Intermolecular atomic radii

Chapter 6. The outer contour in this map is for a density of 0.001 au, which has been found to represent fairly well the outer surface of a free molecule in the gas phase, giving a value of 190 pm for the radius in the direction opposite the bond and 215 pm in the perpendicular direction. In the solid state molecules are squashed together by intermolecular forces giving smaller van der Waals radii. Figure 5.2b shows a diagram of the packing of the Cl2 molecules in one layer of the solid state structure of chlorine. From the intermolecular distances in the direction opposite the bond direction and perpendicular to this direction we can derive values of 157 pm and 171 pm for the two radii of a chlorine atom in the CI2 molecule in the solid state. These values are much smaller than the values for the free molecule in the gas phase. Clearly the Cl2 molecule is substantially compressed in the solid state. This example show clearly that the van der Waals of an atom radius is not a well defined concept because, as we have stated, atoms in molecules are not spherical and are also compressible. 

When the axial base ligand was replaced with the other amines or phosphines, several types of racemization and different reaction rates were observed [15]. In order to explain the different types and reaction rates, we defined the reaction cavity for the reactive group as shown in Fig. 1 [14,16]. The reaction cavity is represented by the concave space limited by the envelope surface of the spheres, whose centers are positions of intra- and intermolecular atoms in the neighborhood of the reactive 1-cyanoethyl group, the radius of each sphere being... 

I The e tron-acceptor ability of the Group IVA elements increases with a rise in their atomic number and, consequently, in the atomic radius. From the standpoint of structural chemistry this is, for instance, clearly illustrated by the structure of (CH3)3MCN crystals (M = Si, Ge, or Sn) in which a minimum intermolecular non-covalent contact betw n M and N atoms is 366 357 and 249 pm respectively. When M = Si this distance corresponds to the... 

The model conceptualises the solution of (noble) gases on the microscopic level as cavities built by water molecules that trap individual (noble) gas atoms. The attracting forces between water and host increase with the atomic radius and the dielectric constant of the (noble) gas. In consequence, the intermolecular forces increase with molecular mass. This explains why the ratios of elemental noble gas concentrations in water at atmospheric equilibrium are enriched with respect to the atmospheric abundance in favor of the heavier noble gases. 

In this relation, the reduced mass of colliding molecules, /x, is in atomic units, the inverse intermolecular interaction radius a is in A, and the translational gas temperatme Tq, and vibrational quantum are in kelvin. 

This book is mainly concerned with intermolecular effects, and therefore with atomic radii in connection with intermolecular contacts. These are sometimes called non-bonding radii, because they refer to contacts between atoms that are not joined by ordinary chemical bonds. For historical reasons they are also sometimes called van der Waals radii in honor of the famous pioneer of intermolecular interaction studies. A non-bonding atomic radius is rather vaguely defined as the radius of a sphere representing the usual space occupation by each atom in a molecule, so that the spheres of neighboring non-bonded atoms may not overlap. This refers both to intermolecular overlap in condensed phases, and to overlap between atoms in distant parts of the same molecule. A sensible procedure for the determination of these radii uses a careful analysis of the geometrical conditions of proximity between pairs of... 

Intrinsic molecular volume, or the volume of the envelope of atomic spheres, can easily be calculated. Let N be the number of atoms in a molecule, with nuclear positions Xj reckoned in some reference frame, say the inertial reference frame. Let Ri be the atomic intermolecular non-bonding radius of atom i, briefly called henceforth the atomic radius. Let nj be the distance between the nuclei of two atoms joined by a chemical bond. Whenever ry is smaller than the sum of atomic radii, the sphere of atom i cuts into the sphere of atom j a spherical cap of height /ly. Molecular volume, Vm, can be calculated [8,10] by computing the total volume of the atomic spheres and subtracting the volumes of the intersecting caps ... 

Figure 5.2 (a) Electron density contour map of the CI2 molecule (see Chapter 6) showing that the chlorine atoms in a CI2 molecule are not portions of spheres rather, the atoms are slightly flattened at the ends of the molecule. So the molecule has two van der Waals radii a smaller van der Waals radius, r2 = 190 pm, in the direction of the bond axis and a larger radius, r =215 pm, in the perpendicular direction, (b) Portion of the crystal structure of solid chlorine showing the packing of CI2 molecules in the (100) plane. In the solid the two contact distances ry + ry and ry + r2 have the values 342 pm and 328 pm, so the two radii are r 1 = 171 pm and r2 = 157, pm which are appreciably smaller than the radii for the free CI2 molecule showing that the molecule is compressed by the intermolecular forces in the solid state. 

These Es parameters estimated by Eq. 4 for hetero atom substituents can be combined with those originally developed for various alkyl groups as a set of steric constants for QSAR studies of aromatic systems 6). Thus, apart from the original definition for the intramolecular steric effect, the combined set of Es parameters is able to represent intermolecular steric effects as well. The original Taft E, values for unsymmetrical alkyl groups seem to represent effective steric dimension of the groups which is scaled on the same standard as those for symmetric monoatomic substituents where the effective dimension coincides with the van der Waals radius. 

There is an ill-defined boundary between molecular and polymeric covalent substances. It is often possible to recognise discrete molecules in a solid-state structure, but closer scrutiny may reveal intermolecular attractions which are rather stronger than would be consistent with Van der Waals interactions. For example, in crystalline iodine each I atom has as its nearest neighbour another I atom at a distance of 272 pm, a little longer than the I-I distance in the gas-phase molecule (267 pm). However, each I atom has two next-nearest neighbours at 350 and 397 pm. The Van der Waals radius of the I atom is about 215 pm at 430 pm, the optimum balance is struck between the London attraction between two I atoms and their mutual repulsion, in the absence of any other source of bonding. There is therefore some reason to believe that the intermolecular interaction amounts to a degree of polymerisation, and the structure can be viewed as a two-dimensional layer lattice. The shortest I-I distance between layers is 427 pm, consistent with the Van der Waals radius. Elemental iodine behaves in most respects - in its volatility and solubility, for example - as a molecular solid, but it does exhibit incipient metallic properties. 

Possibly the most important structural feature that has been revealed from crystallographic studies performed at two temperatures (298 and 125 K) is the existence of an infinite sheet network (32) of Se-Se interactions as shown in Fig. 6. At room temperature the intermolecular intra- and inferstack Se-Se distances are all similar and have values of 3.9-4.9 A, compared to the van der Waals radius sum for the selenium atom (52) of 4.0 A. However, as the temperature is lowered (298 - 125 K) rather unusual changes occur, viz. the ratio of the decrease in the interstack mfrastack Se-Se distances is not unity but is approximately 2 1 (32, 40). Thus, the distances between the chains shown in Fig. 6 decrease, on the average, by twice as much as the distances between TMTSF molecules in each stack. This most certainly leads to increased interchain bonding and electronic delocalization through the selenium atom network as the temperature is decreased (42). 

At 20°C and a pressure of 1 atm, 1 mol argon gas occupies a volume of 24.0 L. Estimate the van de Waals radius for argon from the onset of the repulsive part of the argon intermolecular potential curve in Figure 9.18, and calculate the fraction of the gas volume that consists of argon atoms. 

---