Leonard-Jones potential

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-... 

Most MC studies of small clusters have used free-volume conditions. However, the choice of boundary conditions has a pronounced effect on the properties of small clusters. For a Leonard-Jones potential and a Boltzmann distribution function, the average potential energy given by Eq. (21) vanishes in the limit of an infinite number of configurations. Physically, this corresponds to the evaporation of particles from the surface and is not unexpected. If there is no constraining force on the cluster, there should be a net escape of... 

It seems that the method to fix the size parameter of the Leonard-Jones potential to match the density of ambient water is unable to predict the internal energy of the high density phases of ice. 

Fig. 10. Covalent and ionic potential curves for some NO-quencher pairs. Equation (26) was used to calculate the ionic curves, using the electron affinities of Table III. The covalent curves are Leonard-Jones potential of NO and the respective quencher, displaced by the electronic excitation energy of the appropriate Rydberg state. See text for further details.

Leonard-Jones potential - A simple but useful function for approximating the interaction between two neutral atoms or molecules separated by a distance r by writing the potential energy as U(r) = (rJry - rJrY, where e and are adjustable parameters. In this form the depth of the potential well is 8 and the minimum occurs at. The (l/r) term is often replaced by other powers of 1/r. 

A more accurate model, in which molecular interactions are described by a Leonard-Jones potential, gives mean fiee path values about 5% lower than this table (see Reference 4). 

M. H. Kalos, Energy of a boson fluid with Leonard-Jones potentials, Phys. Rev. A 2,250-255... 

Colloidal Particles with an interaction range >2.5 x A, where A is a characteristic length, equal to the average distance between particles. The CP-CP interactions can be simulated by a soft-sphere, energy-conserving potential with an attractive tail. The CP-CP forces conservative in nature and can be simulated by the two-body Leonard-Jones potential (see Equation (26.14)). 

It is the method with empirical potential model. As the modeL the approximation that any molecule can behave as if obeying Leonard-Jones potential seems to be satisfactory. This (one-center) LJ model is valid only for rare gases and simple spherical molecules. But this model may also be valid for other simple molecules as a zeroth approximation. We may also use two-center LJ model where interatomic interactions are concentrated to the major two atoms in the molecule. We expect that these one-center and two-center LJ models will play a role of Occam s razor. 

W. T. Ashurst and W. G. Hoover, Argon shear viscosity via a Leonard-Jones potential with equilibrium and non-equilibrium molecular dynamics, Phys. Rev. Lett. 31, 206-207 (1973). 

Inert-gas crystals The electron distribution is similar to that for the free atoms. Therefore, the atoms behave similarly to hard spheres, which pack together to form crystals with a close-packed structure, typically fee. The atoms are bound with the weak van der Waals dispersion force which results from the oscillation of the electrons around the nuclei. The potential energy of interaction between two atoms may be described by the Leonard-Jones potential given by... 

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