Monte Carlo simulation chemical potential, calculating

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. 

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],... 

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. 

Although the simulation of ensembles of particles constitutes a huge literature, it is only one aspect of the use of Monte Carlo methods in chemical physics. Basically, whenever one has to calculate integrals over a high-dimensionality space, the Monte Carlo method is potentially the algorithm of choice. Thus, for example, in few-body simulations of chemical reactions, one must integrate over the initial conditions of the reactant molecules, and... 

Martin M G and J I Siepmann 1999. Novel Configurational-bias Monte Carlo Method tor Branched Molecules Transferable Potentials for Phase Equilibria. 2 United-atom Description of Branched Alkanes Journal of Physical Chemistry 103 4508-4517 Metropolis N, A W Rosenbluth, M N Rosenbluth, A H Teller and E Teller 1953 Equation of State Calculations by Fast Computing Machines. Journal of Chemical Physics 21 1087-1092 Okamoto Y and U H E Hansmann 1995. Thermodynamics of HeUx-coU Transitions Studied by Multicanomcal Algorithms. Journal of Physical Chemistry 99 11276-11287 Panagiotopoulos A Z 1987. Direct Determination of Phase Coexistence Properties of Fluids by Monte Carlo Simulation in a New Ensemble. Molecular Physics 61.813-826 Pangali C, M Rao and B J Berne 1978 On a Novel Monte Carlo Scheme for Simulating Water and Aqueous Solutions Chemical Physics Letters 55 413-417. 

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