On the Estimation of the Free Energy, From a Single Equilibrium Statistical Ensemble, via Particle Reinsertion

Accessible Molecular System Creator: Building Molecular Configurations Based on the Inaccessible Molecular Volume and Accessible Molecular Surface via Static Monte Carlo Sampling

Monte Carlo (MC) stochastic sampling is a powerful tool in classical molecular simulations that directly connects the observable macroscopic properties of matter and the underlying atomistic interactions. This connection operates within the framework of the statistical mechanics proposed by Gibbs. Most MC simulations are "dynamic," creating statistical ensembles of microstates via a Markovian chain, where each microstate in the ensemble depends only on its previous microstate. Herein, we re-examine an alternative form of MC that generates ensemble members through a "static" approach, building molecular systems stepwise. The basic theory for such an approach traces back to Rosenbluth and Rosenbluth, who proposed "static" stepwise sampling of a polymeric chain. It is almost as old as the Metropolis importance sampling approach used in dynamic MC, although the latter has been considerably more popular than the former. Herein, we address the main obstacle in static MC that has hindered the widespread adoption of Rosenbluth-based approaches in atomistic simulations. The obstacle lies in mapping the molecular accessible volume for adding a molecule in a Rosenbluth-like static sampling of atomistic configurations. We demonstrate a breakthrough by leveraging the ability to analytically map the inaccessible molecular volume and the accessible molecular surface owing to interatomically excluded volume interactions. This advance substantially enhances the ability to create molecular samples using a Rosenbluth-like static building process. The proposed approach can be used as a tool for creating initial configurations in MC or molecular dynamics simulations─a field where Rosenbluth-like static building has been applied. Additionally, this approach can be used as the first step in a perturbation scheme that accurately estimates free energy differences by estimating the chemical work related to molecule addition, removal, or reinsertion within the context of free energy perturbation schemes employed in molecular simulations.

Molecular thermodynamics for food science and engineering

We argue that thanks to molecular modeling approaches, many thermodynamic properties required in Food Science and Food Engineering will be calculable within a few hours from first principles in a near future. These new possibilities will enable to bridge via multiscale modeling composition, process and storage effects to reach global optimization, innovative concepts for food or its packaging. An outlook of techniques and a series of examples are given in this perspective. We emphasize solute chemical potentials in polymers, liquids and their mixtures as they cannot be understood and estimated without theory. The presented atomistic and coarse-grained methods offer a natural framework to their conceptualization in polynary systems, entangled or crosslinked homo- or heteropolymers.

Predicting diffusion coefficients of chemicals in and through packaging materials

Most of the physicochemical properties in polymers such as activity and partition coefficients, diffusion coefficients, and their activation with temperature are accessible to direct calculations from first principles. Such predictions are particularly relevant for food packaging as they can be used (1) to demonstrate the compliance or safety of numerous polymer materials and of their constitutive substances (e.g. additives, residues…), when they are used: as containers, coatings, sealants, gaskets, printing inks, etc. (2) or to predict the indirect contamination of food by pollutants (e.g. from recycled polymers, storage ambiance…) (3) or to assess the plasticization of materials in contact by food constituents (e.g. fat matter, aroma…). This review article summarizes the classical and last mechanistic descriptions of diffusion in polymers and discusses the reliability of semi-empirical approaches used for compliance testing both in EU and US. It is concluded that simulation of diffusion in or through polymers is not limited to worst-case assumptions but could also be applied to real cases for risk assessment, designing packaging with low leaching risk or to synthesize plastic additives with low diffusion rates.

Free energy calculations, enhanced by a Gaussian ansatz, for the "chemical work" distribution

The evaluation of the free energy is essential in molecular simulation because it is intimately related with the existence of multiphase equilibrium. Recently, it was demonstrated that it is possible to evaluate the Helmholtz free energy using a single statistical ensemble along an entire isotherm by accounting for the "chemical work" of transforming each molecule, from an interacting one, to an ideal gas. In this work, we show that it is possible to perform such a free energy perturbation over a liquid vapor phase transition. Furthermore, we investigate the link between a general free energy perturbation scheme and the novel nonequilibrium theories of Crook's and Jarzinsky. We find that for finite systems away from the thermodynamic limit the second law of thermodynamics will always be an inequality for isothermal free energy perturbations, resulting always to a dissipated work that may tend to zero only in the thermodynamic limit. The work, the heat, and the entropy produced during a thermodynamic free energy perturbation can be viewed in the context of the Crooks and Jarzinsky formalism, revealing that for a given value of the ensemble average of the "irreversible" work, the minimum entropy production corresponded to a Gaussian distribution for the histogram of the work. We propose the evaluation of the free energy difference in any free energy perturbation based scheme on the average irreversible "chemical work" minus the dissipated work that can be calculated from the variance of the distribution of the logarithm of the work histogram, within the Gaussian approximation. As a consequence, using the Gaussian ansatz for the distribution of the "chemical work," accurate estimates for the chemical potential and the free energy of the system can be performed using much shorter simulations and avoiding the necessity of sampling the computational costly tails of the "chemical work." For a more general free energy perturbation scheme that the Gaussian ansatz may not be valid, the free energy calculation can be expressed in terms of the moment generating function of the "chemical work" distribution.

Multidimensional direct free energy perturbation

In this work we propose a multidimensional free energy perturbation scheme that allows the evaluation of the free energy difference between a state sampled based on importance sampling and almost any state that can be constructed by the reduction of the number of molecules in the system and the change of either the interaction energy or the thermodynamic state variable (e.g., the temperature) of the system. We show that via this approach it is possible to evaluate any thermodynamic property included but not limited to free energy, chemical potential, and pressure, along a series of isotherms from a single molecular simulation.