Lennard-Jones 10-12 potential function description

The classical kinetic theoty of gases treats a system of non-interacting particles, but in real gases there is a short-range interaction which has an effect on the physical properties of gases. The most simple description of this interaction uses the Lennard-Jones potential which postulates a central force between molecules, giving an energy of interaction as a function of the inter-nuclear distance, r. 

Figure 2.10. Part of the better description of the Morse and Exp.-6 potentials may be due to the fact that they have three parameters, while the Lennard-Jones potential only employs two. Since the equilibrium distance and the well depth fix two constants, there is no additional flexibility in the Lennard-Jones function to fit the form of the repulsive interaction.

Successful computer modelling of physisorption is dependent, inter alia, on th j validity of the solid-fluid and fluid-fluid potential functions (Cracknell et al 1995). A rigorous description of the attractive and repulsive components is complex (see Nicholson, 1997) however, as was indicated in Chapter 1, the pairwise inter action between a single adsorbate atom and a solid atom is still usually expressed in the form of the 12-6 Lennard-Jones potential. For our present purpose, we may write... 

The above description has illustrated the computational design of new inorganic frameworks constmcted from D4R units. Other types of SBUs are also allowed in this method. If ML4 (M—L = 1.65 A) is used as the SBU (Lennard-Jones potential parameters are given in Table 7.3), the potential function of SBU in the unit cell is calculated by Equation (7.3) [35]... 

For small systems, where accurate interaction energy profiles are available, it has been shown that the Morse function actually gives a slightly better description than an Exp.-6, which again performs significantly better than a Lennard-Jones 12-6 potential. This is illustrated for the H2-He interaction in Figure 2.9. 

The intermolecular potential term is represented by a simple Lennard-Jones function that is attenuated at short interatomic distances by a cubic spline so that at small (covalent) intemuclear distances, the description of the interaction is that of the intramolecular term only. The original form of... 

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. 

In the description of the intermolecular bonding, the Lennard-Jones 6-12 potential function (8) is one of the most common, consisting of an attractive and repulsive contribution to the van der Waals component of the lattice energy (Vydw) as shown in Equation 1. "A" and "B" are the atom-atom parameters for describing a particular atom-atom interaction and "r" is the interatomic distance. This potential function has formed the basis of a variety of different force fields (9-11) that were utilized in this paper. A modified (10-12 version of this potential can also be employed (10,11) to describe hydrogen bonding. The 10-12 potential is very similar in construction to Equation 1 except that the attractive part is dependent on r ° rather than r. ... 

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