Point charges, intermolecular interaction

A number of intermolecular potentials have been developed over the years that treat molecules as collections of point charges. The intermolecular electrostatic potential is taken as a sum of the mutual electrostatic interaction of these point charges, summed over interacting pairs of molecules. Occasionally, extra van der Waals terms are added to the potential. 

The link between UpophiUcity and point charges is given by intermolecular electrostatic interactions (Sections 12.1.1.2, 12.1.3 and 12.1.4 address this topic) and ionization constants. The mathematical relationships between Upophilicity descriptors and pKjS are discussed in detail in Chapter 3 by Alex Avdeef. Here, we recall how pKj values are related to the molecular electron flow by taking the difference between the pfCj of aromatic and aUphatic amines as an example. The pfCa of a basic compound depends on the equilibrium shown in Fig. 12.2(A). A chemical effect produces the stabilization or destabiUzation of one of the two forms, the free energy difference (AG) decreases or increases and, consequently. 

Ionic liquids are characterised by the following three definition criteria. They consist entirely out of ions, they have melting points below 100 °C and they exhibit no detectable vapour pressure below the temperature of their thermal decomposition. As a consequence of these properties most ions forming ionic liquids display low charge densities resulting in low intermolecular interaction. Figure 7.1 displays some of the most common ions used so far for the formation of ionic liquids. 

The two electron coulomb integral aa/bb) is smaller than the point charge integral (aa/Ri1) at all finite distances and therefore the use of Eq. (17) introduces an underestimation of an attractive contribution to the intermolecular energy of interaction or, if we put it the other way round, a net repulsion between the molecules results. 

The first two points above have important consequences for the interaction between ions in chemical systems. In such systems, the interaction usually takes place in an electrolyte solution composed of a large number of ions. All the ions in the system are constantly in thermal motion and, due to the strength and long-range nature of the Coulomb interaction, the motion of a particular ion is affected by the continuous change in position of other ions or charged bodies in the system. The Coulomb interaction, therefore, is a many-body interaction, i.e., a particular ion is influenced by many other ions that are, on a molecular scale, quite far away. This is in contrast to the other types of intermolecular interactions where only the interaction between molecules in close contact is of significance. 

It is worthwhile to examine the Hamiltonian in some detail because it enables one to discuss both intramolecular and intermolecular perturbations from the same point of view. To do so, we start from a zero-order Hamiltonian that contains just the spherical part of the field due to the core (which need not be Coulombic as it includes also the quantum defect [42]) and add two perturbations. U due to external effects and V due to the structure of the core. Here, U contains both the effect of external fields (electrical and, if any, magnetic [1]) and the role of other charges that may be nearby [8, 11, 12, 17]. The technical point is that both the effect of other charges and the effect of the core not being a point charge are accounted for by writing the Coulomb interaction between two charges, at points ri and r2, respectively, as... 

Following from formula (4.54), the transfer of energy on excitation of molecules has a noticeable probability even in the case where the impact parameter is much greater than their size d. Since the intermolecular spacings in a condensed medium are of order of d, a charged particle interacts with many of its molecules. The polarization of these molecules weakens the field of the particle, which, in its turn, weakens the interaction of the particle with the molecules located far from the track. This results in that the actual ionization losses are smaller than the value we would get by simply summing the losses in collisions with individual molecules given by formula (5.1). This polarization (density) effect was first pointed out by Swann,205 while the principles of calculation of ionization losses in a dense medium were developed by Fermi.206... 

In aqueous solution, the intermolecular interactions were assumed to be pairwise additive and described by Lennard-Jones (12-6) potentials with added interactions corresponding to point charges. The solid line in Fig. 10.1.1 shows the potential of mean force w(rc) evaluated in a solution of 250 water molecules at T = 25° C [4]. 

The multidimensional potential energy surface was written as the sum of a gas-phase (LEPS) energy surface incorporating the main features of the one-dimensional double-well potential in Example 10.1, solvent-solute interactions described by Lennard-Jones potentials with added (Coulomb) interactions corresponding to point charges, and solvent solvent interactions including intermolecular degrees of freedom. The solvent consisted of 64 water molecules. 

The electrostatic embedding approach appears reasonable in cases of weak interactions, with negligible intermolecular charge transfer, provided that the interactions can be described as some average electric perturbation. By properly modifying the disposition of the point charges more realistic embedding schemes could also be introduced. 

The Coulomb term of the Klopman relationship (Equation 6.50) is based on a point charge model. It does not consider potential differences in the geometric availability of the spatially extended atomic sites for polar intermolecular interactions (which holds true in particular when employing the site-specific net atomic charge, QA [Equation 6.57], as a simple descriptor for the... 

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