The Importance of Intermolecular Forces

Forces of attraction between molecules are responsible for the existence of liquids and solids. In the absence of these intermolecular forces, all molecules would move independently, and all substances would be gases. The natural phases of the elements indicate the importance of intermolecular forces. At room temperature and pressure, only 11 elements are gases. Mercuiy and bromine are liquids, and all the rest of the elements are solids. For all but the 11 gaseous elements, intermolecular forces are too large to ignore under normal conditions. 

Different substituent groups perturb the bonding of the three sulfur atoms to different degrees (72MI43800). The importance of intermolecular forces in defining the molecular dimensions is clearly shown by the fact that, in some crystals, the same molecule can exist in two dimensionally different forms, as in the case of 2-p- dimethylamino-4-phenyl-l-oxa-6,6aA4-dithiapentalene (Table 2) (75AX(B)30). 

The Dutch physicist Johannes van der Waals (1837-1923) was the first to suggest the importance of intermolecular forces and used the concept to derive his equation for gases. (See van der Waals equation. Section 5.8.)... 

The importance of intermolecular forces in explaining the thermodynamic behavior of fluids will be evident in the ensuing Chapters. We have already used them, however, in Example 1.5, to explain the observation that the deviation of steam from ideal gas behavior ... 

The next point of interest has to do with the question of how deep the surface region or region of appreciably unbalanced forces is. This depends primarily on the range of intermolecular forces and, except where ions are involved, the principal force between molecules is of the so-called van der Waals type (see Section VI-1). This type of force decreases with about the seventh power of the intermolecular distance and, consequently, it is only the first shell or two of nearest neighbors whose interaction with a given molecule is of importance. In other words, a molecule experiences essentially symmetrical forces once it is a few molecular diameters away from the surface, and the thickness of the surface region is of this order of magnitude (see Ref. 23, for example). (Certain aspects of this conclusion need modification and are discussed in Sections X-6C and XVII-5.)... 

The presence of intermolecular forces also accounts for the variation in the compression factor. Thus, for gases under conditions of pressure and temperature such that Z > 1, the repulsions are more important than the attractions. Their molar volumes are greater than expected for an ideal gas because repulsions tend to drive the molecules apart. For example, a hydrogen molecule has so few electrons that the its molecules are only very weakly attracted to one another. For gases under conditions of pressure and temperature such that Z < 1, the attractions are more important than the repulsions, and the molar volume is smaller than for an ideal gas because attractions tend to draw molecules together. To improve our model of a gas, we need to add to it that the molecules of a real gas exert attractive and repulsive forces on one another. 

The concept of intermolecular forces is important in the separation of the components of a mixture. Experiment 18 in the Experimental chapter utilizes this concept. 

An important theoretical development for the outer-sphere relaxation was proposed in the 1970s by Hwang and Freed (138). The authors corrected some earlier mistakes in the treatment of the boundary conditions in the diffusion equation and allowed for the role of intermolecular forces, as reflected in the IS radial distribution function, g(r). Ayant et al. (139) proposed, independently, a very similar model incorporating the effects of molecular interactions. The same group has also dealt with the effects of spin eccentricity or translation-rotation coupling (140). 

In addition to the contribution of intermolecular forces, chain entanglement is also an important contributory factor to the physical properties of polymers. While paraffin wax and HDPE are homologs with relatively high molecular weights, the chain length of paraffin is too short to permit chain entanglement, and hence lacks the strength and other characteristic properties of HDPE. 

It is beyond the scope of this review to cover in depth either valence theory or the theory of intermolecular forces and I shall only attempt to deal with some general principles of both which appear to be important for an understanding of potential energy surfaces. Before dealing separately with weak and strong interactions, there is one point they have in common and that is the increasing computational effect that is required as the number of internal coordinates increases. 

Other methods of film formation discussed in this book depend on allowing a melt or a solution of the material to be deposited to spread on the substrate and subsequently to solidify. An ordered structure can sometimes be imposed on such a film by the application of an electric or magnetic field if the film is in a mesophase (otherwise known as a liquid crystal) before solidification. However, any such method presupposes that the melt or solution used will spread evenly over the substrate. It is thus important to understand a little about the conditions which allow a liquid to spread on a solid surface. This topic depends on the nature of intermolecular forces, a subject which is of general relevance to the formation of organic films and which is discussed in the following section. 

Most papers dealing with the spectrum of the carbonate ion CO7 neglect to mention the important paper by Decius, Malan and Thompson 42> on the effect of intermolecular forces on molecules in the crystalline state which refer specifically to the out-of-plane bending mode of CO In this paper they derive the dependence of this mode upon the 12C-13C isotopic ratio. Sterzel and Chlorinski 43) also discuss the effect of isotopes upon the CO2" vibrations these two papers should be consulted when assigning C03 -spectra because the modes depend very much upon the t2C-13C ratio. Orville-Thomas 20> has discussed the dependence of the C03 force constants upon the C-O distance, and shows that this leads to a bond intermediate between a single and a double bond. 

Many new technologies rely on the unusual properties of interfaces— Langmuir-Blodgett and other films, micelles, vesicles, small liquid drops, and so on. Classical thermodynamics is often inadequate as a basis for treating such systems because of their smallness, and experimental probes of the interface are limited, especially for fluid systems. Computer simulation can play an important role here, both in understanding the role of intermolecular forces in obtaining desired properties and, in combination with experiment, in designing better materials and processes [6, 28]. 

In general, a minimum of the energy surface corresponds to a set of stationary vibrational states of the molecular system. The position of the energy minimum is commonly called the equilibrium geometry Re. Analogously, we denote the expectation values for the molecular geometries in the vibrational states 0,1,2,... by R0, Rx, R2, etc. In most cases Ro is very close to Re. There are also exceptions to this correspondence which are important in the theory of intermolecular forces. We distinguish several cases ... 

All the important contributions to the forces between molecules arise ultimately from the electrostatic interactions between the particles that make up the two molecules. Thus our main theoretical insight into the nature of intermolecular forces comes from perturbation theory, using these interactions as the perturbation operator H = Z e, /(4jtSor/y), where is the charge on particle i in one molecule, is the distance between particles i and / in different molecules, and 8q is permittivity of a vacuum. The definitions of the contributions, such as the repulsion, dispersion, and electrostatic terms, which are normally included in model potentials, correspond to different terms in the perturbation series expansion. 

Aprotic polar liquids such as dimethyl sulfoxide and acetonitrile make up another group. These molecules have high dipole moments, so that dipole-dipole interactions are an important part of the description of intermolecular forces. 

Just as the ideal gas forms a convenient point of reference in discussing the properties of real gases, so does the hard-sphere fluid in discussing the properties of liquids. This is especially true at low densities, where the role of intermolecular forces in real systems is not so important. In this limit, the hard-sphere model is useful in developing the theory of solutions, as will be seen in chapter 3. 

The interfacial tension is obviously an important property of a liquid because it gives a direct indication of the magnitude of intermolecular forces. As a result of interfacial tension a liquid which is not in contact with another condensed phase, such as a water droplet in air, assumes the shape which has minimum area. It turns out that this shape is a sphere. As a result, there are no elliptical or square water droplets By maintaining a spherical shape, the area-to-volume ratio, and the number of molecules at the surface are their lowest possible values. One is not surprised by this fact on the basis of experience. 

From a fundamental perspective the Joulc -Thotnson effect is important because it can be linked directly to the nature of intermolecular forces between gas molecules [205]. Consider, for example, a classic ideal gas as the simplest case in which molecules do not interact by definition. For this model it is simple to show that as a consequence of the absence of any intermolecular interactions a Joule-Thomson effect does not exist, that is, <5 = 0 [200, 201]. If, on the other hand, the ideal gas is treated quantum mechanically, it can be demonstrated [206] that a Joule-Thomson effect exists (S 0) despite the lack of intermolecular interactions. 

Nystrom, C. and Karehill, P.G. 1996. The importance of intermolecular bonding forces and the concept of bonding surface area. In Pharmaceutical Powder Compaction Technology (G. Alderbom and G. Nytrom, eds), p. 17. Marcel Dekker, New York. 

A study of the structural properties of primary n-alkylammonium haUdes enabled us to evaluate the relative importance of intermolecular forces of the two types as the polar ends of the layers form strong hydrogen-bonded networks that dominate the packing on crystallization. Here we illustrate trends in the crystal chemistry of the n-alkylammonium halides, and the investigative methods, using as examples n-octadecylammonium chloride, CigH37NH Cl , and their related bromides and iodides... 

Nonadditive effects in open-shell clusters have been investigated only recently and relatively little information is available on their importance and physical origin. From the theoretical point of view, open-shell systems are more difficult to study since the conventional, size-consistent computational tools of the theory of intermolecular forces, like the Mpller-Plesset perturbation theory, coupled cluster theory, or SAPT, are less suitable or less developed for applications to open-shell systems than to closed-shell ones. Moreover, there are many types of qualitatively different open-shell states, exhibiting different behavior and requiring different theoretical treatments. 

---