London dispersion interaction

It is possible to give a qualitative summary of London s quantum mechanical treatment on how an instantaneous dipole moment would arise and on the magnitude of its inter- 

The magnitude of the instantaneous dipole is proportional to the polarizability, a, given by Drude  

For a molecule, the product, hv0 is very nearly equal to its first ionization potential, I, which is the work required to be done to remove one electron from an uncharged molecule. Equation (67) is therefore usually written in the London dispersion form, 

A useful version of Equation (68) was given by Slater and Kirkwood in 1931, 

London dispersion energy is the potential energy between non-polar molecules, Equations (68) and (69) show that Vd is independent of temperature. On the other hand, the first ionization potentials of most substances do not differ very much from one another, so London s equation is more sensitive to the polarizability than it is to the ionization potential. We can rewrite Equations (68) and (69)  

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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. 

The stability constant of complexes between /1-cyclodextrine and p-nitroaniline is higher than that of aniline because the resonace charge delocalization (and London dispersion interactions) is an important factor influencing the stability of these complexes62. This behaviour parallels that of corresponding phenols. 

For instance, steric effects are frequently suggested to be important in determining the selectivity, especially in the reactions of a-substituted dienophiles and in reactions forming the unexpected exo-product with high selectivity (Scheme 5)71,72. London dispersion interactions have also been considered, and it has been argued that these interactions can sometimes override secondary orbital interactions73-75. 

It is instructive to follow the derivation of the London dispersion interaction, for the simplest case of two interacting hydrogen atoms, nsing the Bohr model where the electron is regarded as travelling in well-defined orbits about the nucleus. The orbit of smallest radius, Uq, is the ground state and Bohr calculated that... 

As noted above, London dispersive interactions occur even between molecules of apolar compounds like alkanes, that on average over time exhibit a rather smooth distribution of electrons throughout the whole molecular structure. This interaction occurs in all chemicals because there are momentary (order of femtosecond timescales) displacements of the electrons within the structure such that short-lived electron-rich and electron-poor regions temporarily develop. This continuous movement of electrons implies the continuous presence of short-lived dipoles in the structure. This fleeting dipole is felt by neighboring molecules whose electrons respond in a complementary fashion. Consequently, there is an intermolecular attraction between these molecular regions. In the next moment, these attractive interactions shift elsewhere in the molecule. 

It should be noted that when replacing the London dispersive interactions term by other properties such as, for example, the air-hexadecane partition constant, by expressing the surface area in a more sophisticated way, and/or by including additional terms, the predictive capability could still be somewhat improved. From our earlier discussions, we should recall that we do not yet exactly understand all the molecular factors that govern the solvation of organic compounds in water, particularly with respect to the entropic contributions. It is important to realize that for many of the various molecular descriptors that are presently used in the literature to model yiw or related properties (see Section 5.5), it is not known exactly how they contribute to the excess free energy of the compound in aqueous solution. Therefore, when also considering that some of the descriptors used are correlated to each other (a fact that... 

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... 

Keesom, Debye, and London contributed much to our understanding of forces between molecules [111-113]. For this reason the three dipole interactions are named after them. The van der Waals4 force is the Keesom plus the Debye plus the London dispersion interaction, thus, all the terms which consider dipole-dipole interactions Ctotai = Corient+Cind- -Cdisp. All three terms contain the same distance dependency the potential energy decreases with l/D6. Usually the London dispersion term is dominating. Please note that polar molecules not only interact via the Debye and Keesom force, but dispersion forces are also present. In Table 6.1 the contributions of the individual terms for some gases are listed. 

For the case of two spherical particles of radii ax and a2, separated in vacuo by a shortest distance H, Hamaker197 derived the following expression for the London dispersion interaction energy, VA ... 

London dispersion interactions between transient dipoles of nonpolar but polarizable bodies ... 

London dispersion interactions are, in general, omitted from traditional density functionals. These long-range attractions are an essential component of wide swaths of chemistry and physics, including systems such as DNA, protein folding, nanoarchitectures, and molecular recognition. We will discuss in detail in later... 

In contrast to dipole-dipole forces, London Dispersion interactions are much weaker in nature since they involve nonpolar molecules that do not possess permanent dipole moments. The only modes for molecular attraction are through polarization of electrons, which leads to the creation of small dipole-dipole interactions and mutual attractive forces. Since electron polarization occurs much more readily for electrons farther from the nucleus, this effect is more pronounced for molecules that are larger with a greater number of electrons, especially positioned on atoms with a high atomic number, consisting of more diffuse orbitals. These induced dipole forces are responsible for the liquefaction of gases such as He and Ar at low temperatures and pressures. The relative strength of London Dispersion forces is described by Eq. 3 ... 

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... 

Mercury itself is capable of interacting by two main interatomic forces, the metallic bond and London dispersion forces. Similarly, water has the potential for both hydrogen bond and London dispersion force interactions. However, hydrocarbons cannot interact with either the metallic bond, in the case of mercury, or hydrogen bonds, in the case of water. Therefore, the only primary interatomic force within hydrocarbons and across the interface is due to the London dispersion interaction, and... 

From the theory of London dispersion interactions as extended by Inura and Okano > and otherto include anisotropic interactions, one may estimate CT 0.05. Values of T evaluated on this basis according to Eq. (19) are compared in Table 4 with those deduced from the transition temperatures T j, the axial ratios x, and the function shown in Fig. 9. The agreement is quite satisfactory. The values... 

In the above isotherm equation, K is the equilibrium constant for the molecules (due to London dispersion interactions), while K is the equilibrium constant for the ions and has the form... 

A more vital application is to discern how reinforcement surface treatments improve adhesion to thermoplastic matrices. Since the nonreactive nature of thermoplastics normally precludes interfacial covalent bond formation, secondary bonding forces, such as London dispersion interactions and Lewis add/base interactions, may play a major role in these drcumstances. These secondary binding forces are subject to surface energetics analysis. 

In the last 40 years, techniques to directly measure surface forces and force laws (force vs. separation distance between surfaces) have been developed such as the surface forces apparatus (SFA) [6] and AFM. Surface forces are responsible for the work required when two contacting bodies (such as an AFM tip in contact with a solid surface) are separated from contact to infinite distance. Although the physical origin of all relevant surface forces can be derived from fundamental electromagnetic interactions, it is customary to group these in categories based on characteristic features that dominate the relevant physical behavior. Thus, one speaks of ionic (monopole), dipole—dipole, ion—dipole interactions, electrostatic multipole forces (e.g., quadrupole), induced dipolar forces, van der Waals (London dispersive) interactions, hydrophobic and hydrophilic solvation, structural and hydration forces,... 

While it is possible to account for non-covalent interactions using specialized force fields, common density functionals do not correctly describe the long-range van der Waals (London dispersion) interactions. Efficient dispersion correction schemes for DFT have been developed [14-17], but so far their application in QM/MM refinements is scarce. The importance of London forces for biomolecu-lar structures has been established conclusively [18]. 

Hamaker [4] suggested that the London dispersion interactions between atoms or molecules in macroscopic bodies (such as emulsion droplets) can be added, resulting in strong van der Waals attractions, particularly at close distances of separation between the droplets. For two droplets with equal radii, R, at a separation distance h, the van der Waals attraction G is given by the following equation (due to Hamaker) ... 

Vd = OO for r< a. For two dissimilar molecules, the London dispersion interaction coefficient Cd, from Equation (68), is... 

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