Isobaric-isothermal ensemble Monte Carlo simulations

Monte Carlo simulations were carried out to determine the free energy curve for the reaction in solution. The simulations were executed for the solute surrounded by 250 water molecules (or 180 DMF molecules) in the isothermal-isobaric ensemble at 25 °C and 1 atm, including periodic boundary conditions. As a consequence, the Gibbs free energy is obtained in this case. There is sufficient solvent to adequately represent the bulk participation in the chemical reaction. 

Owicki JC, Scheraga HA. Monte Carlo simulations in the isothermal-isobaric ensemble 2. dilute aqueous solutions. J. Am. Chem. Soc. 1977 99 7413-7418. 

Shah et al. carried out a Monte-Carlo simulation in the isothermal-isobaric (NPT) ensemble of [C4mim][PF6] [12]. The authors calculated the molar volume, cohesive energy density, isothermal compressibility, cubic expansion coefficient, and liquid structure as a function of temperature and pressure. A united atom force field was developed using a combination of ab initio calculations and literature parameter values were also developed. Calculated molar volumes were within 5% of experimental values, and a reasonable agreement was obtained between calculated and experimental values of the isothermal compressibility and cubic expansion coefficient. [PF6] anions were found to cluster preferentially in two favorable regions near the cation, namely around the C2 carbon atom, both below and above the plane of the imidazole ring [12],... 

The isobaric-isothermal ensemble and its close relative, the isotension-isothermal ensemble, are often used in Monte Carlo simulations. Finite-size... 

A Monte Carlo simulation traditionally samples from the constant NVT (canonical) ensemble, but the teclmique can also be used to sample from different ensembles. A common alternative is the isothermal-isobaric, or constant NPT, ensemble. To simulate from this ensemble, it is necessary to have a scheme for changing the volume of the simulation cell in order to keep the pressure constant. This is done by combining random displacements of the particles with random changes in the volume of the simulation cell. The size of each volume change is governed by the maximum volume change, V ax-Thus a new volume is generated from the old volume as follows ... 

Once the force field is chosen, a proper simulation method needs to be selected. Molecular dynamics simulations are applied to determine the solvation behaviour of ionic liquids by means of solving the Newtonian equations of motion for all molecules in the presence of a gradient in potential energy. Ionic liquid phase equilibria are determined by using Monte Carlo simulations in the isothermal isobaric Gibbs ensemble, grand canonical ensemble or osmotic ensemble with clever sampling schemes. 

Simulation of adsorption has been performed in various ensembles canonical, grand canonical, isobaric-isothermal, and Gibbs ensemble. The choice of the ensemble depends on the nature of the investigated system and the aim of the simulations. In the case of adsorption on heterogeneous surfaces, usually the grand canonical Monte Carlo simulation method (GCMC) has been used. 

Using this local bond-order analysis we can sample the equilibrium distribution function for the probability P(n) in a Monte Carlo simulation. In all cases we performed Monte Carlo simulations in the isobaric-isothermal (NPT) ensemble. In this ensemble the average of a microscopic quantity A is given by... 

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. 

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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