Monte Carlo simulation potential parameters

The parameter /r tunes the stiffness of the potential. It is chosen such that the repulsive part of the Leimard-Jones potential makes a crossing of bonds highly improbable (e.g., k= 30). This off-lattice model has a rather realistic equation of state and reproduces many experimental features of polymer solutions. Due to the attractive interactions the model exhibits a liquid-vapour coexistence, and an isolated chain undergoes a transition from a self-avoiding walk at high temperatures to a collapsed globule at low temperatures. Since all interactions are continuous, the model is tractable by Monte Carlo simulations as well as by molecular dynamics. Generalizations of the Leimard-Jones potential to anisotropic pair interactions are available e.g., the Gay-Beme potential [29]. This latter potential has been employed to study non-spherical particles that possibly fomi liquid crystalline phases. 

For the equihbrium properties and for the kinetics under quasi-equilibrium conditions for the adsorbate, the transfer matrix technique is a convenient and accurate method to obtain not only the chemical potentials, as a function of coverage and temperature, but all other thermodynamic information, e.g., multiparticle correlators. We emphasize the economy of the computational effort required for the application of the technique. In particular, because it is based on an analytic method it does not suffer from the limitations of time and accuracy inherent in statistical methods such as Monte Carlo simulations. The task of variation of Hamiltonian parameters in the process of fitting a set of experimental data (thermodynamic and... 

As mentioned above, for the simulation in dimethylformamide (DMF) of the same reaction [53], the parameters for the substrate were not changed from the parametrization in water. For DMF the parameters were adopted from the OPLS parametrization of the pure liquid. The transferability was tested in part by performing a Monte Carlo simulation for CT plus 128 DMF molecules and evaluating the heat of solution for the chloride ion. The obtained value compares favorably with the experimental estimate. It is important to remark here that when potentials are used to simulate different solutions to the ones used in the parametrization process, they no longer are "effective" potentials. This fact becomes more evident in the simulation of solutions of small ions with localized charge that polarizes the neighboring solvent molecules. In this case it is convenient to consider the n-body corrections. 

In this section we discuss model potentials for small metal clusters with parameters fitted to ab initio calculated potential surfaces. We named such potentials as ab initio model potentials This approach was first elaborated by Clementi and coworkers and used for the Monte-Carlo simulation of biological systems in liquid water... 

Other computer simulations were made to test the classical theory. Recently, Ford and Vehkamaki, through a Monte-Carlo simulation, have identified fhe critical clusters (clusters of such a size that growth and decay probabilities become equal) [66]. The size and internal energy of the critical cluster, for different values of temperature and chemical potential, were used, together with nucleation theorems [66,67], to predict the behaviour of the nucleation rate as a function of these parameters. The plots for (i) the critical size as a function of chemical potential, (ii) the nucleation rate as a function of chemical potential and (iii) the nucleation rate as a function of temperature, suitably fit the predictions of classical theory [66]. 

Potential parameters used in the Monte Carlo simulations (qi in elementary charge unit, e in kcal/mol and 0 in A). 

In general, Monte Carlo simulations are such calculations in which the values of some parameters are determined by the average of some randomly generated individuals.45-54 In chemistry applications, the most prevalent methods are the so called Metropolis Monte Carlo (MMC)55 and Reverse Monte Carlo (RMC) ones. The most important quantities in these methods are some kinds of U energy-type potentials (e.g. internal energy, enthalpy,... 

The last term in the formula (1-196) describes electrostatic and Van der Waals interactions between atoms. In the Amber force field the Van der Waals interactions are approximated by the Lennard-Jones potential with appropriate Atj and force field parameters parametrized for monoatomic systems, i.e. i = j. Mixing rules are applied to obtain parameters for pairs of different atom types. Cornell et al.300 determined the parameters of various Lenard-Jones potentials by extensive Monte Carlo simulations for a number of simple liquids containing all necessary atom types in order to reproduce densities and enthalpies of vaporization of these liquids. Finally, the energy of electrostatic interactions between non-bonded atoms is calculated using a simple classical Coulomb potential with the partial atomic charges qt and q, obtained, e.g. by fitting them to reproduce the electrostatic potential around the molecule. 

Modeling physical adsorption in confined spaces by Monte Carlo simulation or non-local density functional theory (DFT) has enjoyed increasing popularity as the basis for methods of characterizing porous solids. These methods proceed by first modeling the adsorption behavior of a gas/solid system for a distributed parameter, which may be pore size or adsorptive potential. These models are then used to determine the parameter distribution of a sample by inversion of the integral equation of adsorption, Eq. (1). 

The Kohn-Sham-Gaspar potential derived from density-functional theory has a similar expression for V c with Xa = 2/3, and only took into account exchange [20],[40]. To include correlation, several forms were proposed for / , with parameters obtained from fits to RPA calculations or more accurate Monte Carlo simulations [41] and different spin interpolations. The current version of the DVM code contains altogether nine choices of Vje, the preferred form being the Vosko, Wilk and Nusair [42] parametrization of the Ceperley and Alder Monte Carlo simulations [43]. 

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