Simulation of chemical reaction equilibria by the reaction ensemble Monte Carlo method: a review†

Gas sorption in solid surfaces: a computational study using rigid and Einstein-solid models

The reactive Monte Carlo (RxMC) method was proposed to describe the sorption of gases in solid materials due to the chemical reaction A + B ⇌ C. Two models were used to simulate the solid; the first model considered simulations with rigid particles in the solid whereas in the second model the particles were allowed to vibrate inside the solid with a given spring constant, i.e. an Einstein solid was used to simulate the substrate. In both models not only physisorption but also chemisorption of the fluid was observed. Sorption curves, at different spring constants, were simulated and it was noted that sorption was always enhanced with the Einstein solid model. Moreover, an inverse dependent function of the spring constant with the temperature was found. Finally, the second model might be used to explain the unusual sorption behavior observed in actual experimental reactions such as CO2 + Li2O ⇌ Li2CO3.

Partial molar enthalpies and reaction enthalpies from equilibrium molecular dynamics simulation

We present a new molecular simulation technique for determining partial molar enthalpies in mixtures of gases and liquids from single simulations, without relying on particle insertions, deletions, or identity changes. The method can also be applied to systems with chemical reactions. We demonstrate our method for binary mixtures of Weeks-Chandler-Anderson particles by comparing with conventional simulation techniques, as well as for a simple model that mimics a chemical reaction. The method considers small subsystems inside a large reservoir (i.e., the simulation box), and uses the construction of Hill to compute properties in the thermodynamic limit from small-scale fluctuations. Results obtained with the new method are in excellent agreement with those from previous methods. Especially for modeling chemical reactions, our method can be a valuable tool for determining reaction enthalpies directly from a single MD simulation.

The READY program: Building a global potential energy surface and reactive dynamic simulations for the hydrogen combustion

READY (REActive DYnamics) is a program for studying reactive dynamic systems using a global potential energy surface (PES) built from previously existing PESs corresponding to each of the most important elementary reactions present in the system. We present an application to the combustion dynamics of a mixture of hydrogen and oxygen using accurate PESs for all the systems involving up to four oxygen and hydrogen atoms. Results at the temperature of 4000 K and pressure of 2 atm are presented and compared with model based on rate constants. Drawbacks and advantages of this approach are discussed and future directions of research are pointed out.

Reaction Ensemble Monte Carlo Simulation of Complex Molecular Systems

Acceptance rules for reaction ensemble Monte Carlo (RxMC) simulations containing classically modeled atomistic degrees of freedom are derived for complex molecular systems where insertions and deletions are achieved gradually by utilizing the continuous fractional component (CFC) method. A self-consistent manner in which to utilize statistical mechanical data contained in ideal gas free energy parameters during RxMC moves is presented. The method is tested by applying it to two previously studied systems containing intramolecular degrees of freedom: the propene metathesis reaction and methyl-tert-butyl-ether (MTBE) synthesis. Quantitative agreement is found between the current results and those of Keil et al. (J. Chem. Phys. 2005, 122, 164705) for the propene metathesis reaction. Differences are observed between the equilibrium concentrations of the present study and those of Lísal et al. (AIChE J. 2000, 46, 866-875) for the MTBE reaction. It is shown that most of this difference can be attributed to an incorrect formulation of the Monte Carlo acceptance rule. Efficiency gains using CFC MC as opposed to single stage molecule insertions are presented.

Pressure enhancement in carbon nanopores: a major confinement effect

Phenomena that only occur at high pressures in bulk phases are observed in nanopores because of a pressure enhancement effect.

Thermodynamic behavior of the CO2 + NO2/N2O4 mixture: a Monte Carlo simulation study

The thermodynamic behavior of the carbon dioxide + nitrogen dioxide (CO2 + NO2) mixture was investigated using a Monte Carlo molecular simulation approach. This system is a particularly challenging one because nitrogen dioxide exists as a mixture of monomers (NO2) and dimers (N2O4) under certain pressure and temperature conditions. The chemical equilibrium between N2O4 and 2NO2 and the vapor-liquid equilibrium of CO2 + NO2/N2O4 mixtures were simulated using simultaneously the reaction ensemble and the Gibbs ensemble Monte Carlo (RxMC and GEMC) methods. Rigid all atoms molecular potentials bearing point charges were proposed to model both NO2 and N2O4 species. Liquid-vapor coexistence properties of the reacting NO2/N2O4 system were first investigated. The calculated vapor pressures and coexisting densities were compared to experimental values, leading to an average deviation of 10% for vapor pressures and 6% for liquid densities. The critical region was also addressed successfully using the subcritical Monte Carlo simulation results and some appropriate scaling laws. Predictions of CO2 + NO2/N2O4 phase diagrams at 300, 313, and 330 K were then proposed. Derivative properties calculations were also performed in the reaction ensemble at constant pressure and temperature for both NO2/N2O4 and CO2 + NO2/N2O4 systems. The calculated heat capacities show a maximum in the temperature range where N2O4 dissociation occurs, in agreement with available experimental data.

Optimal sampling efficiency in Monte Carlo simulation with an approximate potential

Building on the work of Iftimie et al. [J. Chem. Phys. 113, 4852 (2000)] and Gelb [J. Chem. Phys. 118, 7747 (2003)], Boltzmann sampling of an approximate potential (the "reference" system) is used to build a Markov chain in the isothermal-isobaric ensemble. At the end points of the chain, the energy is evaluated at a more accurate level (the "full" system) and a composite move encompassing all of the intervening steps is accepted on the basis of a modified Metropolis criterion. For reference system chains of sufficient length, consecutive full energies are statistically decorrelated and thus far fewer are required to build ensemble averages with a given variance. Without modifying the original algorithm, however, the maximum reference chain length is too short to decorrelate full configurations without dramatically lowering the acceptance probability of the composite move. This difficulty stems from the fact that the reference and full potentials sample different statistical distributions. By manipulating the thermodynamic variables characterizing the reference system (pressure and temperature, in this case), we maximize the average acceptance probability of composite moves, lengthening significantly the random walk between consecutive full energy evaluations. In this manner, the number of full energy evaluations needed to precisely characterize equilibrium properties is dramatically reduced. The method is applied to a model fluid, but implications for sampling high-dimensional systems with ab initio or density functional theory potentials are discussed.