Monte Carlo simulations chemical potentials

Mon K K and Griffiths R B 1985 Chemical potential by gradual insertion of a particle in Monte Carlo simulation Phys. Rev. A 31 956-9... 

Nezbeda I and Kolafa J 1991 A new version of the insertion particle method for determining the chemical potential by Monte Carlo simulation Mol. SImul. 5 391-403... 

To test the results of the chemical potential evaluation, the grand canonical ensemble Monte Carlo simulation of the bulk associating fluid has also been performed. The algorithm of this simulation was identical to that described in Ref. 172. All the calculations have been performed for states far from the liquid-gas coexistence curve [173]. 

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. 

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... 

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. 

The temperature, pore width and average pore densities were the same as those used by Snook and van Megen In their Monte Carlo simulations, which were performed for a constant chemical potential (12.). Periodic boundary conditions were used In the y and z directions. The periodic length was chosen to be twice r. Newton s equations of motion were solved using the predictor-corrector method developed by Beeman (14). The local fluid density was computed form... 

Monte Carlo simulations of this system have shown that by sweeping the chemical potential of Cu, a cluster is allowed to grow withiu the hole risiug four atomic layers above the surface. As iu the experimeuts, it is fouud that its lateral exteusiou remaius coufiued to the area defiued by the borders of the origiual defect. 

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 chapter 3, Profs. A. Gonzalez-Lafont, Lluch and Bertran present an overview of Monte Carlo simulations for chemical reactions in solution. First of all, the authors briefly review the main aspects of the Monte Carlo methodology when it is applied to the treatment of liquid state and solution. Special attention is paid to the calculations of the free energy differences and potential energy through pair potentials and many-body corrections. The applications of this methodology to different chemical reactions in solution are... 

One way to include these local quantum chemical effects is to perform ab initio calculations on an HOD molecule in a cluster of water molecules, possibly in the field of the point charges of the water molecules surrounding the cluster. In 1991 Hermansson generated such clusters from a Monte Carlo simulation of the liquid, and for each one she determined the relevant Bom Oppenheimer potential and the vibrational frequencies. The transition-dipole-weigh ted histogram of frequencies was in rough agreement with the experimental IR spectrum for H0D/D20 [130],... 

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]. 

To evaluate solvent effeets, statistieal meehanical Monte Carlo simulations have been carried out. An important quantity to be computed is the potential of mean force, or free energy profile, as a funetion of the reaction coordinate, X, for a chemical reaction in solution using free energy perturbation method. (44) A straightforward approaeh is to determine free energy differences for incremental changes of certain geometrieal variables that characteristically reflect the... 

What is next Several examples were given of modem experimental electrochemical techniques used to characterize electrode-electrolyte interactions. However, we did not mention theoretical methods used for the same purpose. Computer simulations of the dynamic processes occurring in the double layer are found abundantly in the literature of electrochemistry. Examples of topics explored in this area are investigation of lateral adsorbate-adsorbate interactions by the formulation of lattice-gas models and their solution by analytical and numerical techniques (Monte Carlo simulations) [Fig. 6.107(a)] determination of potential-energy curves for metal-ion and lateral-lateral interaction by quantum-chemical studies [Fig. 6.107(b)] and calculation of the electrostatic field and potential drop across an electric double layer by molecular dynamic simulations [Fig. 6.107(c)]. 

Suter and co-workers presented a novel class of Monte Carlo simulation methods aimed at dense polymer systems.i Properties like the chemical potential and solubilities in polymer systems may be calculated from simulations of this type. The authors presented results on the solubility of long alkanes in polyethylene and for various solutions of long alkanes in near-critical solvents. 

The amount of water adsorbed at 300 K has been determined by way of Cirand Canonical Monte Carlo Simulation, which mimics a real adsorption experiment where the temperature, the volume and chemical potential (related to the pressure of the gas) are kept constant. An equal number of translation, rotation, creation or destruction of molecules has been chosen, around 2.10 per water molecule at fiill saturation, up to 10 at low coverage. 

In the molecular simulation of adsorption in confined space such as pores of adsorbent, the most widely used and success l ensemble is the grand canonical Monte Carlo simulation. In this ensemble, we specify the chemical potential of the fluid,p, that the candidate pore is immersed in, the size of the pore, and the temperature. 

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