The Quantum Theory of Atoms in Molecules, due to Bader, is applied to periodic systems. Results for molecular and crystalline urea are presented. Changes in both bond critical points and atomic properties due to changes of chemical environment are described. A rationale for the different lengths of the in-plane and out-of-plane hydrogen bonds and for the lengthening of the CO bond in bulk urea is provided in terms of the properties of the Laplacian of the oxygen atom electron density distribution. An evaluation of molecular and atomic volume changes indicates that the decrease of molecular volume upon change of phase from gas to solid originates primarily from a contraction of the atomic basins directly involved in hydrogen bonds. Other atoms show a small expansion. The considerable decrease of oxygen and hydrogen atomic volumes is related to the mutual penetration of their van der Waals envelopes following hydrogen bond formation. The results confirm that urea is more polar in the solid phase.

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 Crystal (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 stud ies 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.

Helium is generally understood to be chemically inert and this is due to its extremely stable closed-shell electronic configuration, zero electron affinity and an unsurpassed ionization potential. It is not known to form thermodynamically stable compounds, except a few inclusion compounds. Here, using the ab initio evolutionary algorithm USPEX and subsequent high-pressure synthesis in a diamond anvil cell, we report the discovery of a thermodynamically stable compound of helium and sodium, Na₂He, which has a fluorite-type structure and is stable at pressures >113 GPa. We show that the presence of He atoms causes strong electron localization and makes this material insulating. This phase is an electride, with electron pairs localized in interstices, forming eight-centre two-electron bonds within empty Na₈ cubes. We also predict the existence of Na₂HeO with a similar structure at pressures above 15 GPa.