Lennard-Jones-type potential

Superposed are Lennard-Jones-type potentials that are strongly repulsive at short distances, so that two water molecules cannot overlap. 

In an early attempt to model the dynamics of the chromatin fiber, Ehrlich and Langowski [96] assumed a chain geometry similar to the one used later by Katritch et al. [89] nucleosomes were approximated as spherical beads and the linker DNA as a segmented flexible polymer with Debye-Huckel electrostatics. The interaction between nucleosomes was a steep repulsive Lennard-Jones type potential attractive interactions were not included. 

The interaction between noble gas atoms can be represented by the Lennard-Jones-type potential... 

The interaction of an IL ( C mim][Cl]) with an external field, i.e., an IL confined between electrified walls, was investigated by the Lynden-Bell group [111]. The potential between the ions and the walls was modeled by a Lennard-Jones type potential and additional forces on each charged site in z-direction were obtained by... 

The equilibrium constant, K, can be related to the Lennard-Jones type potential function as follows. The concentration profile of the solute at polymer-solution interface may be described schematically as shown in Figure 3a and 3b. 

Eq 26 indicates that the equilibrium constant K is uniquely related to parameters B and D which characterize the Lennard-Jones type potential function. 

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... 

Rare gas dimers are prototypical systems to examine van der Waals interaction function forms [88, 92, 98-100]. It should be noted that such examinations on the vdW potentials generally employ the assumption that the total interactions between two rare gas atoms are all from the vdW interactions. A seminal work by Halgren [88] found that neither the Lennard-Jones type potentials (Lennard-Jones 12-6 or Lennard-Jones 9-6) nor the Buckingham exp-6 potentials was able to well replicate the high quality reference data, while a buffered 14-7 potential was found to yield much better performance. It should be noted that in the calculation of van der Waals reference energies by Halgren [88], the charge penetration effects have not been separated out. It is well known that there... 

Notation Vn Polynomial of order n P (cos) polynomial of order n in cosine to the angle cos(nS) Fourier term(s) in cosine to the angle Exp-6 exponential + R n - m R + R Lennard-Jones type potential quad electric moments up to quadrupoles polar polarizable fixed not a variable imp. improper torsional angle ss stretch-stretch bb bend-bend sb stretch-bend St stretch-torsional bt bend-torsional tt torsional-torsional btb bend-torisional-bend. 

Some computer simulations of micelles on a molecular level have already been performed with molecular dynamics calculations. The models used in these simulations are based on different approximation levels. In simulations in which solvent molecules were omitted, the solvation shell was simulated by a sphere, and the interactions between the atoms and the sphere was calculated by Lennard-Jones-type potential functions. In more advanced simulations, the solvent molecules were especially considered and specific water models like SPC were used. 

In the framework of solvent shift theories, using a Lennard-Jones type potential for the interaction of a nonpolar dye in a nonpolar matrix, Sesselman et al. [34] developed a simple theory for the interpretation of hole-burning data in the low pressure range (<20 MPa). In this regime, die pressure shift Av varies linearly with the solvent shift Avs, i.e. the difference between the molecular absorption frequency in the matrix and in vacuum, the local hydrostatic compressibility k and the pressure change Ap ... 

A good model of the electrolyte must describe the ions, solvent molecules and their orientation at the molecular level. Molecular dynamics simulations that are performed to visualize the orientation of the electrolyte molecules in the vicinity of the electrode surface are based on a set of parameters that can be varied in order to best described the properties of the system under investigation. The most reasonable models for solvent-solvent and ion-solvent interactions consider distribution of point charges on solvent molecules and take into account Lennard-Jones-type potentials that are strongly repulsive at short distances. Molecular dynamics simulations are typically performed on a system confined between two metal electrodes and the number of confined ions and solvent molecules is often limited by the computing power of modem computers. Some representative examples of results of such calculations are given in ref 60,63-68. 

The interface between two nonpolar atomic solvents interacting through Lennard-Jones-type potentials has been studied [41] diffusion in the interfacial region was found to be anisotropic. 

The energy minimum for a given atomic pair is described by the potential depth, Eij, and position, R j. Other force fields model van der Waals interactions using a modified Hill equation, which replaces the twelfth power term in Eq. (28) with an exponential term [42,43]. Different approaches are also used to describe nonbonded interactions between those atoms that may form hydrogen bonds. Some force fields model these interactions using only Coulombic terms, whereas other force fields employ special functions, such as a modified 10-12 Lennard-Jones-type potential term [46], as shown in Eq. (29). 

The Lennard-Jones type potential is used for the interaction between Fe atoms and lubricant molecules. The parameter c in the Leonard-Jones potential was changed in order to investigate the effect of the interaction between lubricants and the sur ces. There are oxide or any other contaminants present on actual solid sur ces, ndiich may make interaction between surface atoms and lubricant molecules weaker. The calculations are conducted by using the original value e, and the half value of E, denoted by E0.5. 

Table 4 Atomic and molecular data (number of electrons in atomic valtmce shell, atomic chemical hardness jj, atomic ground-state energy Eg, interatomic homopolar binding length with respect to the first Bohr radius oq. along the specific physical and chemical bonding BEC energies) for hydrogen and helium toward assessing their BEC-bonding Lennard-Jones-type potential (181), all in atomic units...

Z. Q. Wu, H. Serizawa and H. Murakawa, New Computer Simulation Method for Evaluation of Crack Growth Using Lennard-Jones Type Potential Function, Key Engineering Materials, 166, 25-32 (1999). 

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