London-type interaction

In case of neutral organic adsorbates (za = zb = 0) we can approximately assume that the short-range interactions have a negligible contribution and delete the two terms with the activity coefficients in Eqs. (76) and (77). This approximation is not valid when one or both adsorbates are ionic species. In this case the activity coefficients should be expressed in terms of the surface composition. As we have already pointed out, the expressions for the activity coefficients developed in [23-29] may be used for this purpose. These expressions can be simplified considerably when only one of the co-adsorbates, say adsorbate A, is an ionic species. Then if we again assume that the short-range London type interactions have a negligible contribution, the activity coefficients may be expressed as ... 

The surface free energy of a solid (7s) can be expressed as a sum of two components 7sd (the dispersive component), describing London-type interactions, and 7ssp (the specific component), including all other interactions (H-bonding, polar, and so forth). 

Screening is determined by induced transition dipole interactions, which decrease as These are dispersive or London type interactions. The change in energy of the ground state given by eqn (9.66) is the van der Waal s interaction. 

There are three types of interactions that contribute to van der Waals forces. These are interactions between freely rotating permanent dipoles (Keesom interactions), dipole-induced dipole interaction (Debye interactions), and instantaneous dip le-induced dipole (London dispersion interactions), with the total van der Waals force arising from the sum. The total van der Waals interaction between materials arise from the sum of all three of these contributions. 

We assume that the double bonds in 1,3-butadiene would be the same as in ethylene if they did not interact with one another. Introduction of the known geometry of 1,3-butadiene in the s-trans conformation and the monopole charge of 0.49 e on each carbon yields an interaction energy <5 — 0.48 ev between the two double bonds. Simpson found the empirical value <5 = 1.91 ev from his assumption that only a London interaction was present. Hence it appears that only a small part of the interaction between double bonds in 1,3-butadiene is a London type of second-order electrical effect and the larger part is a conjugation or resonance associated with the structure with a double bond in the central position. 

Let us make some general comments on this type of LFER. First, reasonable correlations are found for sets of compounds that undergo primarily London dispersive interactions (Fig. 9.11 alkylated and chlorinated benzenes, chlorinated biphenyls). Good correlations are also found for sets of compounds in which polar interactions change proportionally with size (PAHs) or remain approximately... 

To the rare compounds that are not molecular compounds and that must perhaps be regarded as being due to an interaction of the London type belong some very unstable molecules, encountered only in gaseous discharges, for example HgKr, HgA and perhaps also Hg2. These compounds have only a very small heat of dissociation (HgKr 0.8 kcal/mol), and the mercury atom is moreover in an excited state so that a one-electron bond is also not excluded. 

The heats of vaporization are measures of the work that must be done to overcome interatomic attractive forces. Since there are no ordinary electron-pair interactions between noble gas atoms, these weak forces (of the van der Waals or London type) are proportional to the polarizability and inversely proportional to the ionization enthalpies of the atoms they increase therefore as the size and diffuseness of the electron clouds increase. 

Alcohols usually have much higher boiling points than might be expected from their molar masses. For example, both methanol and ethane have a molar mass of 30, but the boiling point for methanol is 65°C while that for ethane is -89°C. This difference can be understood if we consider the types of in-termolecular attractions that occur in these liquids. Ethane molecules are nonpolar and exhibit only weak London dispersion interactions. However, the... 

If, however, the interactions are so strong that the oscillators are always in phase, the two oscillators would behave as one oscillator with charge 2e. Additivity is then restored on a new basis and a London-type expression applies again. Such an expression is found by Coulson and Davieses considering extended oscillators as a model for large chain molecules. 

R. M. Barrer (Imperial College, London) Type V isotherms similar to those shown in your Figure 2 have also been found by us (Barrer and Kanellopoulos, /. Chem. Soc.) when equimolecular mixtures of NH3 and HCl are sorbed between 200° and 300°C in zeolites. The sorptions of NH3 alone and of HCl alone in the same temperature ranges are relatively small, but together they interact strongly and are copiously sorbed. Thus, interaction may be strong between unlike molecules and is responsible for the peculiar isotherm shape observed in mixed sorption. 

We will finish this paragraph by stating that the promising and very frequently used density functional theory (DFT) [6] is not generally applicable for molecular complexes. The reason for this is that it does not cover the intersystem correlation interaction energy, approximately equivalent to the classical dispersion energy. The DFT method yields reliable results for H-bonded and ionic clusters but fails completely in London-type clusters where the dispersion energy is dominant. 

In the context of this discussion, surface heterogeneity will be expressed in terms of the adsorptive potential of the material. The adsorptive potential is a measure of the net attraction between a solid surface and an adsorbed probe molecule. For physical adsorption, these forces arise chiefly from London-type dispersion interactions (van der Waals forces) resulting from induced-dipole/induced-dipole and higher multipolar attractions which in turn depend on the size. 

Intermolecular dispersion energies are calculated as a sum of pixel-pixel terms in a London-type expression, involving the above defined distributed polarizabilities and an overall oscillator strength > Eos To avoid singularities (as before described) due to very short pixel-pixel distances in an inverse sixth-power formula, each term in the sum is damped, as it is shown here for the molecule A...molecule B interaction ... 

As detailed in Chapter 2, van der Waals interactions consist mainly of three types of long-range interactions, namely Keesom (dipole-dipole angle-averaged orientation, Section 2.4.3), Debye (dipole-induced dipolar, angle-averaged, Section 2.5.7), and London dispersion interactions (Section 2.6.1). However, only orientation-independent London dispersion interactions are important for particle-particle or particle-surface attractions, because Keesom and Debye interactions cancel unless the particle itself has a permanent dipole moment, which can occur only very rarely. Thus, it is important to analyze the London dispersion interactions between macrobodies. Estimation of the value of dispersion attractions has been attempted by two different approaches one based on an extended molecular model by Hamaker (see Sections 7.3.1-7.3.5) and one based on a model of condensed media by Lifshitz (see Section 7.3.7). 

D18.4 There are three van der Waals type interactions that depend upon distance as l/r6 they are the Keesom interaction between rotating permanent dipoles, the permanent-dipole-induced-dipole-interaction, and the induced-dipole-induced-dipole, or London dispersion, interaction. In each case, we can visualize the distance dependence of the potential energy as arising from the Mr dependence of the field (and hence the magnitude of the induced dipole) and the Mr3 dependence of the potential energy of interaction of the dipoles (either permanent or induced). 

The basic assumptions underlying the use of most atom-atom potential calculations are that only central forces operate between pairs of atoms and that the total interaction energy is the sum of the interactions between all pairs of atoms—the additivity assumption. The individual atom-atom interaction energies include a repulsive term with a steep rise in the energy at small interatomic distances, an attractive term designed to allow for London-type dispersion attractions and, sometimes, an additional coulombic interaction as well. With an exponential function as the repulsive term, the interaction energy between a pair of atoms can be written as... 

If the two subsystems do not possess any permanent multipole moments neither the electrostatic nor the inductive interaction can exist. Nevertheless, there is always an attraction due to mutually induced multipole moments. This interaction is generally referred to as Van der Waals interaction or London-type dispersion or simply dispersion . The explanation of the origin of this interaction goes back to F. London [16,17]. In the very simplest case of the interaction between two closed shell atoms, e.g., two He atoms in their electronic S ground states, the leading terms of the van der Waals interaction are given by... 

When two molecules interact with each other, several types of electrostatic interactions or forces may be involved, some of which have been described in the preceding sections (e.g., charge-charge, charge-dipole, dipole-dipole interactions). Here, we would like to mention two other kinds of electrical interactions which were not described above namely, short-range repulsive interactions and the London dispersion interaction. The latter interaction plays an especially important role in biological systems. 

Although the London dispersion interaction has a fundamentally quantum chemical, complex many-particle origin, it is probably the bonding type (or its contribution to bonding) that is easiest to understand. It can be represented accurately by rather... 

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