Lennard—Jones particle

Similar calculations have been carried out for an equimolar binary mixture of associating Lennard-Jones particles with spherically symmetric associative potential [173]. The interaction between similar species is given by Eq. (87), whereas the interaction between different species is chosen in the form... 

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...

Intermediate states do not have to be physically meaningful, i.e., they do not have to correspond to systems that actually exist. As an example, assume that we want to calculate the difference in hydration free energies of a Lennard-Jones particle and an ion with a positive charge q of le. For simplicity, we further assume that the Lennard-Jones parameters remain unchanged upon charging the particle. Since a direct calculation of the free energy difference is not likely to succeed in this case, we construct intermediate states in which the particle carries fractional charges [Pg.46]

The three variants of this model are described in Fig. 5.9. The ligands are simple Lennard-Jones particles, at the center of which a point dipole of strength d is embedded. The orientation of the ligand on the site is always the same, say upward, as in Fig. 5.9. The adsorbent macromolecule consists of three subunits denoted by a, b, and c, each of which has one binding site to which we also refer as a, b, and c. Near each site the macromolecule has a dipole of strength D, which can be oriented either upward or downward. The orientation of the dipole D is determined... 

Figure 18. (a) Response versus the dynamical structure factor for the binary mixture Lennard-Jones particles system in a quench from the initial temperature Ti = 0.8 to a final temperature T( = 0.25 and two waiting times t = 1024 (square) and = 16384 (circle). Dashed lines have slope l/Tf while thick hues have slope l/T (t ). (From Ref. 182.) (b) Integrated response function as a function of IS correlation, that is the correlation between different IS configurations for the ROM. The dashed fine has slope Tf = 5.0, where Tf is the final quench temperature, whereas the full lines are the prediction from Eq. (205) andF = F (T ) Teff(2") 0.694, Teff(2 ) 0.634, and 7 eff(2 ) 0.608. The dot-dash line is for t , = 2" drawn for comparison. (From Ref. 178.)... 

This seemingly anomalous result, called the ring effect, has been investigated in more detail (20, 32). With a potential expression as simple as that for a single Lennard-Jones particle as the sorbate, it is possible to vary systematically the size (rrgucst -guest) or interaction (egues, hosi) parameters, as... 

The concept of the ring effect has recently been applied to the diffusion of a binary mixture of Lennard-Jones particles in zeolite NaY (57). The first particle was varied in size while the second was held fixed. The results suggest that when the diameter of the larger sorbate is close to that of the 12-ring window in zeolite NaY, the larger sorbate will diffuse faster than the smaller one. 

The influence of size and shape on the diffusion of hydrophobic solutes was estimated by simulations involving artificial Lennard-Jones particles those intermolecu-lar interaction parameters were based on those for ammonia or oxygen, respectively. The results on the size dependence of diffusion confirmed that the membrane interior differs strongly from a bulk hydrocarbon. In the center of the bilayer, the excess free energy for hydrophobic Lennard-Jones particles remained low irrespective of the size of the particles. This can be explained by the large fraction of accessible volume in that region. 

As a demonstration of the effectiveness of this approach, 500 Lennard-Jones particles were simulated using the RPUT technique during this simulation, the velocity time autocorrelation function was computed along with the normalized time autocorrelation function for and for u i. Each of the simulations was run 50-100 times longer than the time it takes for the correlation... 

G. Ciccotti and G. Jacucci, Phys. Rev. Lett., 35,789 (1975). Direct Computation of Dynamical Response by Molecular Dynamics the Mobility of a Charged Lennard-Jones Particle. 

Figure 7. Two distributions of sample Liapunov exponents for a cluster of three Lennard-Jones particles simulating Ar3 at energy equivalent to 4.15 K. The only difference between the two calculations is in the initial conditions. [Reprinted with permission from C. Amitrano, and R. S. Berry, Phys. Rev. Lett. 68, 729 (1992). Copyright 1992, American Physical Society.]...

Figure 14. The accumulated action as a function of time as a four-particle Lennard-Jones particle passes through its saddle region. The periodicity is not as sharp and clearly marked as with the three-particle cluster in the previous figure. [Reprinted with permission from R. J. Hinde and R. S. Berry, J. Chem. Phys. 99, 2942 (1993). Copyright 1993, American Institute of Physics.]...

A simple generic bead spring model of chains can be used to study universal polymer properties that do not depend on specific chemical details. Bonds between neighbouring Lennard-Jones particles in a chain can be represented by the finite extension non-linear elastic (FENE) potential. 

Results of recent theoretical and computer simulation studies of phase transitions in monolayer films of Lennard-Jones particles deposited on crystalline solids are discussed. DiflFerent approaches based on lattice gas and continuous space models of adsorbed films are considered. Some new results of Monte Carlo simulation study for melting and ordering in monolayer films formed on the (100) face of an fee crystal are presented and confronted with theoretical predictions. In particular, it is demonstrated that the inner structure of solid films and the mechanism of melting transition depend strongly on the effects due to the periodic variation of the gas - solid potential. 

Figure 1. Examples of phase diagrams for the two-dimensional square lattice gas of Lennard-Jones particles of

Critical properties of the two-dimensional lattice gas of Lennard-Jones particles on a square lattice have been studied by Patrykiejew and Borowski [116] with the help of Monte Carlo version of the coherent anomaly method (CAM) developed by Suzuki and coworkers [115], as well as by the conventional Monte Carlo simulation [105]. The detailed presentation of the coherent anomaly method is well beyond the scope of this chapter. Therefore, here I confine myself to a brief description of its foundations and then present the results relevant to the considered problems. 

Figure 2 presents a comparison of the critical temperatures for the square lattice gas model of Lennard-Jones particles obtained from MCCAM, with the results of the... 

A series of model systems of Lennard-Jones particles adsorbed on triangular lattice have been studied by Berker and coworkers [111,112,141,142] with the help of renormalization group (RG) method and by Patrykiejew [100] with the help of Monte Carlo... 

Figure 2.2. The form of the pair correlation function g Rj at very low densities (p — 0) (a) for hard spheres with

Lennard-Jones particles at moderately high densities... 

Note that this is the exact distance of closest approach for two hard sphere particles. For Lennard-Jones particles <7ab is defined in (2.145). This is... 

We now turn to examine some features of the pair correlation functions of the mixture of A and B. Let A and B be two simple spherical molecules interacting through pair potentials which we denote by U R), UAB(R), and Ubb(R). For simplicity, assume Lennard-Jones particles... 

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