Repulsion-dispersion potential

Errors (/>(calc)-/>(expt)) in the predicted molecular crystal structures, calculated by minimizing the static lattice energy, starting from the experimental structure, for a model potential which includes a distributed multipole electrostatic model. The electrostatic term uses a DMA of a 6-31G SCF wave function, with all multipoles scaled by a factor of 0.9. The repulsion-dispersion potentials are taken from the literature (see text). The r.m.s. % error is calculated over the three cell edge lengths. Us is the calculated lattice energy, given at both the experimental and relaxed crystal structures. This can be compared with the experimental heat of sublimation AHsub (Chickos, 1987), where available. 

However, with the exception of these unusually sensitive structures, the accurate electrostatic model does very well in predicting the relative orientation in hydrogen bonding and polar molecules, despite the crudeness of the repulsion-dispersion potential. Attempts to improve the predictions by optimizing the repulsion potential parameters have not yet been successful, as... 

While the enthalpy of formation is the property of interest in chemical thermodynamics of materials, many books focus on the lattice enthalpy when considering trends in stability. The static non-vibrational part of the lattice enthalpy can be deconvoluted into contributions of electrostatic nature, due to electron-electron repulsion, dispersion or van der Waals attraction, polarization and crystal field effects. The lattice enthalpy is in the 0 K approximation given as a sum of the potential energies of the different contributions ... 

The ionic models discussed in section 1.12 involve some sort of empiricism in the evaluation of repulsive and dispersive potentials. They thus need accurate parameterization based on experimental values. They are useful in predicting interaction energies within a family of isostructural compounds, but cannot safely be adopted for predictive purposes outside the parameterized chemical system or in cases involving structural changes (i.e., phase transition studies). 

The interaction parameters for the water molecules were taken from nonempirical configuration interaction calculations for water dimers (41) that have been shown to give good agreement between experimental radial distribution functions and simulations at low sorbate densities. The potential terms for the water-ferrierite interaction consisted of repulsion, dispersion, and electrostatic terms. The first two of these terms are the components of the 6-12 Lennard-Jones function, and the electrostatic term accounts for long-range contributions and is evaluated by an Ewald summation. The... 

The potential, 4>(r, r ), between 2 CO2 molecules has contributions owing to repulsion, dispersion, and quadrupole-quadrupole interaction ... 

All the important contributions to the forces between molecules arise ultimately from the electrostatic interactions between the particles that make up the two molecules. Thus our main theoretical insight into the nature of intermolecular forces comes from perturbation theory, using these interactions as the perturbation operator H = Z e, /(4jtSor/y), where is the charge on particle i in one molecule, is the distance between particles i and / in different molecules, and 8q is permittivity of a vacuum. The definitions of the contributions, such as the repulsion, dispersion, and electrostatic terms, which are normally included in model potentials, correspond to different terms in the perturbation series expansion. 

The short range repulsive part is represented by a Born-Mayer exponential ( ) type, the region of the well by a Morse potential (M) and the long range attractive part by a dispersion potential with a dipole-dipole and a dipole-quadrupole term. These parts are connected by cubic spline functions (S)... 

Because dispersion and repulsion potentials between two partners fall off so rapidly with distance the binding energy depends very much upon the shape of the surface. For example, a molecule bound at the centre of a hemispherical cavity of radius Zq (Fig. 13a) is subject to a dispersion potential 4 times as great as for a molecule located on a smooth surface [31]. Inside a long, narrow capillary, terminated by a hemisphere at whose centre the molecule is located (Fig. 13b) the attractive potential is roughly 7 times that of a plane surface [31]. Inside a topographic depression a bound molecule is in close contact with a larger number of atoms than on a smooth surface. 

The first part of the potential, which is negative and varies inversely with the sixth power of the intermolecular distance, is called the van der Waals or the London dispersion potential. It represents the attraction between the two molecules. The second part is positive and represents repulsion. The fact that it is infinite implies that the molecules are rigid spheres and cannot penetrate each other. A sketch of the dimensions involved is shown in Figure 2.3, as well as the form of Equation 2.10. For i = j, the distanee of closest approach (when the spheres touch one another) is Ojj, which is also the diamet of the molecule. 

In Eq. (72) the second term on the right-hand side is a coulombic potential, sq is the permittivity of vacuum, and ZjBQ are the charges on ions i and j, and is the relative permittivity of pure solvent. The first term, u j(r), is the short-range noncoulombic part of the direct potential, including repulsion, dispersion, or induction forces. 

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