6-12 Lennard-Jones functions

A 6-12 function (also known as a Lennard-Jones function) frequently simulates van der Waats in tcraction s in force fields (ec iia-tion t 1). 

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.

The characteristic ratios of poly(pro-gly), poly(hyp-gly), poly(gly-gly-pro-gly), poly(gly-gly-hyp-gly), and poly(pro-ale) are determined in water, The results confirm the main features of the theoretical conformational maps derived by Rory and coworkers for glycine followed by either l-proline or a nonproline residue. Small adjustments, well within the uncertainty described by Schimme and Rory, are suggested In the conformational map for L-proline followed by glycine. The constants for the Lennard-Jones functions of Scheraga and coworkers, as used by Madison and Scheliman, produce a conformational map for L-proline followed by a nonproline residue which is in somewhat poorer agreement with experiment. The two sets of modified constants introduced by Madison and Scheliman fall to predict the conformational properties of these sequential copolypeptides. 

June et al. (12) used TST as an alternative method to investigate Xe diffusion in silicalite. Interactions between the zeolite oxygen atoms and the Xe atoms were modeled with a 6-12 Lennard-Jones function, with potential parameters similar to those used in previous MD simulations (11). Simulations were performed with both a rigid and a flexible zeolite lattice, and those that included flexibility of the zeolite framework employed a harmonic term to describe the motion of the zeolite atoms, with a force constant and bond length data taken from previous simulations (26). 

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... 

Auerbach et al. (101) used a variant of the TST model of diffusion to characterize the motion of benzene in NaY zeolite. The computational efficiency of this method, as already discussed for the diffusion of Xe in NaY zeolite (72), means that long-time-scale motions such as intercage jumps can be investigated. Auerbach et al. used a zeolite-hydrocarbon potential energy surface that they recently developed themselves. A Si/Al ratio of 3.0 was assumed and the potential parameters were fitted to reproduce crystallographic and thermodynamic data for the benzene-NaY zeolite system. The functional form of the potential was similar to all others, including a Lennard-Jones function to describe the short-range interactions and a Coulombic repulsion term calculated by Ewald summation. 

Schwartz et al.26 deduced values of / from the Lennard-Jones parameters e and r0, which have been derived from viscosity measurements, and analysed and tabulated by Hirschfelder et a/.31. A detailed account of the required calculation has been given by Herzfeld and Litovitz32. The problem is to obtain a satisfactory fit of the exponential interaction potential, with the repulsive region of the Lennard-Jones function... 

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... 

The problem of selecting the appropriate values, r°, for the equilibrium hydrogen-bond lengths is avoided by using only the Lennard-Jones function. 

Many models fail to capture this behavior, however, so temperature transfer-ability is far from an automatic feature of polarizable models.Indeed, it has been demonstrated by several authors that a point dipole-based model designed specifically to reproduce properties of the gas-phase monomer and the bulk liquid at 298 K is doomed to fail at higher temperatures. This failure could arise from insufficiencies in the Lennard-Jones function typically... 

ID. S3rmmetrical Molecule with Central Forces. If we discard the idea of a hard sphere and replace it by a molecule that is capable of exerting both attractive and repulsive forces but acts centrally, we have the closest approach yet to real molecules, and also the model that is most difficult to treat. Such a molecule is characterized completely by the function chosen to represent its force field. A function commonly used is the Lennard-Jones function... 

Atomic repulsion and induced dipole-induced dipole dispersive attraction are typically described by a Lennard-Jones function [16,17] ... 

Most force fields use the Lennard-Jones functional form or close derivatives (9-6 or 14-7 functional forms as opposed to the standard 12-6 form). To compensate for the too hard repulsive component, MM2 and MM3 use the Buckingham potential shown in Eq. (9). 

Soft vdW potentials are often used in simulations of whole-ligand docking approaches. For example, Flog uses a 6-9 Lennard-Jones function for vdW interactions,... 

Ion-ion interactions are often described by a simple combination of Coulomb and Lennard-Jones type potential functions [105, 106] which have also been employed in simulations of electrolyte solutions near interfaces [107-109]. It was noted that these Lennard-Jones functions are inadequate for LiCl solutions at high concentrations [32, 110], as they are too repulsive at intermediate distances. Bom-Mayer-Huggins potential functions of the functional form... 

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