Van-der-Waals potential function

Van der Waals potential functions for non-bonded interactions display an attractive and a repulsive region 93>. Attractive interactions are small, too small to lead to a detectable effect on nitrogen inversion barriers in the present state of data accuracy. The repulsive portion of the curve is however very steep. Thus the presence of bulky substituents leads to appreciable nonbonded repulsions which are stronger in the pyramidal than in the planar state, where repulsions are partially relieved by the opening of the angle 0. As a consequence the pyramidal state is destabilized with respect to the planar TS and the inversion barrier is expected to decrease. 

Tang K T and Toennies J P 1984 An improved simple model for the van der Waals potential based on universal damping functions for the dispersion coefficients J. Chem. Phys. 80 3726... 

The potential energy of a molecular system in a force field is the sum of individnal components of the potential, such as bond, angle, and van der Waals potentials (equation H). The energies of the individual bonding components (bonds, angles, and dihedrals) are function s of th e deviation of a molecule from a h ypo-thetical compound that has bonded in teraction s at minimum val-n es. 

Figure 4-15 A van der Waals Potential Energy Function. The Energy minimum is shallow and the interatomic repulsion energy is steep near the van der Waals radius.

The calculations have been carried out for a one-component, Lennard-Jones associating fluid with one associating site. The nonassociative van der Waals potential is thus given by Eq. (87) with = 2.5a, whereas the associative forces are described by means of Eq. (60), with d = 0.5contact with an attracting wall. The fluid-wall potential is given by the Lennard-Jones (9-3) function... 

Figure 4.13 shows the free energy profile as a function of the helix-helix distance. Equation (4.47) allows the computation of the contributions to the profile by the different intermolecular potentials. The helix-helix and helix-solvent interactions were considered. The helix-helix van der Waals potential shows a significant minimum... 

Comparisons of calculated and measured quenching rates provide a useful measure of the accuracy of the wave function used for the system. As an example, the value of Ze for helium calculated from the zero energy static-exchange wave function of Barker and Bransden (1968) is 0.0347, or 0.0445 when the van der Waals potential is added to the static-exchange equation however, the experimental value obtained by Coleman et al. (1975b) at room temperature is 0.125 0.002 (see section 7.3). This rather large discrepancy, a factor of three, shows that the static-exchange wave function provides a poor representation of the electron-positron correlations in this system. 

Fig. 12.1. Schematic illustration of a van der Waals potential as a function of the intermolecular bond distance R measured from the atom X to the center-of-mass of the diatom, I2 in the present case. The orientation angle 7 and the intramolecular I2 bond distance are fixed. The potential parameters governing the long-range attractive and the short-range repulsive branches, namely A, a, and C, depend, in principle, on r and 7.

In the development of the set of intermolecular potentials for the nitramine crystals Sorescu, Rice, and Thompson [112-115] have considered as the starting point the general principles of atom-atom potentials, proven to be successful in modeling a large number of organic crystals [120,123]. Particularly, it was assumed that intermolecular interactions can be separated into dispersive-repulsive interactions of van der Waals and electrostatic interactions. An additional simplification has been made by assuming that the intermolecular interactions depend only on the interatomic distances and that the same type of van der Waals potential parameters can be used for the same type of atoms, independent of their valence state. The non-electric interactions between molecules have been represented by Buckingham exp-6 functions,... 

It has been traditional to define a van der Waals potential (which combines Coulomb s law and the Lennard-Jones 6-12 potential function) and thereby subsume electronic shell repulsion, London forces, and electrostatic interactions under the term van der Waals interaction. Unfortunately, the resulting expression is an oversimplified treatment of the electrostatic interactions, which are only calculated between close neighbors and are considered to be spatially isotropic. Both of these implicit assumptions are untrue and do not represent physically realistic approximations. We prefer to use the term van der Waals distance for the intemuclear separation at which the 6-12 potential function is a minimum (see Fig. 6), the van der Waals radius being one-half this value when the two interacting atoms are identical, and explicitly treat the Lennard-Jones and electrostatic terms separately. While the term van der Waals interaction may have some value as a shorthand in structure description, it should be avoided when energetics are treated quantitatively. 

Pig. 31. The fraction of intact parents that recoil from the surface as a function of the impact energy. MD simulations for a cluster of 8 NH3 molecules interacting only by a central van der Waals potential and by a potential containing in addition a dipolar attraction. The extra attraction shifts the shattering transition to a higher energy. 

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