Dispersion and repulsion interactions

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

The dotted line in Fig. 2.19 enclosed by two markers x represents the ratio K3/Ki = 0.207 at the inclination angle 6 = 25° observed for the system CO/NaCl(100). The point at which this line intersects the solid one gives the critical temperature which proves equal to 20K if the value U = 1.63 meV is substituted. If dispersion and repulsion interactions estimated as in Table 2.3 are taken into account, the value Tc is shifted to 22 K, which agrees well with the experimental value Tc= 17.5+21.5 K."... 

The interaction in the coordination sphere is described by a 13-term function considering multipole-, polarization-, dispersion-, and repulsion interactions. They succeeded in reproducing free energies of solvation of a large variety of cations to within standard deviations of a few percent. This formalism has been applied by... 

To determine the coupling work between solute and solvent, it is convenient to decompose AGsol into separate, more manageable terms, which typically involve the separation between electrostatic and nonelectrostatic contributions. The former accounts for the work required to assemble the charge distribution of the solute in solution, while the latter is typically used to account for dispersion and repulsion interactions between solute and solvent molecules, as well as for cavitation, i.e. the work required to create the cavity that accommodates the solute. 

The dispersion and repulsion interactions form the Lennard-Jones (Barrer, 1978 Masel, 1996 Razmus and Hall, 1991 Gregg and Sing, 1982 Steele, 1974 Adamson, 1976 Rigby et al., 1986) potential, with an equilibrium distance (r0) where 4 d + 4 r = 0. This distance is taken as the mean of the van der Waals radii of the interacting pair. Once the attractive, dispersion constant, A, is known, B is readily obtained by setting at chp/dr = 0 at r0. Hence, B = Ar /2. The most commonly used expression for calculating A is the Kirkwood-Muller formula ... 

In the Horvath and Kawazoe (HK) method, the L-J (12-6) potential [2,13,17,45] was applied, where only the dispersion and repulsion interactions were included... 

Dispersion and repulsion are the fundamental forces present during the adsorption of nonpolar molecules in silica because the dipole moment of this molecule is null, the quadrupole moment is very low, and interactions with the hydroxyl groups do not exist. In the case of polar molecules, dispersion and repulsion interactions are present. But, specific interactions between the silica surface and the polar molecule, such as the dipole interaction, and, fundamentally, the interactions with the hydroxyl groups [124-126] are responsible for a more intense interaction of the silica surface with the polar molecules in comparison to nonpolar molecules [4],... 

There are two different approach of modelling of dispersion and repulsion interactions in solution within the PCM framework. 

The Lennard-Jones potential (12) includes dispersion and repulsion interactions in the... 

Dispersive and repulsive interactions. The interaction energy of two atoms separated by a distance r (which we know once (p and yr are specified) can be given by the Lennard-Jones (12,6) form, eqn 11.25. 

In order to model the van der Waals interactions, we need a simple empirical expression that is not computationally intensive and that models both the dispersion and repulsive interactions that are known to act upon atoms and molecules. The most commonly used functional form of van der Waals energy ( vdw) in classical force-fields is the Lennard-Jones 12-6 function that has the form ... 

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