Transition Matrix Monte Carlo Method Research Articles

Role of site–site interaction on the phase equilibria of multiple-site associating fluids in a functionalized slit pore

Vapor–liquid phase equilibria for multiple sites associating fluids with different associating strengths are investigated in a slit pore using grand-canonical transition matrix Monte Carlo method. The increase of critical temperature from two-site to four-site associating fluids at constant site strength is quite significant as compared to that of the one-site to two-site associating fluids, which is more pronounced at higher associating strength (ϵ* = 6). Monomer fraction and cluster size distribution are used to investigate the association of fluid particles in coexistence phases. The monomer fraction for both phases decreases with increased associating sites on the fluid particles due to more site–site interaction with neighboring fluid particles and forming a larger cluster. Therefore, the number of associating sites and their distribution play a vital role in the association of fluid particles. Moreover, the saturation chemical potential changes with the arrangement of the sites. For two-site associating fluids, we observe early vapor–liquid transition when the sites are oppositely placed, and when the sites are placed at 90°, the vapor–liquid transition is observed at the higher chemical potential. Moreover, four-site associating fluids with a square arrangement show early vapor–liquid phase transition, mainly because these arrangements of sites effectively interact with surface sites and the molecules in the next layer.

Phase behaviour of confined associating fluid in a functionalized slit pore: a Monte Carlo study

Vapour-liquid phase equilibria of associating fluids under confinement are investigated using Grand-Canonical Transition Matrix Monte Carlo (GC-TMMC) method. Various properties of coexistence phases and critical properties are estimated for multiple associating fluids at different slit widths. The structural features of coexistence phases are examined through monomer fraction, density profile, and orientation profile. The role of surface sites on the phase behaviour under confinement is critically examined. It has a significant effect on the structural behaviour of coexistence phases, leading to a change in the properties of coexistence phases. In particular, the orientation of associating fluid molecules near the functionalized surface is entirely different than in the case of a smooth surface. The orientation of two sites associating (when sites are located oppositely to each other) fluid molecules is normal to surface, forming bonds with surface sites in one direction and another bond with molecules in an adjacent layer.

Vapor–Liquid Equilibria of Mixtures of Molecular Fluids Using the Activity Fraction Expanded Ensemble Simulation Method

The activity fraction expanded ensemble (AFEE) simulation technique has been extended to predict the vapor–liquid coexistence behavior of binary mixtures of molecular fluids. The systems of molecular mixtures studied are thiophene–n-hexane (a mixture of an aromatic compound with a n-alkane) and methane–n-hexane (mixture of n-alkanes with significant difference in size). Comparison with results from the grand canonical transition matrix Monte Carlo method and experimental data available in the literature has also been provided. Further, we have investigated the computational efficiency of the AFEE technique at temperatures where both compounds exhibit subcritical behavior (thiophene–n-hexane at 338.15 K) and where one of the components shows supercritical behavior (methane–n-hexane at 373 K). Canonical Monte Carlo simulations are also performed to obtain the radial distribution functions which have been used to study the structure of the coexisting liquid phases to gain insights into the molecular origins ...

Renormalized multicanonical sampling in multiple dimensions.

This paper extends to two and three dimensions the recently proposed renormalized multicanonical sampling procedure [D. Yevick, Int. J. Mod. Phys. C 27, 1650033 (2016)IJMPEO0129-183110.1142/S0129183116500339], which generates the density of states of a system from that of a smaller system. The accuracy and efficiency of the method is additionally enhanced through a transition matrix Monte Carlo method that incorporates multicanonical sampling. The performance of the resulting procedure is investigated through calculations of the specific heat of the standard Ising model for square lattices with up to 128^{2} spins and for cubic lattices with up to 24^{3} spins. A comparison of the scaling properties to those of other algorithms based on the transition matrix Monte Carlo method demonstrates that the relative advantage of the renormalized procedure increases rapidly with system size.

Accelerated rare event sampling

A sampling procedure for the transition matrix Monte Carlo method is introduced that generates the density of states function over a wide parameter range with minimal coding effort.

Molecular Simulation Study of Vapor-Liquid Equilibrium of Morse Fluids

The Morse potential energy function (PEF) is considered regarding the characterization of interaction forces of particles with tuning parameters. Phase coexistence of Morse fluids is predicted for different steepness and range of the PEF parameters using the grand-canonical transition matrix Monte Carlo (GC-TMMC) method, with quantification of the parameter S, which is the product of a constant with a unit of reciprocal length and the equilibrium distance between two molecules. We found that a lower limit of S exists bounded by infinite critical temperature. The critical properties of the vapor-liquid equilibrium curves are estimated using a rectilinear diameter method and a scaling law approach. A Clausius-Clayperon type relation of S and critical temperature is derived in this work. Vapor-liquid surface tension of Morse fluids by finite size scaling and GC-TMMC is also reported. Surface tensions are found to be higher at lower S.

Efficient combination of Wang–Landau and transition matrix Monte Carlo methods for protein simulations

An efficient combination of the Wang-Landau and transition matrix Monte Carlo methods for protein and peptide simulations is described. At the initial stage of simulation the algorithm behaves like the Wang-Landau algorithm, allowing to sample the entire interval of energies, and at the later stages, it behaves like transition matrix Monte Carlo method and has significantly lower statistical errors. This combination allows to achieve fast convergence to the correct values of density of states. We propose that the violation of TTT identities may serve as a qualitative criterion to check the convergence of density of states. The simulation process can be parallelized by cutting the entire interval of simulation into subintervals. The violation of ergodicity in this case is discussed. We test the algorithm on a set of peptides of different lengths and observe good statistical convergent properties for the density of states. We believe that the method is of general nature and can be used for simulations of other systems with either discrete or continuous energy spectrum.

Vapor–liquid phase coexistence curves for Morse fluids

Phase coexistence of Morse fluids is predicted for parameters in the range describing the behavior of metals using the grand-canonical transition matrix Monte Carlo method. The critical properties of the vapor–liquid equilibrium curves for three fcc metals, Al, Cu, and Au, and two bcc alkali metals, Na and K, are estimated and the critical temperature values are found to be in good agreement with the experimental data for the fcc metals considered but overestimated for the bcc metals. For Na, it was found that the critical density and vapor pressure as a function of temperature (below the critical temperature) estimates to be approximately concurrent with experimental results.

Power law relaxation and glassy dynamics in Lebwohl-Lasher model near the isotropic-nematic phase transition

Orientational dynamics in a liquid crystalline system near the isotropic-nematic (IN) phase transition is studied using molecular dynamics simulations of the well-known Lebwohl-Lasher model. As the IN transition temperature is approached from the isotropic side, we find that the decay of the orientational time correlation functions (OTCF) slows down noticeably, giving rise to a power law decay at intermediate time scales. The angular velocity time correlation function also exhibits a rather pronounced power law decay near the IN boundary. In the mean squared angular displacement at comparable time scales, we observe the emergence of a subdiffusive regime which is followed by a superdiffusive regime before the onset of the long-time diffusive behavior. We observe signature of dynamical heterogeneity through pronounced non-Gaussian behavior in orientational motion particularly at lower temperatures. This behavior closely resembles what is usually observed in supercooled liquids. We obtain the free energy as a function of orientational order parameter by the use of the transition matrix Monte Carlo method. The free energy surface is flat for the system considered here and the barrier between isotropic and nematic phases is vanishingly small for this weakly first-order phase transition, hence allowing large scale, collective, and correlated orientational density fluctuations. This might be responsible for the observed power law decay of the OTCFs.

Efficient Simulation of Binary Adsorption Isotherms Using Transition Matrix Monte Carlo

Molecular simulations of binary adsorption in porous materials are a useful complement to experimental studies of mixture adsorption. Most molecular simulations of binary adsorption are performed using grand canonical Monte Carlo (GCMC) to independently examine a range of state points of interest. A disadvantage of this approach is that it only yields information at a discrete set of state points; therefore, if a complete isotherm is required for arbitrary conditions, some type of data fitting or interpolation must be used in combination with the GCMC data. We show that the transition matrix Monte Carlo (TMMC) method of Shen and Errington (Shen, V. K.; Errington, J. R. J. Chem.Phys. 2005, 122, 064508) is well-suited to simulation of binary adsorption in porous materials. At the completion of a TMMC simulation, the adsorption isotherm for all possible bulk phase compositions and pressures is available without data fitting or interpolation. It is also straightforward to use results from TMMC to compute derivatives of the isotherm such as the mixture thermodynamic correction factors, partial differential ln f(i)/partial differential ln c(j), again without data fitting or interpolation. This approach should be useful in contexts where information on the full adsorption isotherm is needed, such as the design of adsorption- or membrane-based separations.

Determination of Henry's law constants through transition matrix Monte Carlo simulation

We present results for the Henry's law constant of methane, oxygen, nitrogen, and carbon dioxide in saturated liquid ethanol at temperatures of 323 and 373 K. Monte Carlo simulations are conducted in an expanded isothermal–isobaric ensemble in which the interactions between a solute particle and the solvent are gradually increased over a series of steps. A self-adaptive transition matrix Monte Carlo method is used to determine infinite-dilution excess chemical potential values for the solute. The TraPPE force field is used to describe molecular interactions. Henry's law constants follow the trend: nitrogen > oxygen > methane > carbon dioxide. Agreement between modeling and experimental values is reasonable.

Molecular simulation study of miscibility of ternary and quaternary InGaAlN alloys

Molecular simulations are conducted to determine the limits of miscibility of a valence force field model for zinc-blende-structured In1−x−yGaxAlyN semiconductor alloys. The transition matrix Monte Carlo method is used to calculate the free energy of the model alloys as a function of temperature and alloy composition (considering both x and y ranging from zero to unity). Analysis of the free-energy surface provides values for the upper critical solution temperature of the ternary alloys: InGaN (1550 K), InAlN (2700 K), and GaAlN (195 K). The miscibility envelope of the quaternary alloy is determined at 773 K and 1273 K. The excess properties of the mixtures are calculated, and it is found that the excess entropy is negligible, and the excess enthalpy is nearly independent of temperature. Consequently, regular-solution theory provides a good description of the thermodynamic properties of the alloys, and comparison of the simulation results with the phase behavior previously reported using regular-solution theory finds good agreement. Structural properties of the ternary compounds are examined in terms of the local compositions. For InGaN it is found (surprisingly) that there is a slight preference for In atoms to have Ga atoms rather than other In atoms as neighbors, in comparison to a random mixture. The two other ternary compounds exhibit the expected behavior, in which the (small) deviations from random mixing tend to favor segregation of like atoms. Among the ternaries, GaAlN is found to show the greatest deviations from random mixing.

Transition-Matrix Monte Carlo Method for Quantum Systems

We propose an efficient method for Monte Carlo simulation of quantum lattice models. Unlike most other quantum Monte Carlo methods, a single run of the proposed method yields the free energy and the entropy with high precision for the whole range of temperature. The method is based on several recent findings in Monte Carlo techniques, such as the loop algorithm and the transition matrix Monte Carlo method. In particular, we derive an exact relation between the DOS and the expectation value of the transition probability for quantum systems, which turns out to be useful in reducing the statistical errors in various estimates.

FLAT HISTOGRAM METHOD OF WANG–LANDAU AND N-FOLD WAY

We present a method for estimating the density of states of a classical statistical model. The algorithm successfully combines the Wang–Landau flat histogram method with the N-fold way in order to improve the efficiency of the original single-spin-flip version. We test our implementation of the Wang–Landau method with the two-dimensional nearest neighbor Ising model for which we determine the tunneling time and the density of states on lattices with sizes up to 50 × 50. Furthermore, we show that our new algorithm performs correctly at right edges of an energy interval over which the density of states is computed. This removes a disadvantage of the original single-spin-flip Wang–Landau method where results showed systematically higher errors in the density of states at right boundaries. In order to demonstrate the improvements made, we compare our data with the detailed numerical tests presented in a study by Wang and Swendsen where the original Wang–Landau method was tested against various other methods, especially the transition matrix Monte Carlo method (TMMC). Finally, we apply our method to a thin Ising film of size 32 × 32 × 6 with antiparallel surface fields. With the density of states obtained from the simulations we calculate canonical averages related to the energy such as internal energy, Gibbs free energy and entropy, but we also sample microcanonical averages during simulations in order to determine canonical averages of the susceptibility, the order parameter and its fourth order cumulant. We compare our results with simulational data obtained from a conventional Monte Carlo algorithm.

Transition matrix Monte Carlo method

We analyze a new Monte Carlo method which uses transition matrix in the space of energy. This method gives an efficient reweighting technique. The artificial dynamics is a constrained random walk in energy, producing the result that correlation time is proportional to the specific heat.