A new formulation of the Gibbs ensemble (GE) combined with the continuous fractional component Monte Carlo method is presented. In the proposed formulation, only a single fractional molecule per component is used instead of two in the original formulation by Shi and Maginn ( J. Comput. Chem. 2008, 29, 2520−2530). This has the following advantages: (1) one directly obtains chemical potentials, without using test particles. We show analytically that the expressions for the chemical potential are identical to those in the conventional Gibbs ensemble; (2) biasing is applied to each simulation box independently; (3) maximum allowed changes in the scaling parameter of intermolecular interactions can be chosen differently in each simulation box. Obtaining chemical potentials directly facilitates thermodynamic modeling using equations of state, and it can be used as an independent check to ensure that chemical equilibrium is achieved. As a proof of principle, our method is tested for Lennard-Jones (LJ) particles and the TIP3P-Ew water model. Results are compared with the conventional GE. Excellent agreement was found both for average densities and chemical potentials. In our new approach, the acceptance probability for molecule exchanges between the boxes is much higher (typically larger than 40% for LJ particles) than for the conventional GE (typically lower than 2% for LJ particles). It is also shown that the contribution of the fractional molecule should be disregarded when computing ensemble averages such as the average energy per molecule and the average densities. The algorithm can be easily extended to mixtures and molecules with intramolecular interactions.@en

Computing accurate vapor–liquid equilibrium (VLE) diagrams using Monte Carlo simulations is not always straightforward because of the difficulty in inserting and deleting molecules. The acceptance probability of insertions/deletions is sharply reduced at low temperatures and in systems with strong and/or directional interactions, like water and ionic liquids. In this work, we highlight the efficiency of configurational bias continuous fractional component Monte Carlo (CB/CFCMC) for the computation of VLE diagrams of strongly interacting systems. We show that CB/CFCMC improves the particle exchange probability in the Gibbs ensemble about two times at low temperature and about one-third at high temperature compared to CFCMC and about 2 orders of magnitude compared to CBMC. The (CB-)CFCMC methods therefore allow for routine and efficient computation of VLE diagrams in systems with strongly interacting molecules. We demonstrate the successful application of the method in the simulation of VLE diagrams of water and DMF using the Gibbs ensemble and study the adsorption isotherm of water in a DMOF variant using grand-canonical Monte Carlo. Although CFCMC methods drastically improve single-particle insertion, additional trial moves and biasing are needed to study the collective behavior such as growth and decay of water clusters. As a downside of the current CFCMC methods in the Gibbs ensemble, we note that the use of two fractional molecules and the resulting coupling between the gas and the liquid phase leads to less than optimal biasing and efficiency.@en

Computing bubble-points of multicomponent mixtures using Monte Carlo simulations is a non-trivial task. A new method is used to compute gas compositions from a known temperature, bubble-point pressure, and liquid composition. Monte Carlo simulations are used to calculate the bubble-points of carbon dioxide (CO2) and methane (CH4) mixtures in the ionic liquids (ILs) 1-n-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [bmim][Tf2N] and 1-ethyl-3-methylimidazolium diethylphosphate [emim][dep]. The Continuous Fractional Component Monte Carlo (CFCMC) method in the osmotic ensemble has been used to compute the solubility of CO2/CH4 gas mixtures at different temperatures (T), pressures (P), and gas compositions (yi). The effect of T, P, and yi on the real CO2/CH4 selectivity (i.e., the selectivity of CO2 in the presence of CH4) is investigated. The real selectivity will differ from the ideal selectivity, which is defined as the ratio of the Henry's constants, if the solubility of CO2 is influenced by the presence of CH4. The computed real selectivities are compared with the experimentally obtained real and ideal selectivities. The real CO2/CH4 selectivity decreases with increasing temperature and pressure, while the gas phase composition has a minor effect. The real selectivity is approximately identical to the ideal selectivity for relatively low pressures and low solute concentrations in the liquid phase. The real selectivity deviates from the ideal selectivity as the solute concentration in the liquid phase increases.@en

Monte Carlo simulations are used to calculate the solubility of natural gas components in ionic liquids (ILs) and Selexol, which is a mixture of poly(ethylene glycol) dimethyl ethers. The solubility of the pure gases carbon dioxide (CO₂), methane (CH₄), ethane (C₂H₆), and sulfur dioxide (SO₂) in the ILs 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C_nmim][Tf₂N], n = 4, 6), 1-ethyl-3-methylimidazolium diethylphosphate ([emim][dep]), and Selexol (CH₃O[CH₂CH₂O]_nCH₃, n = 4, 6) have been computed at 313.15 K and several pressures. The gas solubility trend observed in the experiments and simulations is: SO₂ > CO₂ > C₂H₆ > CH₄. Overall, the Monte Carlo simulation results are in quantitative agreement with existing experimental data. Molecular simulation is an excellent tool to predict gas solubilities in solvents and may be used as a screening tool to navigate through the large number of theoretically possible ILs.

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