Potential, chemical Lennard-Jones

P. Bryk, A. Patrykiejew, O. Pizio, S. Sokolowski. The chemical potential of Lennard-Jones associating fluids from osmotic Monte Carlo simulations. Mol Phys 92 949, 1997 A method for the determination of chemical potential for associating liquids. Mol Phys 90 665, 1997. 

In the case of a Lennard-Jones fluid, the knowledge of the bulk density in the nonreactive part is all that is needed to calculate the chemical potential. Actually, one can use the equation of state of Nicolas et al. [115] (or the... 

To conclude, the introduction of species-selective membranes into the simulation box results in the osmotic equilibrium between a part of the system containing the products of association and a part in which only a one-component Lennard-Jones fluid is present. The density of the fluid in the nonreactive part of the system is lower than in the reactive part, at osmotic equilibrium. This makes the calculations of the chemical potential efficient. The quahty of the results is similar to those from the grand canonical Monte Carlo simulation. The method is neither restricted to dimerization nor to spherically symmetric associative interactions. Even in the presence of higher-order complexes in large amounts, the proposed approach remains successful. 

The main difference between the three functions is in the repulsive part at short distances the Lennard-Jones potential is much too hard, and the Exp.-6 also tends to overestimate the repulsion. It furthermore has the problem of inverting at short distances. For chemical purposes these problems are irrelevant, energies in excess of lOOkcal/mol are sufficient to break most bonds, and will never be sampled in actual calculations. The behaviour in the attractive part of the potential, which is essential for intermolecular interactions, is very similar for the three functions, as shown in... 

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. 

It is difficult to point to the basic reason why the average-potential model is not better applicable to metallic solutions. Shimoji60 believes that a Lennard-Jones 6-12 potential is not adequate for metals and that a Morse potential would give better results when incorporated in the same kind of model. On the other hand, it is possible that the main trouble is that metal solutions do not obey a theorem of corresponding states. More specifically, the interaction eAB(r) may not be expressible by the same function as for the pure components because the solute is so strongly modified by the solvent. This point of view is supported by considerations of the electronic models of metal solutions.46 The idea that the solvent strongly modifies the solute metal is reached also through a consideration of the quasi-chemical theory applied to dilute solutions. This is the topic that we consider next. 

Equilibrium Systems. Magda et al (12.) have carried out an equilibrium molecular dynamics (MD) simulation on a 6-12 Lennard-Jones fluid In a silt pore described by Equation 41 with 6 = 1 with fluid particle Interactions given by Equation 42. They used the Monte Carlo results of Snook and van Me gen to set the mean pore density so that the chemical potential was the same In all the simulations. The parameters and conditions set In this work were = 27T , = a, r = 3.5a, kT/e = 1.2, and... 

Multiparticle collision dynamics provides an ideal way to simulate the motion of small self-propelled objects since the interaction between the solvent and the motor can be specified and hydrodynamic effects are taken into account automatically. It has been used to investigate the self-propelled motion of swimmers composed of linked beads that undergo non-time-reversible cyclic motion [116] and chemically powered nanodimers [117]. The chemically powered nanodimers can serve as models for the motions of the bimetallic nanodimers discussed earlier. The nanodimers are made from two spheres separated by a fixed distance R dissolved in a solvent of A and B molecules. One dimer sphere (C) catalyzes the irreversible reaction A + C B I C, while nonreactive interactions occur with the noncatalytic sphere (N). The nanodimer and reactive events are shown in Fig. 22. The A and B species interact with the nanodimer spheres through repulsive Lennard-Jones (LJ) potentials in Eq. (76). The MPC simulations assume that the potentials satisfy Vca = Vcb = Vna, with c.,t and Vnb with 3- The A molecules react to form B molecules when they approach the catalytic sphere within the interaction distance r < rc. The B molecules produced in the reaction interact differently with the catalytic and noncatalytic spheres. 

Fig. 2.2. Average electrostatic potential mc at the position of the methane-like Lennard-Jones particle Me as a function of its charge q. mc contains corrections for the finite system size. Results are shown from Monte Carlo simulations using Ewald summation with N = 256 (plus) and N = 128 (cross) as well as GRF calculations with N = 256 water molecules (square). Statistical errors are smaller than the size of the symbols. Also included are linear tits to the data with q < 0 and q > 0 (solid lines). The fit to the tanh-weighted model of two Gaussian distributions is shown with a dashed line. Reproduced with permission of the American Chemical Society...

In contrast to the Gibbs ensemble discussed later in this chapter, a number of simulations are required per coexistence point, but the number can be quite small, especially for vapor-liquid equilibrium calculations away from the critical point. For example, for a one-component system near the triple point, the density of the dense liquid can be obtained from a single NPT simulation at zero pressure. The chemical potential of the liquid, in turn, determines the density of the (near-ideal) vapor phase so that only one simulation is required. The method has been extended to mixtures [12, 13]. Significantly lower statistical uncertainties were obtained in [13] compared to earlier Gibbs ensemble calculations of the same Lennard-Jones binary mixtures, but the NPT + test particle method calculations were based on longer simulations. 

The basic formalism of the X-dynamics method has taken various forms in its application to problems of interest. In an early prototype calculation to assess umbrella sampling in chemical coordinates, the X-dynamics method was used to evaluate the relative free energy of hydration for a set of small molecules which included both nonpolar (C2H6,) and polar (CH3OH, CH3SH, and CH3CN) solutes.1 By assigning a separate X variable to the Lennard-Jones and Coulomb interactions, a linear partition of the potential part of the hybrid Hamiltonian was constructed... 

In the study of reactivity, Jorgensen and col. have normally used both, the OPLS model and potential functions derived from ab initio calculations. As we have already indicated, when intermolecular pair potentials are applied to the study of a chemical process, the evolution of charges, as well as the Lennard-Jones terms, along the reaction coordinate, has to be considered. For the SN2 reaction in water between chloride anion... 

These models retain the form of the nonbonded interaction used in the chemically realistic modeling, i.e., they use either an interaction of the Lennard-Jones or of the exponential-6 type. The repulsive parts of these potentials generate the necessary local excluded volume, whereas the attractive long-range parts can be used to model varying solvent quality for dilute or semi-dilute solutions and to generate a reasonable equation-of-state behavior for polymeric melts. 

The Lennard-Jones potential is a rather crude representation of an actual intermolecular potential, chosen more often for computational simplicity than chemical accuracy. More accurate for many chemical purposes is the Morse potential... 

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