Forces between Atoms and Molecules

We begin with the force between two point charges, q and qi, separated by a distance x in a vacuum from Coulomb s law 

At distances far from the dipole, the length d becomes unimportant and the dipole appears as a point dipole. The potential energy for a point dipole in the held produced by a charge (Eq. VI-3) is 

This orientation interaction thus varies inversely with the sixth power of the distance between dipoles. Remember, however, that the derivation has assumed separations large compared with d. 

Another interaction involving dipoles is that between a dipole and a polar- 

As an exercise, it is not difficult to show that the interaction of a polarizable molecule with a charge q is 

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The elastic properties of materials can be understood, at least qualitatively, by considering the attractive and repulsive forces between atoms and molecules. 

All forces between atoms and molecules are electrostatic in origin, even those between nonpolar molecules. But we shall reserve the term electrostatic for interactions that occur between charged or dipolar atoms and molecules. 

One of the most fundamental problems of chemical physics is the study of the forces between atoms and molecules. We have seen in many preceding chapters that these forces are essential to the explanation of equations of state, specific heats, the equilibrium of phases, chemical equilibrium, and in fact all the problems we have taken up. The exact evaluation of these forces from atomic theory is one of the most difficult branches of quantum theory and wave mechanics. The general principles on which the evaluation is based, however, are relatively simple, and in this chapter we shall learn what these general principles are, and see at least qualitatively the sort of results they lead to. 

Table CXLIL Heats of Sublimation Calculated from Dispersion cules Forces between Atoms and Molecules...

Discuss how forces between atoms and molecules vary with distance (Section 9.7). 

An appropriate account of secondary interaction forces between atoms and molecules is given by Richards (1980). 

The first detailed treatments of the weak forces between atoms and molecules known as van der Waals forces (which are responsible for the constant a of the van der Waals equation of state) were based upon the idea that these forces result from the polarization of one molecule in the field of a permanent dipole moment or quadrupole moment of another molecule,1 or from the interaction of the permanent dipole or quadrupole moments themselves.2 With the development of the quantum mechanics it has been recognized (especially by London3) that for most molecules these interactions are small compared with another interaction, namely, that corresponding to the polarization of one molecule in the rapidly changing field due to the iristan-... 

The idea that there were two terms in the expression for the force between atoms and molecules was recognized by Newton, but really began to take shape this century when a number of theorists, like Mie for example, started to formulate mathematical equations to describe both an attractive term and a repulsive term, as shown in Fig. 5.2. 

The various forms of carbon that we have just described share one important physical property—they are all solids at normal laboratory temperature and pressure. The vast majority of elements are solids under such conditions. What factors contribute to the stability of condensed phases Forces between atoms and molecules certainly play a role in the answer to this question, but the basic structure of condensed phases also contributes to an understanding of their stability. We will begin our treatment from this structural perspective. 

Attractive surface forces, generally referred to as van der Waals forces, exist between all atoms and molecules regardless of what other forces may be involved. They have been discussed in detail by Isrealachvili (4). We shall first examine the origins of the van der Waals forces between atoms and molecules and later consider the attractive forces between macroscopic bodies such as particles. 

The van der Waals forces between atoms and molecules can be divided into three groups (5) ... 

VSEPR) modeL A model that accounts for the geometrical arrangements of shared and unshared electron pairs around a central atom in terms of the repulsive forces between electron pairs. (10.1) van der Waals equation. An equation that describes the relationships among P, V, n, and T for a nonideal gas. (5.7) van der Waals forces. The collective name for certain attractive forces between atoms and molecules, namely, dipole-dipole, dipole-induced dipole, and dispersion forces. (12.2)... 

In preceding chapters the theories underlying some of the methods which have been used to characterize coordination compounds have been discussed in some detail. The present chapter provides a less detailed survey of other methods, stretching from indicators of complex formation through to some which provide insights into physical structure, others into electronic structure, yet others into the forces between atoms and molecules. 

All atoms and molecules in a stem of matter are surroimded by an electrostatic field. By interaction between these fields, attractive or repulsive electrostatic forces - so-called Coulomb forces between atoms and molecules are generated (see section 1.10). If two particles are displaced from their equilibrium state determined by their charge, they are given a mutual potential energy, i.e. a capacity to do work. 

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