The van der Waals Bond

Elements of Rayleigh-Schrodinger (RS) Perturbation Theory Molecular Interactions 

2 Expanded Energy Corrections up to Second Order The Two-state Model of Long-range Interactions 

3 Atom-Linear Dipolar Molecule Induction The Cg Dispersion Coefficient for the H-H Interaction The van der Waals Bond 

In the previous chapters we sketched an elementary model of the chemical bond occurring between atoms in terms of a simple Hiickel theory mostly involving solution of 2 x 2 secular equations. The theory, first concerned with o--bonding in 2 i U2, Hc2, Hei, was next extended to a- and TT-bonding in first-row homonuclear diatomics and to the study of multiple bonds, the fundamental quantity being a bond integral )8, whose form is 

Models for Bonding in Chemistry Valerio Magna 2010 John Wiley Sons, Ltd 

1 n 3 for the dipolar molecules generating the hydrogen bond described in Chapter 5. 

2 Usually, the ground state and some excited states of higher energy. 

The chapter ends with a short outline of the theory of the temperature-dependent Keesom interactions in polar gases. 

Under appropriate conditions of temperature and pressure it is possible to liquefy and solidify all the elements, including the noble gases, and all compounds, including those consisting of non-polar molecules such as CH4, CCI4, etc. The existence of a universal attraction between all atoms and molecules led van der 

Waals to include a term a/K in his equation of state. For molecules with a permanent dipole moment (ju) Keesom calculated the mean interaction energy 

Neither expression, of course, accounts for the interaction between non-polar molecules, a type of interaction first calculated by London and hence called London, or dispersion, energy. This (wave-mechanical) calculation gives 

The relative magnitudes of these three types of interaction can be seen from Table 7.7 for a few simple cases. For a non-polar molecule the London energy is necessarily the only contribution to the lattice energy even for polar molecules ch as NH3 and H2O for which is appreciable, l forms an important part of the lattice energy. Note that these lattice energies are between one and two orders of magnitude smaller than for ionic crystals for example, those of the permanent  

As a contribution to the lattice energy of salts the London interaction can be as large as 20 per cent of the total in cases where the ions are highly polarizable (for example, TII), and the adoption of the CsCl structure rather than the NaCl structure by CsCl, CsBr, and Csl is attributed to the van der Waals energy (see later). 

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Dipoles attract such that their energy varies as 1 /r. Thus the energy of the Van der Waals bond has the form... 

Well, that is the case at the low temperature, when the rubber has a proper modulus of a few GPa. As the rubber warms up to room temperature, the Van der Waals bonds melt. (In fact, the stiffness of the bond is proportional to its melting point that is why diamond, which has the highest melting point of any material, also has the highest modulus.) The rubber remains solid because of the cross-links which form a sort of skeleton but when you load it, the chains now slide over each other in places where there are no cross-linking bonds. This, of course, gives extra strain, and the modulus goes down (remember, E = [Pg.61]

Is it possible to make polymers stiffer than the Van der Waals bonds which usually hold them together The answer is yes - if we mix into the polymer a second, stiffer, material. Good examples of materials stiffened in this way are ... 

Polymers, too, creep - many of them do so at room temperature. As we said in Chapter 5, most common polymers are not crystalline, and have no well-defined melting point. For them, the important temperature is the glass temperature, Tq, at which the Van der Waals bonds solidify. Above this temperature, the polymer is in a leathery or rubbery state, and creeps rapidly under load. Below, it becomes hard (and... 

Creep of polymers is a major design problem. The glass temperature Tq, for a polymer, is a criterion of creep-resistance, in much the way that is for a metal or a ceramic. For most polymers, is close to room temperature. Well below Tq, the polymer is a glass (often containing crystalline regions - Chapter 5) and is a brittle, elastic solid -rubber, cooled in liquid nitrogen, is an example. Above Tq the Van der Waals bonds within the polymer melt, and it becomes a rubber (if the polymer chains are cross-linked) or a viscous liquid (if they are not). Thermoplastics, which can be moulded when hot, are a simple example well below Tq they are elastic well above, they are viscous liquids, and flow like treacle. 

T ike metals minerals also exhibit typical crystalline structures. As an example, the structure of molybdenite is shown in Figure 1.17. It is hexagonal with six-pole symmetry and contains two molecules per unit cell. Each sulfur atom is equidistant from three molybdenum atoms and each molybdenum atom is surrounded by six sulfur atoms located at the comers of a trigonal prism. There are two types of bonds that can be established between the atoms which constitute the molybdenite crystal stmcture. They are the covalent bonds between sulfur and molybdenum atoms and the Van der Waals bonds between sulfur-sulfur atoms. The Van der Waals bond is considerably weaker than the covalent sulfur-molybdenum bond. This causes the bonds of sulfur-sulfur to cleave easily, imparting to molybdenite the property of being a dry lubricant. Molybdenite adheres to metallic surfaces with the development of a molecular bond and the friction between metallic surfaces is replaced by easy friction between two layers of sulfur atoms. 

The observed range of the shear modulus varies between 1.5 GPa in filaments of regular count to 3 GPa in microfilaments, which correlates with the degree of orientation and crystalline perfection in the fibres [40]. Compared to the theoretical value of the modulus of shear between two hydrogen-bonded chains of 4.1 GPa, it indicates softening due to the van der Waals bonding between the hydrogen-bonded planes. 

In van der Waals solids (e.g., solid Ne figure 1.2C), the reticular positions are occupied by inert atoms held together by van der Waals forces. The van der Waals bond is rather weak, and the bond does not survive a high thermal energy (Fm3m solid Ne, for instance, is stable below 20 K). The van der Waals bond also exists, however, in molecular compounds (e.g., solid CO2). The reticular positions in this case are occupied by neutral molecules (CO2). Within each molecule, the bond is mainly covalent (and interatomic distances are considerably shorter), but... 

A van der Waals bond (B) is formed between apolar molecular groups that have come into close proximity. Spontaneous transient distortion of electron clouds (momentary faint dipole, 55) may induce an opposite dipole in the neighboring molecule. The van der Waals bond, therefore, is a form of electrostatic attraction, albeit of very low strength (inversely proportional to the seventh power of the distance). 

Organic solids have received much attention in the last 10 to 15 years especially because of possible technological applications. Typically important aspects of these solids are superconductivity (of quasi one-dimensional materials), photoconducting properties in relation to commercial photocopying processes and photochemical transformations in the solid state. In organic solids formed by nonpolar molecules, cohesion in the solid state is mainly due to van der Waals forces. Because of the relatively weak nature of the cohesive forces, organic crystals as a class are soft and low melting. Nonpolar aliphatic hydrocarbons tend to crystallize in approximately close-packed structures because of the nondirectional character of van der Waals forces. Methane above 22 K, for example, crystallizes in a cubic close-packed structure where the molecules exhibit considerable rotation. The intermolecular C—C distance is 4.1 A, similar to the van der Waals bonds present in krypton (3.82 A) and xenon (4.0 A). Such close-packed structures are not found in molecular crystals of polar molecules. 

Van der Waals complexes between 1,2,4,5-tetrazine (38) and a number of light gases (He, Ar, H2) were observed and characterized by laser spectroscopic studies of free supersonic expansion of (38) in the carrier gas. The observed complexes are of the form X (38) or X2- (38), where X is He, Ar or H2. The spectra are consistent with the gas in both types of complexes being bound on or near the out of plane C2 axis on top of and/or below the 1,2,4,5-tetrazine ring. For the He and H2 complexes, analysis of the rotational structure indicates that the van der Waals bond length is 3.3 A (78JCP(68)2487,79JCP(7l)4757). 

One type of weak bond between molecules is known as the van der Waals bond (or force), and these forces increase steadily with the increasing size of the molecule. 

Because of the small dissociation energies, the absorption of an infrared (IR) photon corresponding to one vibrational or even only a single rotational quantum of the diatom suffices to break the van der Waals bond. A typical example is the breakup of rare gas-hydrogen compounds,... 

The hydrogen bond is not as strong as the ionic and covalent bonds, but is stronger than the van der Waals bond. 

The system Hamiltonian can be approximated, as in the ARRKM theory, by decoupling the diatom vibrational motion from overall rotational motion of the molecule and from the van der Waals bond stretching. With this approximation. 

Suppose that the system is prepared in a specified vibrational state of the diatom with a vibrational quantum number v, while the van der Waals bond is maintained in its ground vibrational state (n = 0). The several frequencies appeared in the preceding equations, corresponding to motion along the several coordinates, are defined by... 

This is the maximum kinetic energy accessible to the van der Waals bond when motion is limited to the interior of the dividing surface that just contains the con torus. 

When applied to a particular case, N is chosen using the prescription introduced by Davis and Gray. For example, in Hel2 the frequency of the van der Waals bond is 26.4cm and the diatom vibrational state with v = 20 has a local frequency r(v) = 93.81 cm, implying that 4 < A < oo. 

Figure 19. A schematic plot of the ideal bottlenecks on the Poincare surface of section for van der Waals molecule predissociation. R is the van der Waals bond length and P is the conjugate momentum. 5i is the intramolecular bottleneck dividing surface and S2 is the intermoleculear bottleneck dividing surface.

Triplet-state non-radiative lifetimes of aniline and aniline.Ar complexes. Estimate of the van der Waals bond energy in the highly excited triplet CgH NHj.He Fluorescence excitation and dispersed fluorescence... 

Figure 18. Partial electron transfer d (B XY) versus the van der Waals bond force constants. Adapted from Ref. [270].

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