Intermolecular bond/bonding radii

The average radius of the first solvation shell is usually less than the equilibrium distance R in the Lennard-Jones potential. Each additional intermolecular bond further stabilizes the reference molecule, so an increased density can improve the stability of the system by increasing the average coordination number. 

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. 

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. 

Fig. 17a, b. Proposed lattice match between I5- column and PVA chains in the complex the intermolecular hydrogen bonds are shown by dashed lines. On the projection along the complex axis (b), solid lines outline van der Warrs radius of each molecule. O hydrogen, O carbon, OH group... 

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. 

The concept behind this theory is illustrated in Fig. 17. The vibrating molecule is approximated as a spherical cavity within a continuum solvent, and the vibrational motion is approximated as a spherical breathing of the cavity. The radius of the cavity is determined by a balancing of forces the tendency of the solvent to collapse an empty cavity, the intermolecular van der Waals attraction of the vibrator for the solvent molecules, and the intermolecular repulsion between the solvent molecules and the core of the vibrator. When the vibrator is in v = 1, the mean bond length of the vibrating bonds is longer due to anharmonicity. The increased bond length... 

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). 

A unique feature of H20 is the formation and sharing of hydrogen bonds with other molecules. Such bonds play a major role in determining the structure of both liquid and solid phases of H20. It is believed that for intermolecular spacings of less than 2 A, the two water molecules exert strong repulsive forces on each other. As such, there exists a hard sphere radius of little interpenetration of the molecules. Usually, the repulsive part of Lennard-Jones 6—12 potential can be considered appropriate to describe these repulsive characteristics. At distances of separation greater than 5 A, dipole-dipole interaction plays a dominant role. This is reasonable, because each H20 molecule has a large dipole moment, p = 1.84 D. 

There are short intermolecular Te— Te distances (3.864 A) in the parent 1,3-ditellurole system (1) as compared to the covalent radius of Te the following bond lengths (A) and angles were found <85JA6298>. 

Each molecule is tetrahedrally co-ordinated by only four others and the intermolecular distance is only 2 76 A, so that the effective radius of the water molecule is 1-38 A. The distinctive features of this structure—the low co-ordination and the short intermolecular distance—as well as the relatively high melting point of ice, all point to the existence of hydrogen bonds binding the molecules together. 

The van der Waals radius determines the shortest distance over which intermolecu-iar forces operate it is aiways larger than the covalent radius. Intermolecular forces are much weaker than bonding (intramolecular) forces. Ion-dipole forces occur between ions and poiar molecules. Dipole-dipole forces occur between oppositely charged poles on polar molecules. Hydrogen bonding, a special type of dipole-dipole force, occurs when H bonded to N, O, or F is attracted to the lone pair of N, O, or F in another molecule. Electron clouds can be distorted (polarized) in an electric field. Dispersion (London) forces are instantaneous dipole-induced dipole forces that occur among all particles and increase with number of electrons (molar mass). Molecular shape determines the extent of contact between molecules and can be a factor in the strength of dispersion forces. 

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