Potential energy intermolecular forces

Because of the relative magnitudes of intermolecular forces (potential energy) and average speed (kinetic energy), the particles in a gas are far apart and moving randomly, those in a liquid are in contact and moving relative to each other, and those in a solid are in contact and in fixed positions. These molecular-level differences account for macroscopic differences in shape, compressibility, and ability to flow. 

In a solution of a solute in a solvent there can exist noncovalent intermolecular interactions of solvent-solvent, solvent-solute, and solute—solute pairs. The noncovalent attractive forces are of three types, namely, electrostatic, induction, and dispersion forces. We speak of forces, but physical theories make use of intermolecular energies. Let V(r) be the potential energy of interaction of two particles and F(r) be the force of interaction, where r is the interparticle distance of separation. Then these quantities are related by... 

What Do We Need to Know Already This chapter uses the concepts of potential energy (Section A), coulombic interactions (Section 2.4), polar molecules and dipoles (Section 3.3), and intermolecular forces in gases (Section 4.12). 

We have been using intermolecular interaction and intermolecular force almost interchangeably. However, it is important to distinguish the force from the potential energy of interaction. In classical mechanics, the magnitude of the force,... 

F, is related to the distance dependence of the potential energy, p, by F = —dEp/dr. How does the intermolecular force depend on separation for a typical intermolecular interaction that varies as 1/r6 ... 

In this section we will briefly review some of the main different approaches that have been used up to now in order to evaluate the potential energy of each configuration in a Monte Carlo run. As we have already stated, the force fields that describe intra- and intermolecular interactions are at the heart of such statistical calculations because the free energy differences that we want to evaluate are directly dependent on the changes of those interactions. In fact, the important advances of the last ten years in the power of computer techniques for chemical reactions in the condensed phase, that we have mentioned in the Introduction, have been due, to a great extent, to the continual evolution in force fields, with added complexity and improved performance. 

These results shown in Figures 1 and 2 demonstrate the similarity of the effects of short-range forces on the properties of nonelectrolytes and concentrated electrolytes. One finds both positive and negative deviations from ideality and these effects may be ascribed to the difference between the intermolecular potential energy of attraction of unlike species to the mean of the corresponding potentials for pairs of like molecules. Previous discussion of these systems has focused on the hydration of the positive ion as the dominant effect, but we see in Figure 1 that... 

Precise intermolecular potentials are available for monatomic He, Ne, Ar and Xe. This permits accurate calculations of the VPIE s of these gases, their mixtures, and rare gas isotopomer mixtures. To begin, we are reminded that the mean intermolecular potential energy, , and mean force constant < V2U> can be obtained from the pair correlation function of the fluid, g(r),... 

The problem of influence of the electric field intensity on the permittivity of solvents has been discussed in many papers. The high permittivity of water results from the intermolecular forces and is a cumulative property. The electric field intensity is the lowest at the potential of zero charge (pzc), thus allowing water molecules to adsorb in clusters. When the electrode is polarized, the associated molecules, linked with hydrogen bonds, can dissociate due to a change in the energy of their interaction with the electrode. Moreover, the orientation of water molecules may also change when the potential is switched from one side of the pzc to the otha. 

Vraf is the molar free volume in the liquid, and A is the contribution to the potential energy from intermolecular forces. Assuming that... 

The "force of interaction , F, between two spherical non-polar molecules is a function of the intermolecular separation , r. For most purposes, however, it is more convenient to use the "potential energy of interaction , 0(r), rather than the force of interaction F(r). These two functions are simply related ... 

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. 

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