Alternative implementations of the Gibbs ensemble Monte Carlo calculation

Accelerated convergence via adiabatic sampling for adsorption and desorption processes

Under isothermal conditions, phase transitions occur through a nucleation event when conditions are sufficiently close to coexistence. The formation of a nucleus of the new phase requires the system to overcome a free energy barrier of formation, whose height rapidly rises as supersaturation decreases. This phenomenon occurs both in the bulk and under confinement and leads to a very slow kinetics for the transition, ultimately resulting in hysteresis, where the system can remain in a metastable state for a long time. This has broad implications, for instance, when using simulations to predict phase diagrams or screen porous materials for gas storage applications. Here, we leverage simulations in an adiabatic statistical ensemble, known as adiabatic grand-isochoric ensemble (μ, V, L) ensemble, to reach equilibrium states with a greater efficiency than its isothermal counterpart, i.e., simulations in the grand-canonical ensemble. For the bulk, we show that at low supersaturation, isothermal simulations converge slowly, while adiabatic simulations exhibit a fast convergence over a wide range of supersaturation. We then focus on adsorption and desorption processes in nanoporous materials, assess the reliability of (μ, V, L) simulations on the adsorption of argon in IRMOF-1, and demonstrate the efficiency of adiabatic simulations to predict efficiently the equilibrium loading during the adsorption and desorption of argon in MCM-41, a system that exhibits significant hysteresis. We provide quantitative measures of the increased rate of convergence when using adiabatic simulations. Adiabatic simulations explore a wide temperature range, leading to a more efficient exploration of the configuration space.

Classical statistical mechanics in the μVL and μpR ensembles

Molecular expressions for thermodynamic properties and derivatives of the entropy up to third order in the adiabatic grand-isochoric μVL and adiabatic grand-isobaric μpR ensembles are systematically derived using the methodology developed by Lustig for the microcanonical and canonical ensembles [J. Chem. Phys. 100, 3048 (1994)10.1063/1.466446; Mol. Phys. 110, 3041 (2012)10.1080/00268976.2012.695032]. They are expressed by phase-space functions, which represent derivatives of the entropy with respect to the chemical potential, the volume, and the Hill energy L in the μVL ensemble and with respect to the chemical potential, the pressure, and the Ray energy R in the μpR ensemble. The derived expressions are validated for both ensembles by Monte Carlo simulations for the simple Lennard-Jones model fluid at three selected state points.

Rigorous expressions for thermodynamic properties in the NpH ensemble

Molecular expressions for thermodynamic properties of fluids and derivatives of the entropy up to third order in the isoenthalpic-isobaric ensemble are derived by using the methodology developed by Lustig for the microcanonical and canonical ensembles [J. Chem. Phys. 100, 3048 (1994)JCPSA60021-960610.1063/1.466446; Mol. Phys. 110, 3041 (2012)MOPHAM0026-897610.1080/00268976.2012.695032]. They are expressed in a systematic way by phase-space functions, which represent derivatives of the phase-space volume with respect to enthalpy and pressure. The expressions for thermodynamic properties contain only ensemble averages of combinations of the kinetic energy and volume of the system. Thus, the calculation of thermodynamic properties in the isoenthalpic-isobaric ensemble does not require volume derivatives of the potential energy. This is particularly advantageous in Monte Carlo simulations when the interactions between molecules are described by very accurate ab initio pair and nonadditive three-body potentials. The derived expressions are validated by Monte Carlo simulations for the simple Lennard-Jones model fluid as a test case.

The central role of entropy in adiabatic ensembles and its application to phase transitions in the grand-isobaric adiabatic ensemble

Entropy has become increasingly central to characterize, understand, and even guide assembly, self-organization, and phase transition processes. In this work, we build on the analogous role of partition functions (or free energies) in isothermal ensembles and that of entropy in adiabatic ensembles. In particular, we show that the grand-isobaric adiabatic (μ, P, R) ensemble, or Ray ensemble, provides a direct route to determine the entropy. This allows us to follow the variations of entropy with the thermodynamic conditions and thus explore phase transitions. We test this approach by carrying out Monte Carlo simulations on argon and copper in bulk phases and at phase boundaries. We assess the reliability and accuracy of the method through comparisons with the results from flat-histogram simulations in isothermal ensembles and with the experimental data. Advantages of the approach are multifold and include the direct determination of the μ-P relation, without any evaluation of pressure via the virial expression, the precise control of the system size (number of atoms) via the input value of R, and the straightforward computation of enthalpy differences for isentropic processes, which are key quantities to determine the efficiency of thermodynamic cycles. A new insight brought by these simulations is the highly symmetric pattern exhibited by both systems along the transition, as shown by scaled temperature-entropy and pressure-entropy plots.

Simulation of the density of states in isothermal and adiabatic ensembles

This paper provides a unified treatment of the fundamental methods used to obtain the density of states via molecular simulations with isothermal ensembles (IEs) and adiabatic ensembles (AEs). Our analysis and results show that provides a natural bridge to go back and forth between IE and AE simulation data. They also underline the difference between the density of states of potential energy macrostates and that of total energy macrostates Omega, even though both provide access to the thermodynamic properties of the system. Visited-states approaches and transition matrix methods are described and applied to the Lennard-Jones fluid to target omega and Omega as functions of energy and volume macrostates. It is shown that one can obtain omega via a generalized acceptance-ratio formula that is applicable regardless of the conditions at which the ensemble is simulated. In this way, one can obtain while performing conventional IE or AE simulations, and do it at no extra cost and with a higher accuracy than is achievable with histogram methods.

A unified methodological framework for the simulation of nonisothermal ensembles

A general framework is developed for the simulation of nonisothermal statistical-mechanical ensembles. This framework is intended to synthesize the formulation of advanced Monte Carlo simulation methods such as multihistogram reweighting, replica-exchange methods, and expanded ensemble techniques so that they can be applied to different nonisothermal ensembles. Using Lennard-Jones systems as test cases, novel implementations of these methods are demonstrated with different ensembles including the microcanonical, isobaric-isoenthalpic, and isobaric-semigrand ensembles. In particular, it is shown that the use of multiensemble methods allows the efficient simulation of microcanonical density of states, entropies, vapor-liquid and solid-liquid equilibrium for pure component systems, and fluid-phase coexistence for binary mixtures. In these applications, comparisons are also presented that highlight the advantages of the proposed multiensemble implementations over alternative methods used before.

Direct Monte Carlo simulation methods for nonreacting and reacting systems at fixed total internal energy or enthalpy

A Monte Carlo computer simulation method is presented for directly performing property predictions for fluid systems at fixed total internal energy, U, or enthalpy, H, using a molecular-level system model. The method is applicable to both nonreacting and reacting systems. Potential applications are to (1) adiabatic flash (Joule-Thomson expansion) calculations for nonreacting pure fluids and mixtures at fixed (H,P), where P is the pressure; and (2) adiabatic (flame-temperature) calculations at fixed (U,V) or (H,P), where V is the system volume. The details of the method are presented. The method is compared with existing related simulation methodologies for nonreacting systems, one of which addresses the problem involving fixing portions of U or of H, and one of which solves the problem at fixed H considered here by means of an indirect approach. We illustrate the method by an adiabatic calculation involving the ammonia synthesis reaction.