London dispersion theory

The original van der Waals idea was that pressure in a fluid is the result of both repulsive forces or excluded volume effects, which increase as the molar volume decreases, and attractive forces which reduce the pressure. Since the molecules have a finite size, there would be a limiting molar volume, b, which could be achieved only at infinite pressure. At large intermolcular separations, London dispersion theory establishes that attractive forces increase as r6, where r is the intermolecular distance. Since volume is proportional to r3, this provides some explanation also for the attractive term in the van der Waals equation of state. 

Expression (1.60) is analogous to (1.49), which was obtained by Hamaker on the basis of the London dispersion theory for the interaction between a sphere and a plane. Hence, for a small value of the gap between the contiguous bodies (i.e., in the zone of direct... 

Kristyan, S., Pulay, P., 1994, Can (Semi)Local Density Functional Theory Account for the London Dispersion Forces , Chem. Phys. Lett., 229, 175. 

The most celebrated result of London s theory is the dispersion interaction... 

The pair potential of colloidal particles, i.e. the potential energy of interaction between a pair of colloidal particles as a function of separation distance, is calculated from the linear superposition of the individual energy curves. When this was done using the attractive potential calculated from London dispersion forces, Fa, and electrostatic repulsion, Ve, the theory was called the DLVO Theory (from Derjaguin, Landau, Verwey and Overbeek). Here we will use the term to include other potentials, such as those arising from depletion interactions, Kd, and steric repulsion, Vs, and so we may write the total potential energy of interaction as... 

A fourth potential problem is that HF theory does not model van der Waals attractive interactions between nonbonded molecules. Whereas hydrogen bonding is well represented by the HF-SCF model, weak London dispersion attractions are not. 

Types ionic, covalent, metallic, hydrogen bonding, van der Waals theory (including London dispersion forces)... 

Kristyan S, Pulay P (1994) Can (semi)local density-functional theory account for London dispersion forces, Chem Phys Lett, 229 175-180... 

By time averaging Ej t> nt>, the London dispersion energy is obtained. Recently a book on the theory of intermolecular forces that treats the subject in a comprehensive manner [153] has been published. 

Dispersional Interaction between Molecules. We still wish to consider briefly energies due to interaction between fluctuating induced electric charge distributions of atoms and molecules. In constrast to electrostatic and induced interactions, these are present even when the molecules do not possess permanent electric moments. These dispersional interactions cannot be dealt with on a classical electrostatics level owing to their relation to London s quantum dispersion theory, they have been termed London dispersional interactions. 

For the substituted polysilylenes, (SiRR ) , the coupling constant can be varied systematically by changing the side groups (this change affects e and Vd via the backbone polarizability) or the solvent (this change affects Vj) via the London dispersion forces e is expected to be only weakly solvent dependent for nonpolar systems). Therefore, in principle, the three distinct phase behaviors predicted by the theory may be observed by judicious choice of polymer-solvent pairs. 

Physical adsorption is a universal phenomena, producing some, if not the major, contribution to almost every adhesive contact. It is dependent for its strength upon the van der Waals attraction between individual molecules of the adhesive and those of the substrate. Van der Waals attraction quantitatively expresses the London dispersion force between molecules that is brought about by the rapidly fluctuating dipole moment within an individual molecule polarizing, and thus attracting, other molecules. Grimley (1973) has treated the current quantum mechanical theories involved in simplified mathematical terms as they apply to adhesive interactions. 

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... 

O. A. von Lilienfeld, I. Tavernelli, U. Rothhsberger, and D. Sebastiani (2004) Optimization of Effective Atom Centered Potentials for London Dispersion Forces in Density Functional Theory. Phys. Rev. Lett. 93, p. 153004... 

The role of the medium, in which contacting and pull-off are performed, has been mentioned but not considered so far. However, the surroundings obviously influence surface forces, e.g., via effective polarizability effects (essentially multibody interactions e.g., by the presence of a third atom and its influence via instantaneous polarizability effects). These effects can become noticeable in condensed media (liquids) when the pairwise additivity of forces can essentially break down. One solution to this problem is given by the quantum field theory of Lifshitz, which has been simplified by Israelachvili [6]. The interaction is expressed by the (frequency-dependent) dielectric constants and refractive indices of the contacting macroscopic bodies (labeled by 1 and 2) and the medium (labeled by 3). The value of the Hamaker constant Atota 1 is considered as the sum of a term at zero frequency (v =0, dipole-dipole and dipole-induced dipole forces) and London dispersion forces (at positive frequencies, v >0). 

Grimme S (2011) Density functional theory with London dispersion corrections. Wiley In-terdiscip Rev-Comput Mol Sci 1 211-228... 

These jr-bonding effects are part of the theory of the HSAB Principle. We can also imagine that London dispersion energies between atoms or groups in an A B complex could stabilize it. Since these dispersion energies, or van der Waals energies, depend on the product of the polarizabilities of the two groups, soft-soft combinations would be stabilized in this way. The hydride ion is very polarizable, and its softness depends on this factor, presumably. 

---