Leonard-Jones

Bond stretching is most often described by a harmonic oscillator equation. It is sometimes described by a Morse potential. In rare cases, bond stretching will be described by a Leonard-Jones or quartic potential. Cubic equations have been used for describing bond stretching, but suffer from becoming completely repulsive once the bond has been stretched past a certain point. 

Most of the methods proposed include a van der Waals term for describing nonbonded interactions between atoms in the two regions. This is usually represented by a Leonard-Jones 6-12 potential of the form... 

Here, k provides a measure of the anisotropy in the well depth and for rodlike molecules is the ratio 8 1 where and Eg are the well depths when the molecules are side-by-side and end-to-end, respectively. The scaling parameter Eq is the well depth when the molecules are in the cross configuration as we can see by setting u, uj = u, f = uj f = 0 in Eqs. (4), (6) and (7). We should note that in the limit k and k tend to unity, that is x and x vanish then the Gay-Berne potential is reduced to the Leonard-Jones 12-6 potential. 

The eorresponding result for the surface tension [9] provides quite reasonable accuracy for a Leonard Jones fluid or an inert gas fluid, except helium whieh displays large quantum effeets. Thus we ean eonelude that the leading mechanisms of surface tension in a simple fluid is the loss of binding energy of the liquid phase at the gas-liquid interface and the seeond most important meehanism is likely to be the adsorption-depletion at the interface whieh ereates a moleeularly smooth density profile instead of an abrupt step in the density. 

The GvdW theory has been applied also to mixtures of Leonard-Jones fluids [15,16], The extension to mixtures is straightforward with respect to the binding energy and interaction with an external field but not quite so straightforward with respect to the excluded volume effect. The GvdW(S) theory produces for a mixture of c components an equation of state of the form... 

The interaction between nucleosomes plays an important role for the stability of the 30 nm fiber recent experiments on liquid crystals of mononucleosomes [44-47] and also less concentrated mononucleosome solutions [48,49] show an attractive interaction that can be parameterized by an anisotropic Leonard-Jones type potential [50]. Also, an electrostatic interaction potential has been computed using the crystallographic structure of the nucleosome [51]. The influence of these potentials on the structure of the fiber is discussed below together with the corresponding models. 

Here Vij denotes the distance between atoms i and j and g(i) the type of the amino acid i. The Leonard-Jones parameters Vij,Rij for potential depths and equilibrium distance) depend on the type of the atom pair and were adjusted to satisfy constraints derived from as a set of 138 proteins of the PDB database [18, 17, 19]. The non-trivial electrostatic interactions in proteins are represented via group-specific dielectric constants ig(i),g(j) depending on the amino-acid to which atom i belongs). The partial charges qi and the dielectric constants were derived in a potential-of-mean-force approach [20]. Interactions with the solvent were first fit in a minimal solvent accessible surface model [21] parameterized by free energies per unit area (7j to reproduce the enthalpies of solvation of the Gly-X-Gly family of peptides [22]. Ai corresponds to the area of atom i that is in contact with a ficticious solvent. Hydrogen bonds are described via dipole-dipole interactions included in the electrostatic terms... 

A slightly different technique was used by Allen [536]. A large number of solvent molecules were allowed to move each according to a Langevin equation in a force field of all the other molecules (which interact by Leonard-Jones potentials). In this system, there are two reactants, AB and C, and the reaction is of the type... 

The integral in Equation 7.41 must be calculated by computer for a Leonard-Jones potential (Figure 7.9). This curve agrees remarkably well with experimentally mea-... 

Species MW MW 0) Leonard—Jones parameters Critical constants ... 

The binary diffusivity, D, of the reactants in which the Leonard-Jones parameters (o, Q) are available, is calculated through the Chapman-Enskog theory by,... 

Figure 1. A schematic picture of the one dimensional tem under study in the first part of this chapter. The particle of interest corresponds to an index i = b and has mass M, while the particles of the thermal bath have mass m. We use as space coordinates the displacement of particle i from particle i — 1. The particles of the systmn interact via a nearest-neighbor interaction. We shall consider both the case where this interaction is linear (Section II) and where it is of the Leonard-Jones type (Section IV).

L. Verier, Phys. Rev., 159, 98 (1967). Computer Experiments on Classical Fluids. I. Thermodynamic Properties of Leonard—Jones Molecules. 

CONH (amide), Leonard—Jones parameters Cieplak 1991 CONH (peptide)... 

Leonard-Jones, J. E. (1949a). Proc. r. Soc., London A198, 1. 

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