Chemical bonding in crystals: new directions

Analysis of the chemical bonding in the position space, instead of or besides that in the wave function (Hilbert) orbital space, has become increasingly popular for crystalline systems in the past decade. The two most frequently used investigative tools, the Quantum Theory of Atoms in Molecules and Crystals (QTAIMAC) and the Electron Localization Function (ELF) are thoroughly discussed. The treatment is focussed on the topological peculiarities that necessarily arise from the periodicity of the crystal lattice and on those facets of the two tools that have been more debated, especially when these tools are applied to the condensed phase. In particular, in the case of QTAIMAC, the physical and chemical significance of the bond paths for the very weak or the supposedly repulsive interactions, the distinctive features and the appropriateness of the several schemes that have been proposed to classify chemical bonds, and, finally, the relative importance of the local and integrated electron density properties for describing intermolecular interactions. In the case of the ELF, particular attention is devoted to how this function is formulated and to the related physical meaning, and to how can the ELF be chemically interpreted and properly analysed in crystals. Several examples are reported to illustrate all these points and for critically examine the answers obtained and the problems encountered. The discussed examples encompass the case of molecular crystals, Zintl phases, intermetallic compounds, metals, supported and unsupported metal-metal bonds in organometallics, ionic solids, crystal surfaces, crystal defects, etc. Whenever possible joint ELF and QTAIMAC studies are considered, with particular emphasis on the comparison of the bond description afforded by the ELF and the Laplacian of the electron density. Two recently proposed functions, the Localized Orbital Locator (LOL) and the Source Function in its integrated or local form are also presented, in view of their potential interest for studies of chemical bonding in crystals. The use of approximated ELF and LOL, as derived from the density functional form of the positive kinetic energy density, is also discussed.