomic shell structure is exploited to characterize the numerous core critical points so that the important effort is applied to the more significant valence structure. Efficient algorithms are adapted or newly developed for the main tasks of topological study: finding the critical points, determining the 1D and 2D bundles of (3, 1) and (3, + 1) CPs, and integrating well-defined properties within the accumulation and depletion basins. As an application of the tools and concepts developed we perform a quantitative analysis of chemical bonding on group IV semiconductors, mainly devoted to the properties of the diamond phase but also including the main effects of allotropy influences on these elements. The topological analysis of the Laplacian provides a complementary and very different image than the topology of the electron density. Whereas the Laplacian graphs show a qualitative agreement with Lewis classical model, the basin population analysis excludes direct quantitative relationships with Lewis pair and octet rules. In addition to the expected core and valence basins, all group IV elements show very important interstitial basins, that accumulate a large number of electrons and dominate the compressibility behavior of the crystals.