Determination of Atom-Surface van der Waals Potentials from Transmission-Grating Diffraction Intensities
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Molecular beams of rare gas atoms and ${\mathrm{D}}_{2}$ have been diffracted from 100-nm-period ${\mathrm{SiN}}_{x}$ transmission gratings. The relative intensities of the diffraction peaks out to the eighth order depend on the diffracting particle and are interpreted in terms of effective slit widths. These differences have been analyzed by a new theory which accounts for the long-range van der Waals ${\ensuremath{-}C}_{3}/{l}^{3}$ interaction of the particles with the walls of the grating bars. The values of the ${C}_{3}$ constant for two different gratings are in good agreement and the results exhibit the expected linear dependence on the dipole polarizability.Atomic radius
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Existing neutron diffraction data for hydrogen-bonded solids have been studied in the light of the van der Waals criterion for hydrogen bonding. It was found that for the formation of A--H. . .B bonds the distance A. . .B should be less than the sum of the A-H covalent bond distance, the van der Waals radius of H and that of B. It has also been shown that with decrease in A. . . B distance, the A--H bond extends in a quantitative manner irrespective of what atoms A and B are. Particularly, for A-H. . .A bonds when the overlap of the van der Waals radii of two A atoms exceeds a certain high value, the A-H bond is extended so much that the H atom is placed at the midpoint between A and A resulting in a symmetrical hydrogen bond.
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A review of gas-phase spectroscopic data of van der Waals complexes shows that heteroatomic contacts are systematically longer and their energies lower than the averages for corresponding homoatomic ones. The differences depend on electronic polarisabilities α of contacting atoms, according to empirical formulae Δrw = c[(α2 – α1)/α1]⅔ (α1 < α2) and ΔE = a(α2 – α1)n (n = 1–1.2). A novel system of van der Waals radii, corrected for this effect, is suggested for rare gases, H, N, O, halogens and metals; for di- and poly-atomic molecules as well as for isolated atoms.
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Jellium
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The van der Waals volume is a widely used descriptor in modeling physicochemical properties. However, the calculation of the van der Waals volume (V(vdW)) is rather time-consuming, from Bondi group contributions, for a large data set. A new method for calculating van der Waals volume has been developed, based on Bondi radii. The method, termed Atomic and Bond Contributions of van der Waals volume (VABC), is very simple and fast. The only information needed for calculating VABC is atomic contributions and the number of atoms, bonds, and rings. Then, the van der Waals volume (A(3)/molecule) can be calculated from the following formula: V(vdW) = summation operator all atom contributions - 5.92N(B) - 14.7R(A) - 3.8R(NR) (N(B) is the number of bonds, R(A) is the number of aromatic rings, and R(NA) is the number of nonaromatic rings). The number of bonds present (N(B)) can be simply calculated by N(B) = N - 1 + R(A) + R(NA) (where N is the total number of atoms). A simple Excel spread sheet has been made to calculate van der Waals volumes for a wide range of 677 organic compounds, including 237 drug compounds. The results show that the van der Waals volumes calculated from VABC are equivalent to the computer-calculated van der Waals volumes for organic compounds.
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Abstract Due to the paucity of data on non-bonding interactions for metal atoms, no complete tabulation is available for crystallographic van der Waals radii for metallic elements. In this work several sets of van der Waals radii for metal atoms are derived indirectly. Unique data resources used for the derivation are (i) average volumes of elements in crystals, (ii) single covalent radii, (iii) Allinger´s van der Waals radii, as well as (iv) bond valence parameters for metal-oxygen bonds. The van der Waals radii for metal atoms deduced from these various approaches are basically comparable with each other, but are strikingly different from those from Bondi’s system of van der Waals radii. A complete set of new values for metallic elements up to Am, derived from bond valence parameters, are recommended.
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We employ natural steric analysis (introduced in a previous paper) to evaluate a set of effective ab initio van der Waals radii for free and covalently bonded atoms and ions of H–Ar (Z=1–18) determined using a helium atom probe. We critically examine the degree of anisotropy, dependence on charge state, and other intrinsic limitations of a simple atomic van der Waals hard sphere representation of the accurate steric surface. We also evaluate the ab initio steric force (gradient of steric energy at van der Waals contact) as a measure of “hardness” of the atomic van der Waals spheres. Comparison with empirical van der Waals radii shows reasonable agreement (within the acknowledged uncertainties of the latter values in the most important cases), but suggest a wider range of variability and anisotropy than could be adequately represented by any fixed constant radius. Simple expressions for incorporating the dependence on natural atomic charge or correcting for other types of intermolecular contact are given, extending the accuracy and usefulness of the atomic van der Waals sphere concept.
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Plot of the van der Waals surface of various molecules. The van der Waals surface of a molecule is represented by treating each atom as a sphere with the van der Waals radius. Covalently bonded polyatomic molecules will be smaller than the sum of van der Waals surfaces due to the overlap of intersecting spheres.
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