Potential short-range interactions

Short-Range Interaction Potentials Short-range interaction potentials apply to those interactions that attenuate rapidly as the distance between the atoms increases. The most commonly used short-range interaction potential is probably the Lennard-Jones 12-6 potential (as shown in Fig. 1) ... 

It is thus seen that the dipole-induced dipole propagation gives an exponential rather than an inverse x cube dependence of U x) with x. As with the dispersion potential, the interaction depends on the polarizability, but unlike the dispersion case, it is only the polarizability of the adsorbed species that is involved. The application of Eq. VI-43 to physical adsoiption is considered in Section XVII-7D. For the moment, the treatment illustrates how a long-range interaction can arise as a propagation of short-range interactions. 

Sutton and Chen extended the potential to longer range to enable the study of certain problems such as the interactions between clusters of afoms [Sutton and Chen 1990]. Their objective was to combine the superior Fiimis-Sinclair description of short-range interactions with a van der Waals tail to model the long-range interactions. The form of the Sutton-Chen potential is ... 

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. 

In a classical simulation a force-field has to be provided. Experience with molecular liquids shows that surprisingly good results can be obtained with intermolecular potentials based on site-site short-range interactions and a number of charged sites... 

The local conformational preferences of a PE chain are described by more complicated torsion potential energy functions than those in a random walk. The simulation must not only establish the coordinates on the 2nnd lattice of every second carbon atom in the initial configurations of the PE chains, but must also describe the intramolecular short range interactions of these carbon atoms, as well as the contributions to the short-range interactions from that... 

In comparison with other spectroscopic techniques, NMR is blessed with short-range interactions that render it possible to characterize and influence the spin evolution over relatively long periods of time without excessive loss from dissipative processes. This implies that the spin evolution to a large extent (but certainly not exclusively) may be described as unitary evolution of coherence/polarization potentially supplemented with corrections due to relaxation. 

A number of techniques have been employed to model the framework structure of silica and zeolites (Catlow Cormack, 1987). Early attempts at calculating the lattice energy of a silicate assumed only electrostatic interactions. These calculations were of limited use since the short-range interactions had been ignored. The short-range terms are generally modelled in terms of the Buckingham potential,... 

The first part of its trajectory involves short-range interactions of a chemical nature, and therefore these are usually called chemical effects. However, these chemical effects are nothing else than the chemical potential (p), 33of the electron with opposite sign (see Section 6.3.13). 

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. 

Let us consider a slit-like pore of width D along whose walls the ip(x) potential is localized (Fig. 4). We shall regard the interaction of monomers with the walls as a short-range interaction and the characteristic radius of interaction as being of the order of the segment size a. The exact assignment of the form of the potential is immaterial for our purposes, since it describes the effective interaction of units with the pore walls, renormalized by the solvent molecules. Conditions are to be as follows ... 

The Lennard-Jones potential is simpler than the Buckingham potential since it has two rather than three parameters. Computations involving the Lennard-Jones potential are also faster as they do not involve any exponential terms. However, with the performance of the computers currently available, the Buckingham potential, which gives a better description of short-range interactions, may be preferred. 

At this point, we have defined an ideal reference state for the RNA in which there are no net interactions with ions, and introduced the RNA activity coefficient as a factor that assesses the deviation of the RNA from ideal behavior due to its interactions with all the ions in solution. No assumptions have been made about the nature of the ion interactions anions and cations, long- and short-range interactions all contribute. The ion interaction coefficients (Eqs. (21.4a) and (21.4b)) also reflect the ion—RNA interactions that create concentration differences in a dialysis experiment, and there is an intimate relationship between activity coefficients (y) and interaction coefficients (F), as developed below. This relationship will be extremely useful y comes from the chemical potential and gives access to free energies and other thermodynamic functions, while F is directly accessible by both experiment and computation (see Pappu et al., this volume, 111.20). 

---