Rigorous expressions for thermodynamic properties in the NpH ensemble

Calculation of thermodynamic properties of helium using path integral Monte Carlo simulations in the NpT ensemble and ab initio potentials

We apply the methodology of Lustig, with which rigorous expressions for all thermodynamic properties can be derived in any statistical ensemble, to derive expressions for the calculation of thermodynamic properties in the path integral formulation of the quantum-mechanical isobaric-isothermal (NpT) ensemble. With the derived expressions, thermodynamic properties such as the density, speed of sound, or Joule-Thomson coefficient can be calculated in path integral Monte Carlo simulations, fully incorporating quantum effects without uncontrolled approximations within the well-known isomorphism between the quantum-mechanical partition function and a classical system of ring polymers. The derived expressions are verified by simulations of supercritical helium above the vapor-liquid critical point at selected state points using recent highly accurate ab initio potentials for pairwise and nonadditive three-body interactions. We observe excellent agreement of our results with the most accurate experimental data for the density and speed of sound and a reference virial equation of state for helium in the region where the virial equation of state is converged. Moreover, our results agree closer with the experimental data and virial equation of state than the results of semiclassical simulations using the Feynman-Hibbs correction for quantum effects, which demonstrates the necessity to fully include quantum effects by path integral simulations. Our results also show that nonadditive three-body interactions must be accounted for when accurately predicting thermodynamic properties of helium by solely theoretical means.

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.

Topology of thermodynamic potentials using physical models: Helmholtz, Gibbs, Grand, and Null

Thermodynamic potentials play a substantial role in numerous scientific disciplines and serve as basic constructs for describing the behavior of matter. Despite their significance, comprehensive investigations of their topological characteristics and their connections to molecular interactions have eluded exploration due to experimental inaccessibility issues. This study addresses this gap by analyzing the topology of the Helmholtz energy, Gibbs energy, Grand potential, and Null potential that are associated with different isothermal boundary conditions. By employing Monte Carlo simulations in the NVT, NpT, and μVT ensembles and a molecular-based equation of state, methane, ethane, nitrogen, and methanol are investigated over a broad range of thermodynamic conditions. The predictions from the two independent methods are overall in very good agreement. Although distinct quantitative differences among the fluids are observed, the overall topology of the individual thermodynamic potentials remains unaffected by the molecular architecture, which is in line with the corresponding states principle-as expected. Furthermore, a comparative analysis reveals significant differences between the total potentials and their residual contributions.

Exploring the role of microbial proteins in controlling environmental pollutants based on molecular simulation

Molecular simulation has been widely used to study microbial proteins' structural composition and dynamic properties, such as volatility, flexibility, and stability at the microscopic scale. Herein, this review describes the key elements of molecular docking and molecular dynamics (MD) simulations in molecular simulation; reviews the techniques combined with molecular simulation, such as crystallography, spectroscopy, molecular biology, and machine learning, to validate simulation results and bridge information gaps in the structure, microenvironmental changes, expression mechanisms, and intensity quantification; illustrates the application of molecular simulation, in characterizing the molecular mechanisms of interaction of microbial proteins with four different types of contaminants, namely heavy metals (HMs), pesticides, dyes and emerging contaminants (ECs). Finally, the review outlines the important role of molecular simulations in the study of microbial proteins for controlling environmental contamination and provides ideas for the application of molecular simulation in screening microbial proteins and incorporating targeted mutagenesis to obtain more effective contaminant control proteins.

Numerical Discrimination of Thermodynamic Monte Carlo Simulations in All Eight Statistical Ensembles

Generalized expressions for thermodynamic properties in terms of ensemble averages are discussed for adiabatic and isothermal ensembles. They are implemented in the simulation code ms2 and validated by Monte Carlo simulations for the Lennard-Jones fluid. A comparison of the eight statistical ensembles regarding size scaling behavior, convergence, and stability is provided for state points throughout the homogeneous fluid region. The resulting data are in good agreement but differ in their statistical distributions. In closed systems, the statistical quality of the data is better than in open systems. Overall, the microcanonical ensemble performs best.

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.