The available data on the van der Waals radii of atoms in molecules and crystals are summarized. The nature of the continuous variation in interatomic distances from van der Waals to covalent values and the mechanisms of transformations between these types of chemical bonding are discussed.

Van der Waals Radii of Elements

Photon cross sections from 1 keV to 100 MeV for elements Z=1 to Z=100

Irena, a tool suite for analysis of both X-ray and neutron small-angle scattering (SAS) data within the commercial Igor Pro application, brings together a comprehensive suite of tools useful for investigations in materials science, physics, chemistry, polymer science and other fields. In addition to Guinier and Porod fits, the suite combines a variety of advanced SAS data evaluation tools for the modeling of size distribution in the dilute limit using maximum entropy and other methods, dilute limit small-angle scattering from multiple non-interacting populations of scatterers, the pair-distance distribution function, a unified fit, the Debye–Bueche model, the reflectivity (X-ray and neutron) using Parratt's formalism, and small-angle diffraction. There are also a number of support tools, such as a data import/export tool supporting a broad sampling of common data formats, a data modification tool, a presentation-quality graphics tool optimized for small-angle scattering data, and a neutron and X-ray scattering contrast calculator. These tools are brought together into one suite with consistent interfaces and functionality. The suite allows robust automated note recording and saving of parameters during export.

Irena: tool suite for modeling and analysis of small-angle scattering

Starting from a microscopic tight-binding model and using second-order perturbation theory, we derive explicit expressions for the intrinsic and Rashba spin-orbit interaction induced gaps in the Dirac-like low-energy band structure of an isolated graphene sheet. The Rashba interaction parameter is first order in the atomic carbon spin-orbit coupling strength $\ensuremath{\xi}$ and first order in the external electric field $E$ perpendicular to the graphene plane, whereas the intrinsic spin-orbit interaction which survives at $E=0$ is second order in $\ensuremath{\xi}$. The spin-orbit terms in the low-energy effective Hamiltonian have the form proposed recently by Kane and Mele. Ab initio electronic structure calculations were performed as a partial check on the validity of the tight-binding model.

Intrinsic and Rashba spin-orbit interactions in graphene sheets

The hydration of the alkali metal ions in aqueous solution has been studied by large angle X-ray scattering (LAXS) and double difference infrared spectroscopy (DDIR). The structures of the dimethyl sulfoxide solvated alkali metal ions in solution have been determined to support the studies in aqueous solution. The results of the LAXS and DDIR measurements show that the sodium, potassium, rubidium and cesium ions all are weakly hydrated with only a single shell of water molecules. The smaller lithium ion is more strongly hydrated, most probably with a second hydration shell present. The influence of the rubidium and cesium ions on the water structure was found to be very weak, and it was not possible to quantify this effect in a reliable way due to insufficient separation of the O–D stretching bands of partially deuterated water bound to these metal ions and the O–D stretching bands of the bulk water. Aqueous solutions of sodium, potassium and cesium iodide and cesium and lithium hydroxide have been studie...

A study of the hydration of the alkali metal ions in aqueous solution.

Incoherent scattering factors for all spherically symmetric free atoms have been computed from numerical SCF Hartree—Fock wavefunctions. The complete Waller—Hartree theory with all exchange terms has been used.

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Compton Scattering Factors for Spherically Symmetric Free Atoms

Radii corresponding to the principal maxima in the radial distribution functions r2ψi2(r) have been obtained for the ground states of all the atoms in the periodic table. The relativistic wavefunctions employed were solutions of the Dirac equations. Slater's ρ⅓ method for including exchange and Latter's method for the self‐interaction correction were used in ``creating'' the potential.The radii corresponding to these maxima are used as measures of the size of each orbital. The relation between the orbital radii of the valence electrons is shown as plots for the first, second, and third series of transition elements.In the elements below nobelium, only four maxima occur in the total charge‐density function. The relation of these maxima to the shell structure of the atom and the effect of shielding by outer electrons are discussed. The effect of the relativistic contraction on orbitals of low angular momentum is shown.

Orbital Radii of Atoms and Ions

Incoherent scattering factors for all aspherical free atoms have been computed from numerical SCF Hartree–Fock wavefunctions. The complete Waller–Hartree theory with all exchange terms has been used.

Don T. Cromer

Papers

Compton Scattering Factors for Spherically Symmetric Free Atoms

Orbital Radii of Atoms and Ions

Compton scattering factors for aspherical free atoms.