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Determining fluid pressure in Monte Carlo simulations can be a challenging task due to the reduced arsenal of computational tools available to perform such measurements. In addition, none of these tools is general enough to calculate the equilibrium pressure for a wide variety of models. The Gibbs–Duhem method, for example, is a very useful option, but only for pure (one component) systems. To enrich this arsenal, we propose here a direct method to calculate pressure in the canonical ensemble, which could easily be extended to mixtures at low densities. In analogy with the Widom method, our approach is based on the free energy variation with volume, described in terms of the removal of an empty or particle-occupied lattice column. We tested our approach for the lattice gas model and compared the results with exact Onsager solutions. Furthermore, the appearance of thermodynamic instabilities (loops) in the pressure isotherms during the phase transition and their relationship with interface effects are discussed. Finally, a phase diagram is obtained from these isotherms using the Hill construction. [ABSTRACT FROM AUTHOR]

The surface of a material often undergoes dramatic structure evolution under a chemical environment, which, in turn, helps determine the different properties of the material. Here, we develop a general-purpose method for the automated search of optimal surface phases (ASOPs) in the grand canonical ensemble, which is facilitated by the stochastic surface walking (SSW) global optimization based on global neural network (G-NN) potential. The ASOP simulation starts by enumerating a series of composition grids, then utilizes SSW-NN to explore the configuration and composition spaces of surface phases, and relies on the Monte Carlo scheme to focus on energetically favorable compositions. The method is applied to silver surface oxide formation under the catalytic ethene epoxidation conditions. The known phases of surface oxides on Ag(111) are reproduced, and new phases on Ag(100) are revealed, which exhibit novel structure features that could be critical for understanding ethene epoxidation. Our results demonstrate that the ASOP method provides an automated and efficient way for probing complex surface structures that are beneficial for designing new functional materials under working conditions. [ABSTRACT FROM AUTHOR]

Finite temperature auxiliary field-based quantum Monte Carlo methods, including determinant quantum Monte Carlo and Auxiliary Field Quantum Monte Carlo (AFQMC), have historically assumed pivotal roles in the investigation of the finite temperature phase diagrams of a wide variety of multidimensional lattice models and materials. Despite their utility, however, these techniques are typically formulated in the grand canonical ensemble, which makes them difficult to apply to condensates such as superfluids and difficult to benchmark against alternative methods that are formulated in the canonical ensemble. Working in the grand canonical ensemble is furthermore accompanied by the increased overhead associated with having to determine the chemical potentials that produce desired fillings. Given this backdrop, in this work, we present a new recursive approach for performing AFQMC simulations in the canonical ensemble that does not require knowledge of chemical potentials. To derive this approach, we exploit the convenient fact that AFQMC solves the many-body problem by decoupling many-body propagators into integrals over one-body problems to which non-interacting theories can be applied. We benchmark the accuracy of our technique on illustrative Bose and Fermi--Hubbard models and demonstrate that it can converge more quickly to the ground state than grand canonical AFQMC simulations. We believe that our novel use of HS-transformed operators to implement algorithms originally derived for non-interacting systems will motivate the development of a variety of other methods and anticipate that our technique will enable direct performance comparisons against other many-body approaches formulated in the canonical ensemble. [ABSTRACT FROM AUTHOR]

In spatial updating grand canonical Monte Carlo, particle transfers are implemented by examining the local environment around a point in space. In the present work, these algorithms are extended to very high densities by allowing the volume to fluctuate, thus forming a great grand canonical ensemble. Since fluctuations are unbounded, a constraint must be imposed. The constrained ensemble may be viewed as a superposition of either constant-pressure or grand canonical ensembles. Each simulation of the constrained ensemble requires a set of weights that must be determined iteratively. The outcome of a single simulation is the density of states in terms of all its independent variables. Since all extensive variables fluctuate, it is also possible to estimate absolute free energies and entropies from a single simulation. The method is tested on a system of hard spheres and the transition from the fluid to a face-centered cubic crystal is located with high precision.

We present two efficient iterative Monte Carlo algorithms in the grand canonical ensemble with which the chemical potentials corresponding to prescribed (targeted) partial densities can be determined. The first algorithm works by always using the targeted densities in the kT log(rho(i)) (ideal gas) terms and updating the excess chemical potentials from the previous iteration. The second algorithm extrapolates the chemical potentials in the next iteration from the results of the previous iteration using a first order series expansion of the densities. The coefficients of the series, the derivatives of the densities with respect to the chemical potentials, are obtained from the simulations by fluctuation formulas. The convergence of this procedure is shown for the examples of a homogeneous Lennard-Jones mixture and a NaCl-CaCl(2) electrolyte mixture in the primitive model. The methods are quite robust under the conditions investigated. The first algorithm is less sensitive to initial conditions.

Using a newly developed grand canonical Monte Carlo approach based on fractional exchanges of dissolved ions and water molecules, we studied equilibrium partitioning of both components between laterally extended apolar confinements and surrounding electrolyte solution. Accurate calculations of the Hamiltonian and tensorial pressure components at anisotropic conditions in the pore required the development of a novel algorithm for a self-consistent correction of nonelectrostatic cut-off effects. At pore widths above the kinetic threshold to capillary evaporation, the molality of the salt inside the confinement grows in parallel with that of the bulk phase, but presents a nonuniform width-dependence, being depleted at some and elevated at other separations. The presence of the salt enhances the layered structure in the slit and lengthens the range of inter-wall pressure exerted by the metastable liquid. Solvation pressure becomes increasingly repulsive with growing salt molality in the surrounding bath. Depending on the sign of the excess molality in the pore, the wetting free energy of pore walls is either increased or decreased by the presence of the salt. Because of simultaneous rise in the solution surface tension, which increases the free-energy cost of vapor nucleation, the rise in the apparent hydrophobicity of the walls has not been shown to enhance the volatility of the metastable liquid in the pores. [ABSTRACT FROM AUTHOR]

We present a method to estimate the transition rates of molecular systems under different environmental conditions that cause the formation or the breaking of bonds and require the sampling of the Grand Canonical Ensemble. For this purpose, we model the molecular system in terms of probable "scenarios," governed by different potential energy functions, which are separately sampled by classical MD simulations. Reweighting the canonical distribution of each scenario according to specific environmental variables, we estimate the grand canonical distribution, then use the Square Root Approximation method to discretize the Fokker-Planck operator into a rate matrix and the robust Perron Cluster Cluster Analysis method to coarse-grain the kinetic model. This permits efficiently estimating the transition rates of conformational states as functions of environmental variables, for example, the local pH at a cell membrane. In this work, we formalize the theoretical framework of the procedure, and we present a numerical experiment comparing the results with those provided by a constant-pH method based on non-equilibrium Molecular Dynamics Monte Carlo simulations. The method is relevant for the development of new drug design strategies that take into account how the cellular environment influences biochemical processes. [ABSTRACT FROM AUTHOR]

We derive a hierarchy of equations, which allow a general n-body distribution function to be measured by test-particle insertion of between 1 and n particles. We apply it to measure the pair and three-body distribution functions in a simple fluid using snapshots from Monte Carlo simulations in the grand canonical ensemble. The resulting distribution functions obtained from insertion methods are compared with the conventional distance-histogram method: the insertion approach is shown to overcome the drawbacks of the histogram method, offering enhanced structural resolution and a more straightforward normalization. At high particle densities, the insertion method starts breaking down, which can be delayed by utilizing the underlying hierarchical structure of the insertion method. Our method will be especially useful in characterizing the structure of inhomogeneous fluids and investigating closure approximations in liquid state theory. [ABSTRACT FROM AUTHOR]

We present a multilevel Monte Carlo simulation method for analyzing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically exact results, at the most detailed level. We apply the method to a mixture of size-asymmetric hard spheres, in the grand canonical ensemble. A three-level version of the method is compared with a previously studied two-level version. The extra level interpolates between the full mixture and a coarse-grained description where only the large particles are present—this is achieved by restricting the small particles to regions close to the large ones. The three-level method improves the performance of the estimator, at fixed computational cost. We analyze the asymptotic variance of the estimator and discuss the mechanisms for the improved performance. [ABSTRACT FROM AUTHOR]

A modification of the original Grand Canonical Monte Carlo (GCMC) method to handle Donnan equilibrium is proposed that provides an equilibrium between two implicit-solvent bath electrolytes with different dielectric constants. A solvation energy penalty (described by the Born theory) and an electrical potential difference (Donnan potential) exist between the two baths, the 'system' under investigation and the 'reservoir'. These terms are deducted from the chemical potential of the 'reservoir', and the resulting chemical potential is used in the 'system'. The simulation performed with this chemical potential in the acceptance probabilities of the ion insertion/deletions is called Donnan GCMC and provides a thermodynamic state in the 'system' that is in equilibrium with the electrolyte in the 'reservoir'. The simulation provides the distribution of ions between the two baths (concentrations in both media) from a single run instead of a numerical procedure that requires several GCMC runs. Using individual ion insertion/deletions, the Donnan potential can be determined. • An extension of the Grand Canonical Monte Carlo method to simulate Donnan equilibrium. • Solvation free energy and interaction with the Donnan potential are included in the acceptance criterion to equilibrate. • Donnan equilibrium is determined with a single simulation. [ABSTRACT FROM AUTHOR]

The uniform electron gas (UEG) is one of the key models for the understanding of warm dense matter—an exotic, highly compressed state of matter between solid and plasma phases. The difficulty in modelling the UEG arises from the need to simultaneously account for Coulomb correlations, quantum effects, and exchange effects, as well as finite temperature. The most accurate results so far were obtained from quantum Monte Carlo (QMC) simulations with a variety of representations. However, QMC for electrons is hampered by the fermion sign problem. Here, we present results from a novel fermionic propagator path integral Monte Carlo in the restricted grand canonical ensemble. The ab initio simulation results for the spin‐resolved pair distribution functions and static structure factor are reported for two isotherms θ=1,2 (T in the units of the Fermi temperature). Furthermore, we combine the results from the linear response theory in the Singwi‐Tosi‐Land‐Sjölander scheme with the QMC data to remove finite‐size errors in the interaction energy. We present a new corrected parametrization for the interaction energy v(rs,θ) and the exchange–correlation free energy fxc(rs,θ) in the thermodynamic limit, and benchmark our results against the restricted path integral Monte Carlo by Brown et al. [Phys. Rev. Lett. 110, 146405 (2013)] and configuration path integral Monte Carlo/permutation‐blocking path integral Monte Carlo by Dornheim et al. [Phys. Rev. Lett. 117, 115701 (2016)]. [ABSTRACT FROM AUTHOR]

We study the monatomic water model of Molinero and Moore the grand canonical ensemble Monte Carlo simulation. Measurements of the probability distribution of the number density obtained via multicanonical sampling and histogram reweighting provide accurate estimates of the temperature dependence of both the liquid–vapor coexistence densities and the surface tension. Using finite-size scaling methods, we locate the liquid–vapor critical point at Tc = 917.6 K, ρc = 0.311 g cm−3. When plotted in scaled variables, in order to test the law of corresponding states, the coexistence curve of monatomic water is close to that of real water. In this respect, it performs better than extended simple point charge (SPC/E), TIP4P, and TIP4P/2005 water. [ABSTRACT FROM AUTHOR]

We propose and develop a mesoscale particle-in-field simulation scheme, the Field-Accelerated Monte Carlo (FAMC) method, for speeding up particle-based continuum Monte Carlo (CMC) simulations based on soft interacting models. A key difference from the previously reported single-chain-in-mean-field method [K. C. Daoulas and M. Müller, J. Chem. Phys. 125, 184904 (2006)] is that the auxiliary fields in FAMC are constructed based on lattice-independent interacting potentials. As a result, FMAC simulations asymptotically approach CMC simulations with an increase in the lattice resolution of the auxiliary fields and are able to reproduce structural properties at morphology, conformation, and segment levels. A suite of schemes for computing and updating the auxiliary fields in FAMC simulations are developed in tandem to further enhance the computational efficiency of the method. The capacity of the FAMC method is demonstrated and tested against CMC simulations in simulating polymer solutions with explicit solvent under the canonical (nVT) ensemble and stress-free mircophase formation under the isothermal–isobaric (nPT) ensemble. In both cases, FAMC simulations reproduce structure properties with quantitative accuracy at a fraction of the computational cost. [ABSTRACT FROM AUTHOR]

A generalized identity exchange algorithm is presented for Monte Carlo simulations in the grand canonical ensemble. The algorithm, referred to as molecular exchange Monte Carlo, may be applied to multicomponent systems of arbitrary molecular topology and provides significant enhancements in the sampling of phase space over a wide range of compositions and temperatures. Three different approaches are presented for the insertion of large molecules, and the pros and cons of each method are discussed. The performance of the algorithms is highlighted through grand canonical Monte Carlo histogram-reweighting simulations performed on a number of systems, which include methane+n-alkanes, butane+perfluorobutane, water+impurity, and 2,2,4-trimethylpentane+neopentane. Relative acceptance efficiencies for molecule transfers of up to 400 times that of standard configurational-bias Monte Carlo are obtained. [ABSTRACT FROM AUTHOR]

While ionic liquids have promising applications as industrial solvents, predicting their fluid phase properties and coexistence remains a challenge. Grand canonical Monte Carlo simulation is an effective method for such predictions, but equilibration is hampered by the apparent requirement to insert and delete neutral sets of ions simultaneously in order to maintain charge neutrality. For relatively high densities and low temperatures, previously developed methods have been shown to be essential in improving equilibration by gradual insertion and deletion of these neutral sets of ions. We introduce an expanded ensemble approach which may be used in conjunction with these existing methods to further improve efficiency. Individual ions are inserted or deleted in one Monte Carlo trial rather than simultaneous insertion/deletion of neutral sets. We show how charge neutrality is maintained and show rigorous quantitative agreement between the conventional and the proposed expanded ensemble approaches, but with up to an order of magnitude increase in efficiency at high densities. The expanded ensemble approach is also more straightforward to implement than simultaneous insertion/deletion of neutral sets, and its implementation is demonstrated within open source software. [ABSTRACT FROM AUTHOR]

We describe a Monte Carlo scheme for simulating polydisperse fluids within the grand canonical ensemble. Given some polydisperse attribute σ, the state of the system is described by a density distribution ρ(σ) whose form is controlled by the imposed chemical potential distribution μ(σ). We detail how histogram extrapolation techniques can be employed to tune μ(σ) such as to traverse some particular desired path in the space of ρ(σ). The method is applied in simulations of size-disperse hard spheres with densities distributed according to Schulz and log-normal forms. In each case, the equation of state is obtained along the dilution line, i.e., the path along which the scale of ρ(σ) changes but not its shape. The results are compared with the moment-based expressions of Monsoori et al. [J. Chem. Phys. 54, 1523 (1971)] and Salacuse and Stell [J. Chem. Phys. 77, 3714 (1982)]. It is found that for high degrees of polydispersity, both expressions fail to give a quantitatively accurate description of the equation of state when the overall volume fraction is large. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The grand canonical ensemble has been used to study the evaluation of single ion activity coefficients in homogeneous ionic fluids. In this work, the Coulombic interactions are truncated according to the minimum image approximation, and the ions are assumed to be placed in a structureless, homogeneous dielectric continuum. Grand canonical ensemble Monte Carlo calculation results for two primitive model electrolyte solutions are presented. Also, a formula involving the second moments of the total correlation functions is derived from fluctuation theory, which applies for the derivatives of the individual ionic activity coefficients with respect to the total ionic concentration. This formula has previously been proposed on the basis of somewhat different considerations. [ABSTRACT FROM AUTHOR]

Nested sampling has emerged as a powerful sampling technique to directly compute the partition function of a realistic molecular system. However, it does so with a non-standard sampling of phase space, which excludes the use of molecular dynamics simulations. Here we show how to use the standard canonical (NVT) sampling of phase space to directly compute the partition function. There are two components to the nested NVT sampling procedure. First, the temperatures at which the simulations should be run are chosen sequentially, from high to low, based on a histogram reweighting strategy. Second, a harmonic umbrella biasing potential is added, where necessary, to enhance the sampling. We also show how to evaluate the expectation value of an observable and compute the free energy as a function of an order parameter. NVT sampling procedures are common and readily available in conventional Monte Carlo and molecular dynamics codes. The proposed algorithm is easy to integrate into existing codes, which opens up the nested sampling technique to a wide audience. [ABSTRACT FROM AUTHOR]

Reports that the cavity-biased grand-canonical ensemble method was applied to the simulation of a lipid bilayer using an enhanced Monte Carlo sampling technique. Details of the Monte Carlo enhancements; Enhancement of the sampling of the lipid conformations.

A critic issue of the application of the conventional grand-canonical Monte Carlo (GCMC) method in high-density systems is the low acceptance ratio of insertion. Previous studies have revealed that this can be overcome by the cavity-biased (CB) insertion method in simulations of vapours, fluids and liquids. Here, we demonstrate that the method is also highly efficient in metals. Using the Fe–H system as an example, we find that the acceptance ratio of inserting H into Fe lattice is increased by several times using the CB GCMC method. The method is more valid than the conventional one at bulk H concentration over 5‰, implying that the CB GCMC method is highly efficient when there are deep traps for H in simulation systems, i.e. dislocations and interfaces. Application of the method in nanocrystalline Fe shows that the CPU time required for obtaining an equilibrium distribution of H is reduced by 60%. [ABSTRACT FROM AUTHOR]

In inhomogeneous systems the diffusion paths available to particles are often restricted by the topology of the system itself. In search of a realistic scheme to simulate such inhomogeneous systems, we developed a new method, of local control of the chemical potential. The local control method, which limits creation and destruction of particles to a control volume, can be successfully implemented in both Monte Carlo (MC) and molecular dynamics (MD) simulations of the grand canonical ensemble (GC). We present applications of local GCMC calculations of the one-dimensional lattice gas and hard rods confined by hard walls, as well as local GCMC and GCMD of a three-dimensional bulk Lennard-Jones fluid system. The simulation results compare successfully with analytical solutions and equation of state approximations. [ABSTRACT FROM AUTHOR]

A model consisting of hard charged spheres inside hard spherical pores is investigated by grand canonical ensemble Monte Carlo calculations. It is found that the mean ionic density profiles in the pores are almost the same when the wall of the pore is moderately charged as when it is uncharged. Also, a bulklike phase is found to be present at the center of the pores in surprisingly small systems. Finally, the Poisson–Boltzman approximation is discussed in the light of our Monte Carlo results. [ABSTRACT FROM AUTHOR]

Density profiles and partition coefficients are obtained for hard-sphere fluids inside hard, spherical pores of different sizes by grand canonical ensemble Monte Carlo calculations. The Monte Carlo results are compared to the results obtained by application of different kinds of integral equation approximations. Also, some exact, analytical results for the partition coefficients are given, which are valid in the case of (very) small pores or at low density, respectively. [ABSTRACT FROM AUTHOR]

Grand canonical Monte Carlo simulation and theoretical calculations based on Ornstein–Zernike (OZ) integral equation and third order+second order perturbation density functional theory (DFT) are performed to study a system of spherical particles interacting through a core-softened (CS) potential combining a repulsive square soft core and an attractive square well. Both theoretical predictions and simulation results reveal peculiar homogeneous and inhomogeneous local structures originating from the discontinuous nature of the CS potential. The bulk radial distribution function displays discontinuities at the distances coinciding with the ranges of the successive repulsive and attractive parts in the CS potential function. The density profiles of confined CS fluid show the shapes arising from the complex interplay among the steric effects and the competition between the repulsive and attractive parts of the CS potential. Satisfactory agreement between the theoretical results and simulation data leads to the following conclusions: (i) a modified hypernetted chain approximation combined with a hard sphere bridge function, which has been recently proposed by one of the authors of this study, is sufficiently reliable for the structural studies of CS fluid, and (ii) the third order+second order perturbation DFT, which has proven successful for the study of inhomogeneous structure of model fluids with continuous intermolecular potential function, posses a high adaptability to be applied for various types of interaction potentials and performs well also in the case of discontinuous CS model. [ABSTRACT FROM AUTHOR]

A new grand canonical Monte Carlo algorithm for continuum fluid models is proposed. The method is based on a generalization of sequential Monte Carlo algorithms for lattice gas systems. The elementary moves, particle insertions and removals, are constructed by analogy with those of a lattice gas. The updating is implemented by selecting points in space (spatial updating) either at random or in a definitive order (sequential). The type of move, insertion or removal, is deduced based on the local environment of the selected points. Results on two-dimensional square-well fluids indicate that the sequential version of the proposed algorithm converges faster than standard grand canonical algorithms for continuum fluids. Due to the nature of the updating, additional reduction of simulation time may be achieved by parallel implementation through domain decomposition. [ABSTRACT FROM AUTHOR]

Open statistical ensemble simulations are used to study the mechanism of nucleation of atmospheric water on sodium-chloride ion pair in a wide range of temperature and relative humidity values. The extended simple point-charge model is used for water molecules. Ions-water nonadditive interactions are taken into account by introducing the mutual polarization of ions and water in the field of each other. Gibbs free-energy variations are calculated from Na+–Cl- pair-correlation function and used as a criterion for determining the possible stable states of the cluster. In this relation, it was found that the dissociation of ion pairs in water clusters occurs even at vapor pressures of only a few millibars. In the conditions under consideration solvent-separated ion-pair states are found to be more probable than contact ion-pair configurations. The susceptibilities of water and ions are found to play an essential role in the stabilization of ions at large separations. The structure of ion-induced clusters is analyzed in terms of binary correlation functions. The nonpair interactions influence essentially the structure of ion solvation shells. The results of simulation show that the separation of the charges in water clusters containing simple ions can take place under atmospheric conditions. [ABSTRACT FROM AUTHOR]

Abstract: Accurate determination of thermodynamic properties of petroleum reservoir fluids is of great interest to many applications, especially in petroleum engineering and chemical engineering. Molecular simulation has many appealing features, especially its requirement of fewer tuned parameters but yet better predicting capability; however it is well known that molecular simulation is very CPU expensive, as compared to equation of state approaches. We have recently introduced an efficient thermodynamically consistent technique to regenerate rapidly Monte Carlo Markov Chains (MCMCs) at different thermodynamic conditions from the existing data points that have been pre-computed with expensive classical simulation. This technique can speed up the simulation more than a million times, making the regenerated molecular simulation almost as fast as equation of state approaches. In this paper, this technique is first briefly reviewed and then numerically investigated in its capability of predicting ensemble averages of primary quantities at different neighboring thermodynamic conditions to the original simulated MCMCs. Moreover, this extrapolation technique is extended to predict second derivative properties (e.g. heat capacity and fluid compressibility). The method works by reweighting and reconstructing generated MCMCs in canonical ensemble for Lennard-Jones particles. In this paper, system's potential energy, pressure, isochoric heat capacity and isothermal compressibility along isochors, isotherms and paths of changing temperature and density from the original simulated points were extrapolated. Finally, an optimized set of Lennard-Jones parameters (ε, σ) for single site models were proposed for methane, nitrogen and carbon monoxide. [Copyright &y& Elsevier]