On the existence of a hysteresis loop in open and closed end pores

We have studied the adsorption of argon at 87 K in slit pores of finite length with a smooth graphitic potential, open at both ends or closed at one end. Simulations were carried out using conventional GCMC (grand canonical Monte Carlo) or kMC (kinetic Monte Carlo) in the canonical ensemble with extremely long Markov chain, of at least 2 × 10⁸ configurations; selected simulations with much longer Markov chains do not show any change in the results. When the pore width is in the micropore range (0.65 nm), type I isotherms are obtained for both pore models and for both simulation methods. However, wider pores (1, 2 and 3 nm in width) all exhibit hysteresis loops in the GCMC simulations, while in the canonical ensemble simulations, the isotherms pass through a sigmoid van der Waals type loop in the transition region. This loop locates the true equilibrium transition. For the pores with one closed end, this transition is close to, or coincides with, the adsorption branch of the GCMC hysteresis loop, but for the open-ended pores, it is more closely associated with the desorption branch. In a separate study of adsorption hysteresis in an infinitely long slit pore, using both simulation techniques, the van der Waals loop follows the adsorption branch of the GCMC isotherm to the transition, then reverts to a long vertical section that falls midway between the two hysteresis branches and finally moves to the desorption transition close to the evaporation pressure. An examination of molecular distributions inside the pores reveals two coexisting phases in the canonical simulations, whereas in the grand canonical simulations, the molecules are uniformly distributed along the length of the pores.     

Grand Molecular Dynamics: A Method for Open Systems

We present a new molecular dynamics method for studying the dynamics of open systems. The method couples a classical system to a chemical potential reservior. In the formulation, following the extended system dynamics approach, we introduce a variable, v to represent the coupling to the chemical potential reservoir. The new variable governs the dynamics of the variation of number of particles in the system. The number of particles is determined by taking the integer part of v. The fractional part of the new variable is used to scale the potential energy and the kinetic energy of an additional particle: i.e., we introduce a fractional particle. We give the ansatz Lagrangians and equations of motion for both the isothermal and the adiabatic forms of grand molecular dynamics. The averages calculated over the trajectories generated by these equations of motion represent the classical grand canonical ensemble (μVT) and the constant chemical potential adiabatic ensemble (μVL) averages, respectively. The microcanonical phase space densities of the adiabatic and isothermal forms the molecular dynamics method are shown to be equivalent to adiabatic constant chemical potential ensemble, and grand canonical ensemble partition functions. We also discuss the extension to multi-component systems, molecular fluids, ionic solutions and the problems and solutions associated with the implementation of the method. The statistical expressions for thermodynamic functions such as specific heat; adiabatic bulk modulus, Grüneissen parameter and number fluctuations are derived. These expressions are used to analyse trajectories of constant chemical potential systems.     

Connectivity effects for slit pores linked by a channel

This paper describes a Monte Carlo computer simulation study of connectivity effects in a system of two parallel slit pores and a quasi-one-dimensional joint. A numerical method for evaluation of accessible volume in computer simulation studies of adsorption in pores is presented and applied to simple slit pores and systems of interconnected pores. A local version of the grand canonical ensemble Monte Carlo method is used to study adsorption under conditions mimicking mass transfer limitations.     

Molecular Dynamics Simulations With First Order Coupling to a Bath of Constant Chemical Potential

Abstract

In molecular dynamics simulations the temperature or pressure can be controlled by applying a weak first-order coupling to a bath of constant temperature or pressure. This weak coupling technique to control system properties using a first-order relaxation equation is analyzed from a statistical mechanics point of view. It is shown, how the weak coupling scheme can be generalized and applied to a bath of contstant chemical potential. The presented method, to which in the following will be referred to as chemical potential weak coupling, is applied and tested on a Lennard-Jones fluid. The thermodynamic quantities known from the literature are accuratly reproduced.

The temperature and chemical potential weak coupling methods aim to sample the canonical and grand canonical ensembles respectively. By analyzing the fluctuations in energy and number of particles, the tight relation between the ensembles and the distributions obtained from the weak coupling simulations is demonstrated. The influence of the choice of the coupling parameters on the quality of the approximation of the ensemble distribution is discussed.     

Generalized-ensemble algorithms for molecular simulations of biopolymers.

In complex systems with many degrees of freedom such as peptides and proteins, there exists a huge number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review uses of the generalized-ensemble algorithms in biomolecular systems. Three well-known methods, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present three new generalized-ensemble algorithms that combine the merits of the above methods. The effectiveness of the methods for molecular simulations in the protein folding problem is tested with short peptide systems.     

Interactions between lignin and urea researched by molecular simulation

Molecular simulations of interactions between urea molecules and lignin polymer have been carried out with the aim of understanding the mechanism of urea slow-release behaviours in lignin–urea materials. It has been found, by docking technology and natural bond orbital analysis, that H-bonds and π-electronic conjugation effect are the main driving forces to keep urea molecules adsorbed on the lignin. In the NPT (isothermal–isobaric ensemble) simulations, mean-squared displacement results show that water molecules can promote the urea molecules gradually away from the lignin. Furthermore, in NVT (canonical ensemble) molecular dynamic simulations, results on diffusion constants of urea molecules in lignin–urea system show that diffusion constant of urea molecules in a urea–water–lignin system increases with an increase in the water content. Conclusions gained from two different kinds of simulation are in agreement with each other and are consistent with the experimental observations.     

An efficient algorithm in the grand canonical ensemble: constructing adsorption isotherms

A new computational method is presented that efficiently describes open thermodynamic systems within the grand canonical ensemble formalism. The method is based on the j-walking algorithm, which circumvent sampling difficulties by coupling random walkers in different thermodynamic states. By imposing detailed balance, a new acceptance probability is derived and applied to the construction of adsorption isotherms for atomic monolayers. The method converges much faster than the standard grand canonical Monte Carlo method and permits the construction of accurate adsorption isotherms and the identification of phase transitions occurring in the adsorbed material.     

Direct Determination of Fluid Phase Equilibria by Simulation in the Gibbs Ensemble: A Review

This paper provides an extensive review of the literature on the Gibbs ensemble Monte Carlo method for direct determination of phase coexistence in fluids. The Gibbs ensemble technique is based on performing a simulation in two distinct regions in a way that ensures that the conditions of phase coexistence are satisfied in a statistical sense. Contrary to most other available techniques for this purpose, such as thermodynamic integration, grand canonical Monte Carlo or Widom test particle insertions, the Gibbs ensemble technique involves only a single simulation per coexistence point. A significant body of literature now exists on the method, its theoretical foundations, and proposed modifications for efficient determination of equilibria involving dense fluids and complex intermolecular potentials. Some practical aspects of Gibbs ensemble simulation are also discussed in this review. Applications of the technique to date range from studies of simple model potentials (for example Lennard–Jones, square-well or Yukawa fluids) to calculations of equilibria in mixtures with components described by realistic potentials. We conclude by discussing the limitations of the technique and potential future applications.     

Molecular simulation of water removal from simple gases with zeolite NaA

Water vapor removal from some simple gases using zeolite NaA was studied by molecular simulation. The equilibrium adsorption properties of H(2)O, CO, H(2), CH(4) and their mixtures in dehydrated zeolite NaA were computed by grand canonical Monte Carlo simulations. The simulations employed Lennard-Jones + Coulomb type effective pair potential models, which are suitable for the reproduction of thermodynamic properties of pure substances. Based on the comparison of the simulation results with experimental data for single-component adsorption at different temperatures and pressures, a modified interaction potential model for the zeolite is proposed. In the adsorption simulations with mixtures presented here, zeolite exhibits extremely high selectivity of water to the investigated weakly polar/non-polar gases demonstrating the excellent dehydration ability of zeolite NaA in engineering applications.     

Smart Monte Carlo Algorithm for the Adsorption of Molecules at a Surface

Abstract

A modified grand canonical ensemble Monte Carlo (GCMC) technique has been developed to simulate adsorption isotherms for molecules on or near a surface. The speed and accuracy of the simulation is increased by using a non-uniform distribution function, related to the force field exerted by the surface and the current configuration, to generate coordinates for the creation of new particles in the simulation. With this method, isotherms are generated more efficiently than with current techniques in which the creation step relies on a uniform distribution to generate the coordinates of a new molecule. This is shown by comparing the calculation of an isotherm for a simple molecule adsorbed on a graphite substrate from a traditional GCMC simulation with that calculated using this new technique.     

Folding energetics of ligand binding proteins. I. Theoretical model

Heat capacity curves as obtained from differential scanning calorimetry are an outstanding source for molecular information on protein folding and ligand-binding energetics. However, deconvolution of C(p) data of proteins in the presence of ligands can be compromised by indeterminacies concerning the correct choice of the statistical thermodynamic ensemble. By convent, the assumption of constant free ligand concentration has been used to derive formulae for the enthalpy. Unless the ligand occurs at large excess, this assumption is incorrect. Still the relevant ensemble is the grand canonical ensemble. We derive formulae for both constraints, constancy of total or free ligand concentration and illustrate the equations by application to the typical equilibrium Nx <=> N + x <=> D + x. It is demonstrated that as long as the thermodynamic properties of the ligand can be completely corrected for by performing a reference measurement, the grand canonical approach provides the proper and mathematically significantly simpler choice. We demonstrate on the two cases of sequential or independent ligand-binding the fact, that similar binding mechanisms result in different and distinguishable heat capacity equations. Finally, we propose adequate strategies for DSC experiments as well as for obtaining first estimates of the characteristic thermodynamic parameters, which can be used as starting values in a global fit of DSC data.     

Molecular simulation of cage occupancy and selectivity of binary THF–H2 sII hydrate

The hydrogen capacity of the binary THF–H₂ sII hydrate is determined by the cage occupancy and by the selectivity of guest molecules. Grand canonical Monte Carlo (GCMC) simulation is used to study the cage occupancy and selectivity of guest molecules from the equilibrium configuration of the binary sII hydrate. The cage framework is regarded as a rigid body and the number of guest molecules is varied to preserve the grand canonical ensemble. The occupancy and selectivity were investigated at a temperature of 270 K for pressures ranging from 0.1 to 200 MPa. It was found that most large cages select THF as guest molecules while small cages include only hydrogen molecules. Multiple occupancy of hydrogen, up to four molecules in large cages and two molecules in small cages, was found as the pressure increases. GCMC results show that the hydrogen capacity is approximately 1.1 wt% at 200 MPa.     

Adaptive conformational sampling based on replicas

Computer simulations of biomolecules such as molecular dynamics simulations are limited by the time scale of conformational rearrangements. Several sampling techniques are available to search the multi-minima free energy landscape but most efficient, time-dependent methods do generally not produce a canonical ensemble. A sampling algorithm based on a self-regulating ladder of searching copies in the dihedral subspace is developped in this paper. The learning process using short- and long-term memory functions allows an efficient search in phase space while combining a deterministic dynamics and stochastic swaps with the searching copies conserves a canonical limit. The sampling efficiency and accuracy are indicated by comparing the ansatz with conventional molecular dynamics and replica exchange simulations.     

Object-oriented Programming Paradigms for Molecular Modeling

This paper discusses the application of object-oriented programming (OOP) design concepts to the development of molecular simulation code. A number of new languages such as Fortran 90 (F90) have been developed over the last decade that support the OOP design philosophy. We briefly describe the salient features of F90 and some basic object-oriented design principles. As an illustration of the design concepts we implement a general interface in F90 for calculating pairwise interactions that can be extended easily to any number of different forcefield models. The ideas presented here are used in the development of a mu ltipurpose si mulation c ode, named Music. An example of the use of Music for grand canonical Monte Carlo (GCMC) simulations of flexible sorbate molecules in zeolites is given. The example illustrates how OOP allowed existing code for molecular dynamics and GCMC to be easily combined to perform hybrid GCMC simulations with minimal coding effort.     

Speeding up Monte Carlo molecular simulation by a non-conservative early rejection scheme

Monte Carlo (MC) molecular simulation describes fluid systems with rich information, and it is capable of predicting many fluid properties of engineering interest. In general, it is more accurate and representative than equations of state. On the other hand, it requires much more computational effort and simulation time. For that purpose, several techniques have been developed in order to speed up MC molecular simulations while preserving their precision. In particular, early rejection schemes are capable of reducing computational cost by reaching the rejection decision for the undesired MC trials at an earlier stage in comparison to the conventional scheme. In a recent work, we have introduced a ‘conservative’ early rejection scheme as a method to accelerate MC simulations while producing exactly the same results as the conventional algorithm. In this paper, we introduce a ‘non-conservative’ early rejection scheme, which is much faster than the conservative scheme, yet it preserves the precision of the method. The proposed scheme is tested for systems of structureless Lennard-Jones particles in both canonical and NVT-Gibbs ensembles. Numerical experiments were conducted at several thermodynamic conditions for different number of particles. Results show that at certain thermodynamic conditions, the non-conservative method is capable of doubling the speed of the MC molecular simulations in both canonical and NVT-Gibbs ensembles.     

Modeling of the Psychophysical Response Curves Using the Grand Canonical Ensemble in Statistical Physics

This paper aims to investigate the peripheral mechanism of taste perception by the use of the grand canonical ensemble in statistical physics. It allows a better understanding of this process and its interpretation at a microscopic level. The experimental part allowed us to obtain psychophysical curves relative to four nutritive sweeteners (sucrose, fructose, glucose, and maltitol). These curves represent the intensity of sweetness as a function of sugar concentration in water. A Sensory Measuring Unit for Recording Flux (SMURF) device is used to obtain intensity–time curves for each of the studied sweeteners. To model these curves we have established the expressions of some models using grand canonical ensemble formalism in statistical physics and applying some simplification approaches. The fitting of the psychophysical data with statistical models by numerical simulation demonstrates a good correlation between the models and the experimental curves. Some physicochemical parameters interfere in the expression of the established models. These parameters are classified in two categories: on one hand, the steric aspect, which is manifested by the density of taste receptor site, and the number of molecules per receptor site and on the other hand, an energetic aspect illustrated by the concentration at half saturation, which gives indirectly the sweet molecule-receptor site energy of interaction.     

Computation of elastic constants of solids using molecular simulation: comparison of constant volume and constant pressure ensemble methods

We compute the elastic stiffness tensor of fcc argon at 60 K and 1 bar using molecular simulation tools. Three different methods are investigated: explicit deformations of the simulation box, strain fluctuations at constant pressure and stress fluctuations at constant volume. Statistical ensemble sampling is done using molecular dynamics and Monte Carlo simulations. We observe a good agreement between the different methods and sampling algorithms excepted with molecular dynamics simulations in the (NpT) ensemble. There, we notice a strong dependence of the computed elastic constants with the barostat parameter, whereas molecular dynamics simulations in the (NVT) ensemble are not affected by the thermostat parameter.     

Influences of lithium doping and fullerene impregnation on hydrogen storage in metal organic frameworks

Using the grand canonical ensemble Monte Carlo method, two similar metal organic frameworks (isoreticular MOFs [IRMOF]-12 and -14) and their modified structures by doping lithium (Li) atoms above the organic units and/or impregnating with fullerenes in their cavities have been employed to investigate the capacities of H₂ storage. Our simulations show that the H₂ uptakes of Li-C₆₀@Li-IRMOF-12 and Li-C₆₀@Li-IRMOF-14 achieve the U.S. Department of Energy targets before 2017 both in gravimetric density and in volumetric density at 243 K and 100 bar. Combining the results of IRMOF-10-based structures, we further study the relationships between the H₂ uptakes and the physical properties of the materials to identify the influence factors on the H₂ storage at room temperature.     

Ab initio simulation of a 57-residue protein in explicit solvent reproduces the native conformation in the lowest free-energy cluster

An enhanced conformational sampling method, multicanonical molecular dynamics (McMD), was applied to the ab intio folding of the 57-residue first repeat of human glutamyl- prolyl-tRNA synthetase (EPRS-R1) in explicit solvent. The simulation started from a fully extended structure of EPRS-R1 and did not utilize prior structural knowledge. A canonical ensemble, which is a conformational ensemble thermodynamically probable at an arbitrary temperature, was constructed by reweighting the sampled structures. Conformational clusters were obtained from the canonical ensemble at 300 K, and the largest cluster (i.e., the lowest free-energy cluster), which contained 34% of the structures in the ensemble, was characterized by the highest similarity to the NMR structure relative to all alternative clusters. This lowest free-energy cluster included native-like structures composed of two anti-parallel α-helices. The canonical ensemble at 300 K also showed that a short Gly-containing segment, which adopts an α-helix in the native structure, has a tendency to be structurally disordered. Atomic-level analyses demonstrated clearly that inter-residue hydrophobic interactions drive the helix formation of the Gly-containing segment, and that increasing the hydrophobic contacts accompanies exclusion of water molecules from the vicinity of this segment. This study has shown, for the first time, that the free-energy landscape of a structurally well-ordered protein of about 60 residues is obtainable with an all atom model in explicit water without prior structural knowledge.     

On the Sampling Method for Grand Canonical Monte Carlo Simulations

Abstract

A bulk Lennard-Jones fluid was simulated using the grand canonical Monte Carlo method. Three different sampling methods were used in the transition matrix, namely the Metropolis, Barker and a third novel method. While it can be shown that the Metropolis method will give the most accurate ensemble averages in the limit of an infinitely long run, the new method termed “Modified Barker Sampling” (MBS), is shown to be superior for the runs of practical length for the particular system studied.