Molecular mechanics London dispersion interactions

Among all the low energy interactions, London dispersion forces are considered as the main contributors to the physical adsorption mechanism. They are ubiquitous and their range of interaction is in the order 2 molecular diameters. For this reason, this mechanism is always operative and effective only in the topmost surface layers of a material. It is this low level of adhesion energy combined with the viscoelastic properties of the silicone matrix that has been exploited in silicone release coatings and in silicone molds used to release 3-dimensional objects. However, most adhesive applications require much higher energies of adhesion and other mechanisms need to be involved. 

The selection of the solvent is based on the retention mechanism. The retention of analytes on stationary phase material is based on the physicochemical interactions. The molecular interactions in thin-layer chromatography have been extensively discussed, and are related to the solubility of solutes in the solvent. The solubility is explained as the sum of the London dispersion (van der Waals force for non-polar molecules), repulsion, Coulombic forces (compounds form a complex by ion-ion interaction, e.g. ionic crystals dissolve in solvents with a strong conductivity), dipole-dipole interactions, inductive effects, charge-transfer interactions, covalent bonding, hydrogen bonding, and ion-dipole interactions. The steric effect should be included in the above interactions in liquid chromatographic separation. 

Polarizability is a measure of the ease with which the electrons of a molecule are distorted. It is the basis for evaluating the nonspecific attraction forces (London dispersion forces) that arise when two molecules approach each other. Each molecule distorts the electron cloud of the other and thereby induces an instantaneous dipole. The induced dipoles then attract each other. Dispersion forces are weak and are most important for the nonpolar solvents where other solvation forces are absent. They do, nevertheless, become stronger the larger the electron cloud, and they may also become important for some of the higher-molecular-weight polar solvents. Large solute particles such as iodide ion interact by this mechanism more strongly than do small ones such as fluoride ion. Furthermore, solvent polarizability may influence rates of certain types of reactions because transition states may be of different polarizability from reactants and so be differently solvated. 

As shown above, there have been identified several mechanisms involved in the interactions between atoms and molecules, denominated collectively as the van der Waals forces. In atomic and completely nonpolar molecular systems (hydrocarbons, fluorocarbons, etc.) the London dispersion forces provide the major contribution to the total interaction potential. However, in many molecular systems containing atoms of very different electronegativities and polarizabilities the dipole-dipole (Keesom) and dipole-induced dipole (Debye) forces may also make significant contributions to the total interaction. 

Absorption mechanisms involve secondary molecular forces. Here it is hypothesized that molecules near the interface are attracted to each other by London dispersion forces, dipole-dipole interactions, hydrogen bonding, or other secondary molecular forces. The strength of these forces varies from 0.1 to 10 J/mol. Although most adhesives exhibit some dipole interactions, it is difficult to account for the relatively large strength of many practical joints purely on these secondary molecular forces. 

The Hamaker approach of pairwise addition of London dispersion forces is approximate because multi-body intermolecular interactions are neglected. In addition, it is implicitly assumed in the London equation that induced dipole-induced dipole interactions are not retarded by the finite time taken for one dipole to reorient in response to instantaneous fluctuations in the other. Because of these approximations an alternative approach was introduced by Lifshitz. This method assumes that the interacting particles and the dispersion medium are all continuous i.e. it is not a molecular theory. The theory involves quantum mechanical calculations of the dielectric permittivity of the continuous media. These calculations are complex, and are not detailed further here. 

In Sections 4.1 and 4.2 we discussed the fact that the electric moments of molecules play an important role in the description of the intermolecular forces between two molecules separated by a large distance. Their contribution to the interaction energy is of purely classical, i.e. electrostatic nature. Here, we want to show now that also the contribution from quantum mechanical dispersion or London forces, i.e. the dispersion energy E, can be related to molecular properties of the two interacting molecules. In particular, we will see that it is related to the frequency-dependent polarizabilities, which is in line with the physical interpretation of the dispersion forces as arising from the interaction of induced dipole moments, which implies that both charge distributions are perturbed by their interaction. 

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