Monte Carlo grand canonical ensemble calculations

Chesnut D A and Salsburg Z W 1963 Monte Carlo procedure for statistical mechanical calculation in a grand canonical ensemble of lattice systems J. Chem. Phys. 38 2861-75... 

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]. 

The grand canonical ensemble is appropriate for adsorption systems, in which the adsorbed phase is in equilibrium with the gas at some specified temperature. The use of a computer simulation allows us to calculate average macroscopic properties directly without having to explicitly calculate the partition function. The grand canonical Monte Carlo (GCMC) method as applied in this work has been described in detail earlier (55). The aspects involving binary fluid mixtures have been described previously in our Xe-Ar work (30). 

There are many excellent reviews on the standard molecular dynamics method dealing with calculations in the microcanonical ensemble as well as on the Monte Carlo method involving calculations in the canonical, isothermal isobaric, and grand canonical ensemble (< ). In the present article, we shall limit ourselves exclusively to those developments that have taken place since the work of Andersen (4). In the molecular dynamics method, the developments are the constant-pressure, constant-temperature, constant-temperature-constant-pressure, variable shape simulation cell MD, and isostress calculations in the Monte Carlo method, it is the variable shape simulation cell calculation. 

Rowley, L.A., Nicholson, D., and Parsonage, N.G. (1978). Long-range corrections to grand canonical ensemble Monte Carlo calculations for adsorption systems. J. Comput. Phys., 26, 66—79. 

Sloth, P. and Sorensen, T.S., Hard, charged spheres in spherical pores, grand canonical ensemble Monte Carlo calculations, J. Chem. Phys., 96 (1), 548-554, 1992. 

Sorensen, T.S. and Sloth, P., Ion and potential distribution in charged and non-charged primitive spherical pores in equilibrium with primitive electrolyte solution calculated by grand canonical ensemble Monte Carlo simulation, J. Chem. Soc. Faraday Trans., 88 (4), 571-589, 1992. 

Theoretical studies, like first-principles calculations, grand canonical ensemble Monte Carlo (GCMC) simulations, second order Moller-Plesset perturbation theory (MP2) calculations and density functional theory (DFT) calculations, have been utilized to investigate optimal structures and their properties. Combined experimental and theoretical data provide a window to the plan of design of these network structures and lead to a new direction to investigate porous networks. 

The grand canonical ensemble simulations model systems in which the chemical potential (/x), the volume and temperature are held fixed while the number of particles changes. The approach is very useful for simulating phase behavior which requires a constant chemical potential. Grand Canonical Monte Carlo simulation has been used to calculate sorption isotherms for a number of difierent microporous silicate systems. The simulations are used to model the equilibrium between zeolite and sorbate phases and, as such, it provides a natural way of simulating sorption isothermsl ... 

The MSI Cerius2 3.8 software package was used to study physical sorption of N2 and O2 on LiLSX zeolite as function of pressure of the sorbing species. Calculations are based on the application of a Monte Carlo simulation algorithm in the Grand Canonical Ensemble [58,59]. The interaction-potential parameters used in the forcefield expression of this investigation are published in [60], together with details of the simulation setup. 

The steady-state dynamics is assumed to be governed by a Kawasaki-type particle-vacancy NN pair-exchange mechanism inside the system combined with a Glauber-type particle creation/annihilation mechanism at the two edges A and B. Hence, neither the particle number nor the total energy are conserved quantities. This implementation corresponds to a canonical ensemble inside the lattice and a grand canonical ensemble at the edges. The total density is hence a dependent variable which has to be calculated. The dynamical processes are subject to the conventional Monte Carlo Metropolis criterion. ... 

Standard molecular dynamics calculations, i.e., those that solve Hamilton s equation, are performed on NVE ensembles, i.e., samples with a constant number of atoms N), fixed volume (V), and constant energy ( ). In standard Monte Carlo simulations the more widely applicable NVT ensembles are used, i.e., constant temperature (T) rather than energy, although both schemes can be modified to work in different ensembles. In particular, free energies can be directly evaluated using Monte Carlo methods in the Grand Canonical ensemble, although technical difficulties involved... 

This method has been applied to the prediction of the fractional occupancy of the large cavities of an S-II hydrate of hydrogen. Figure 6 compares the results of this simple approach using the spherical cell vdW-P model with those obtained from more elaborate grand canonical ensemble Monte Carlo calculations. The overall agreement is reasonable. 

In the last section we have assumed that we perform our simulation for a fixed number, N, of particles at constant temperature, T, and volume, V, the canonical ensemble. A major advantage of the Monte Carlo technique is that it can be easily adapted to the calculation of averages in other thermodynamic ensembles. Most real experiments are performed in the isobaric-isothermal (constant- ) ensemble, some in the grand-canonical (constant-pFT) ensemble, and even fewer in the canonical ensemble, the standard Monte Carlo ensemble, and near to none in the microcanonical (constant-NFE) ensemble, the standard ensemble for molecular-dynamics simulations. 

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