Lennard-Jones interactions computer simulations

A few groups replace the Lennard-Jones interactions by interactions of a different form, mostly ones with a much shorter interaction range [144,146]. Since most of the computation time in an off-lattice simulation is usually spent on the evaluation of interaction energies, such a measure can speed up the algorithm considerably. For example, Viduna et al. use a potential in which the interaction range can be tuned... 

Thermodynamic information can also be obtained from simulations. Currently we are measuring the differences in chemical potential of various small molecules in dimethylimidazolium chloride. This involves gradually transforming one molecule into another and is a computationally intensive process. One preliminary result is that the difference in chemical potential of propane and dimethyl ether is about 17.5 kj/mol. These molecules are similar in size, but differ in their polarity. Not surprisingly, the polar ether is stabilized relative to the non-polar propane in the presence of the ionic liquid. One can also investigate the local arrangement of the ions around the solute and the contribution of different parts of the interaction to the energy. Thus, while both molecules have a favorable Lennard-Jones interaction with the cation, the main electrostatic interaction is that between the chloride ion and the ether molecule. 

Ionic monolayers can be, and have also been, analyzed theoretically either with advanced lattice theories or with Monte Carlo or molecular dynamics simulation. Basic principles and some illustrations of monolayer compositions have already been discussed in sec. 3.5. The step from Langmuir to Gibbs monolayers is theoretically realized through the choice of the adsoption energy. As before, the selection of the various parameters (x -interaction parameters in lattice theories, constants in the Lennard-Jones, interactions in MD, etc.) and approximations (choice of lattice, accounting for stereoisomery, or extent of truncation, respectively) remain a central issue. In view of the growing power of computers, increasingly better results may be expected in the near future. 

Reif MM, Hunenherger PH (2011) Computation of methodology-independent single-ion solvation properties Irom molecular simulations. IV. Optimized Lennard-Jones interaction parameter sets for the alkali and halide ions in water. J Phys Chem 134 144104... 

The simplest model of a tethered membrane is composed of purely repulsive spheres which are connected together to form a planar triangulated network. In MC simulations, the spheres are taken as hard spheres, while in MD simulations, they interact with a purely repulsive Lennard-Jones interaction, eq. (9.3). A variety of tethering potentials have been used, as discussed in Section 9.2, usually for a hexagonal sheet of size L containing N = 3L -L l)/4 monomers. These systems are often referred to as open since the perimeter is free. To minimize finite size effects, some simulations have been done on closed systems in which the monomers are connected to form a spherical shell. Abraham used periodic boundary conditions and a computational cell which was allowed to vary in size using a constant-pressure MD technique. More recently, simulations have been carried out for membranes in which linear chains of n monomers are... 

The mesoscale model consists of a set of crosslink nodes (i.e., junctions) connected via single finite-extensible nonlinear elastic (FENE) bonds (that can be potentially cross-linked and/or scissioned), which represent the chain segments between crosslinks. In addition, there is a repulsive Lennard-Jones interaction between all crosslink positions to simulate volume exclusion effects. The Eennard-Jones and FENE interaction parameters were adjusted and the degree of polymerization (p) for a given length of a FENE bond calibrated until the MWD computed from our network matched the experimental MWD of the virgin material [112]. 

This discontinuity may result in numerical instabilities during a simulation, because the value of the force may be computed to be much larger than the largest number understood by the computer. In order to avoid the discontinuity the entire potential can be shifted by a constant M(rc). As a result, the Lennard-Jones interaction energy becomes zero at fc in a smooth, continuous way (Fig. 14.2). A long-range correction is then needed, because the potential is actually not zero at the cutoff... 

Ligand-Protein Interactions The energy of formation of ligand-protein contacts can be computed as a sum of non-bonded (Lennard-Jones and electrostatic) terms similar to those used in a molecular dynamics simulation. 

Extensive computer simulations have been caiTied out on the near-surface and surface behaviour of materials having a simple cubic lattice structure. The interaction potential between pairs of atoms which has frequently been used for inert gas solids, such as solid argon, takes die Lennard-Jones form where d is the inter-nuclear distance, is the potential interaction energy at the minimum conesponding to the point of... 

To illustrate the relationship between the microscopic structure and experimentally accessible information, we compute pseudo-experimental solvation-force curves F h)/R [see Eq. (22)] as they would be determined in SEA experiments from computer-simulation data for T z [see Eqs. (93), (94), (97)]. Numerical values indicated by an asterisk are given in the customary dimensionless (i.e., reduced) units (see [33,75,78] for definitions in various model systems). Results are correlated with the microscopic structure of a thin film confined between plane parallel substrates separated by a distance = h. Here the focus is specifically on a simple fluid in which the interaction between a pair of film molecules is governed by the Lennard-Jones (12,6) potential [33,58,59,77,79-84]. A confined simple fluid serves as a suitable model for approximately spherical OMCTS molecules confined... 

In a statistical Monte Carlo simulation the pair potentials are introduced by means of analytical functions. In the election of that analytical form for the pair potential, it must be considered that when a Monte Carlo calculation is performed, the more time consuming step is the evaluation of the energy for the different configurations. Given that this calculation must be done millions of times, the chosen analytic functions must be of enough accuracy and flexibility but also they must be fastly computed. In this way it is wise to avoid exponential terms and to minimize the number of interatomic distances to be calculated at each configuration which depends on the quantity of interaction centers chosen for each molecule. A very commonly used function consists of a sum of rn terms, r being the distance between the different interaction centers, usually, situated at the nuclei. In particular, non-bonded interactions are usually represented by an atom-atom centered monopole expression (Coulomb term) plus a Lennard-Jones 6-12 term, as indicated in equation (51). 

FFs that are parameterized for high-pressure conditions can still lead to behavior that differs from that observed in experiments. For instance, it is common practice to treat the interatomic interactions with Lennard-Jones (LJ) potentials. Although this method is convenient from a computational standpoint, it is known that LJ potentials do not reproduce experimentally observed behavior such as necking, where a material attempts to minimize surface area and will break under large tensile stresses. Many other examples exist where particular types of FFs cannot reproduce properties of materials, and once again, we emphasize that one should ensure that the FF used in the simulation is sufficiently accurate. 

The computer simulations employed the molecular dynamics technique, in which particles are moved deterministically by integrating their equations of motion. The system size was 864 Lennard-Jones atoms, of which one was the solute (see Table II for potential parameters). There were no solute-solute interactions. Periodic boundary conditions and the minimum image criterion were used (76). The cutoff radius for binary interactions was 3.5 G (see Table II). Potentials were truncated beyond the cutoff. 

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