Radius, van der Waals

Figure 2-118, Cross-section of the 3D model of formic add (HCOOH), The van der Waals radius of each atom of the molecule is taken and by fusing the spheres the van der Waals surface is...

When a specific value above is n ot hn own, the rule of Pauling (the van der Waals radius is approximately 0.76 A larger than the cova-len t radiiis) is u sed. 

Figure 4-15 A van der Waals Potential Energy Function. The Energy minimum is shallow and the interatomic repulsion energy is steep near the van der Waals radius.

FIGURE 1 6 Molecular models of methane (CH4) (a) Framework (tube) models show the bonds connecting the atoms but not the atoms themselves (b) Ball and stick (ball and spoke) models show the atoms as balls and the bonds as rods (c) Space filling models portray overall molecular size the radius of each sphere approximates the van der Waals radius of the atom (d) An electrostatic potential map of methane... 

Van der Waals radius (Section 2 17) A measure of the effec tive size of an atom or a group The repulsive force between two atoms increases rapidly when they approach each other at distances less than the sum of their van der Waals radii Van der Waals strain (Section 3 2) Destabilization that results when two atoms or groups approach each other too closely Also known as van der Waals repulsion Vicinal (Section 6 14) Describing two atoms or groups at tached to adjacent atoms... 

IP, ionization potential [/], EA, electron affinity [7], av atom polanzabihty [2], r, van der Waals radius [3], Xp- Pauling electronegativity... 

V, Charton stenc parameter [176], r, eftecuve van der Waals radius... 

Van der Waals radius (Section 2.17) A measure of the effective size of an atom or a group. The repulsive force between two atoms increases rapidly when they approach each other at distances less than the sum of their van der Waals radii. 

It is obvious, fipom some of the series of substituents in Table 7-11, that the steric constant reflects intuitive notions of group size, and Taft " pointed out close parallels with van der Waals radii. For asymmetrical groups a single van der Waals radius cannot be defined, and the situation is complicated by conformational flexibility. Nevertheless, empirical relationships can be established, and Kutter and Hansch gave Eq. (7-55),... 

Atom Van der Waals radius, nm Covalent radius, nm Atom represented to scale... 

The molecular and bulk properties of the halogens, as distinct from their atomic and nuclear properties, were summarized in Table 17.4 and have to some extent already been briefly discussed. The high volatility and relatively low enthalpy of vaporization reflect the diatomic molecular structure of these elements. In the solid state the molecules align to give a layer lattice p2 has two modifications (a low-temperature, a-form and a higher-temperature, yS-form) neither of which resembles the orthorhombic layer lattice of the isostructural CI2, Br2 and I2. The layer lattice is illustrated below for I2 the I-I distance of 271.5 pm is appreciably longer than in gaseous I2 (266.6 pm) and the closest interatomic approach between the molecules is 350 pm within the layer and 427 pm between layers (cf the van der Waals radius of 215 pm). These values are... 

For each atom type there are two parameters to be determined, the van der Waals radius and the atom softness, Rq and, It should be noted that since the van der Waals energy is calculated between pairs of atoms, but parameterized against experimental data, the derived parameters represent an effective pair potential, which at least partly includes many-body contributions. 

The simplest shape for the cavity is a sphere or possibly an ellipsoid. This has the advantage that the electrostatic interaction between M and the dielectric medium may be calculated analytically. More realistic models employ moleculai shaped cavities, generated for example by interlocking spheres located on each nuclei. Taking the atomic radius as a suitable factor (typical value is 1.2) times a van der Waals radius defines a van der Waals surface. Such a surface may have small pockets where no solvent molecules can enter, and a more appropriate descriptor may be defined as the surface traced out by a spherical particle of a given radius rolling on the van der Waals surface. This is denoted the Solvent Accessible Surface (SAS) and illustrated in Figm e 16.7. 

Valence, 286 Valence electrons, 269 and ionization energies, 269 Vanadium atomic radius, 399 eleciron configuration, 389 oxidation numbers, 391 pentoxide catalyst, 227 properties, 400, 401 van der Waals forces, 301 elements that form molecular crystals using, 301 and molecular shape, 307 and molecular size, 307 and molecular substances, 306 and number of electrons, 306 van der Waals radius, 354 halogens, 354 Vanillin, 345... 

The radii av a2 and coordination numbers zv z2 follow from x-ray analysis (cf. Section I.B), and aQ/2 — 1.25 A corresponds to Pauling s van der Waals radius of 1.40 A for a covalently bound oxygen atom.25 The value of eQlk — 166.9°K was chosen to obtain agreement between calculated and experimental values of the equilibrium vapor pressure of argon hydrate at 0°C. 

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