Grand Canonical Monte Carlo Simulations Guided by an Analytic Equation of State—Transferable Anisotropic Mie Potentials for Ethers

TAMie Force Field for Alkanethiols: Multifidelity Gaussian Processes for Dealing with Scarce Experimental Data

This study extends the transferable anisotropic Mie potential (TAMie) to alkanethiols. The force field parameters are optimized by using an analytic equation of state as a surrogate model. Given the lack of experimental density data at elevated temperatures where Monte Carlo simulations have high statistical precision, the equation of state is supplemented by a linear multifidelity Gaussian process approach to bridge the temperature gap. Force field parameters are adjusted by minimizing squared deviations of calculated vapor pressures and liquid densities from experimental data of 1-propanethiol, 1-butanethiol and 1-pentanethiol leading to small mean absolute relative deviations in liquid densities and vapor pressures. The force field is transferable to higher 1-thiols, as shown for 1-hexanethiol and 1-octanethiol. Individual parameter sets are provided for methanethiol and ethanethiol. The shear viscosity of pure substances is predicted in fair agreement with experimental data, considering that it is not included in the parametrization. Further, the phase behavior of binary mixtures of alkanethiols with alkanes is studied, and predictions of the TAMie model are found in excellent agreement with experimental data.

Transferable Anisotropic Mie Potential Force Field for Alkanediols

The development of force fields for polyfunctional molecules, such as alkanediols, requires a careful account of different average intramolecular conformations for gas states compared to dense liquid states, where intra- and intermolecular hydrogen bonds compete. In the present work, the transferable anisotropic Mie (TAMie) potential is extended to 1,n-alkanediols. Using the convention that intramolecular nonbonded interactions up to and including the third neighbor are excluded, all force field parameters developed previously for 1-alcohols were transferred to 1,5-pentanediol and beyond, with good agreement with experimental phase equilibrium data. To obtain trans-gauche ratios of 1,2-ethanediol and 1,3-propanediol that are consistent with experimental results, the propensities for intra- and intermolecular hydrogen bonds had to be balanced. This was achieved by parameterizing the intramolecular dihedral energy functions governing the O-C-C-O and O-C-C-C angles while intramolecular charge-charge interactions were active. All partial charges belonging to a functional group are collected in a charge group and all interactions among two charge groups are evaluated even if they are separated by less than three bonds. With this approach, it is possible to apply the nonbonded parameters from 1-alcohols to alkanediols without further refinement. The agreement with experimental phase equilibrium and shear viscosity data is of similar quality as for the 1-alcohols and the trans-gauche ratio agrees with literature results from spectroscopic measurements and ab initio calculations.

Extension of the MolMod Database to Transferable Force Fields

MolMod, a web-based database for classical force fields for molecular simulations of fluids [Mol. Sim. 45, 10 (2019), 806-814], was extended to transferable force fields. Eight transferable force fields, including all-atom and united-atom type force fields, were implemented in the MolMod database: OPLS-UA, OPLS-AA, COMPASS, CHARMM, GROMOS, TraPPE, Potoff, and TAMie. These transferable force fields cover a large variety of chemical substance classes. The system is designed such that new transferable force fields can be readily integrated. A graphical user interface was implemented that enables the construction of molecules. The MolMod database compiles the force field for the specified component and force field type and provides the corresponding data and meta data as well as ready-to-use input files for the molecule for different simulation engines. This helps the user to flexibly choose molecular models and integrate them swiftly in their individual workflows, reducing risks of input errors in molecular simulations.

Comparison of the United- and All-Atom Representations of (Halo)alkanes Based on Two Condensed-Phase Force Fields Optimized against the Same Experimental Data Set

The level of accuracy that can be achieved by a force field is influenced by choices made in the interaction-function representation and in the relevant simulation parameters. These choices, referred to here as functional-form variants (FFVs), include for example the model resolution, the charge-derivation procedure, the van der Waals combination rules, the cutoff distance, and the treatment of the long-range interactions. Ideally, assessing the effect of a given FFV on the intrinsic accuracy of the force-field representation requires that only the specific FFV is changed and that this change is performed at an optimal level of parametrization, a requirement that may prove extremely challenging to achieve in practice. Here, we present a first attempt at such a comparison for one specific FFV, namely the choice of a united-atom (UA) versus an all-atom (AA) resolution in a force field for saturated acyclic (halo)alkanes. Two force-field versions (UA vs AA) are optimized in an automated way using the CombiFF approach against 961 experimental values for the pure-liquid densities ρ_liq and vaporization enthalpies ΔH_vap of 591 compounds. For the AA force field, the torsional and third-neighbor Lennard-Jones parameters are also refined based on quantum-mechanical rotational-energy profiles. The comparison between the UA and AA resolutions is also extended to properties that have not been included as parameterization targets, namely the surface-tension coefficient γ, the isothermal compressibility κ_T, the isobaric thermal-expansion coefficient α_P, the isobaric heat capacity c_P, the static relative dielectric permittivity ϵ, the self-diffusion coefficient D, the shear viscosity η, the hydration free energy ΔG_wat, and the free energy of solvation ΔG_che in cyclohexane. For the target properties ρ_liq and ΔH_vap, the UA and AA resolutions reach very similar levels of accuracy after optimization. For the nine other properties, the AA representation leads to more accurate results in terms of η; comparably accurate results in terms of γ, κ_T, α_P, ϵ, D, and ΔG_che; and less accurate results in terms of c_P and ΔG_wat. This work also represents a first step toward the calibration of a GROMOS-compatible force field at the AA resolution.

Perturbation theories for fluids with short-ranged attractive forces: A case study of the Lennard-Jones spline fluid

It is generally not straightforward to apply molecular-thermodynamic theories to fluids with short-ranged attractive forces between their constituent molecules (or particles). This especially applies to perturbation theories, which, for short-ranged attractive fluids, typically must be extended to high order or may not converge at all. Here, we show that a recent first-order perturbation theory, the uv-theory, holds promise for describing such fluids. As a case study, we apply the uv-theory to a fluid with pair interactions defined by the Lennard-Jones spline potential, which is a short-ranged version of the LJ potential that is known to provide a challenge for equation-of-state development. The results of the uv-theory are compared to those of third-order Barker–Henderson and fourth-order Weeks–Chandler–Andersen perturbation theories, which are implemented using Monte Carlo simulation results for the respective perturbation terms. Theoretical predictions are compared to an extensive dataset of molecular simulation results from this (and previous) work, including vapor–liquid equilibria, first- and second-order derivative properties, the critical region, and metastable states. The uv-theory proves superior for all properties examined. An especially accurate description of metastable vapor and liquid states is obtained, which might prove valuable for future applications of the equation-of-state model to inhomogeneous phases or nucleation processes. Although the uv-theory is analytic, it accurately describes molecular simulation results for both the critical point and the binodal up to at least 99% of the critical temperature. This suggests that the difficulties typically encountered in describing the vapor–liquid critical region are only to a small extent caused by non-analyticity.

Accurate thermodynamics of simple fluids and chain fluids based on first-order perturbation theory and second virial coefficients: uv-theory

We develop a simplification of our recently proposed uf-theory for describing the thermodynamics of simple fluids and fluids comprising short chain molecules. In its original form, the uf-theory interpolates the Helmholtz energy between a first-order f-expansion and first-order u-expansion as (effective) lower and upper bounds. We here replace the f-bound by a new, tighter (effective) lower bound. The resulting equation of state interpolates between a first-order u-expansion at high densities and another first-order u-expansion that is modified to recover the exact second virial coefficient at low densities. The theory merely requires the Helmholtz energy of the reference fluid, the first-order u-perturbation term, and the total perturbation contribution to the second virial coefficient as input. The revised theory-referred to as uv-theory-is thus simpler than the uf-theory but leads to similar accuracy, as we show for fluids with intermolecular pair interactions governed by a Mie potential. The uv-theory is thereby easier to extend to fluid mixtures and provides more flexibility in extending the model to non-spherical or chain-like molecules. The usefulness of the uv-theory for developing equation-of-state models of non-spherical molecules is here exemplified by developing an equation of state for Lennard-Jones dimers.

Algebraic second virial coefficient of the Mie m - 6 intermolecular potential based on perturbation theory

We propose several simple algebraic approximations for the second virial coefficient of fluids whose molecules interact by a generic Mie m - 6 intermolecular pair potential. In line with a perturbation theory, the parametric equations are formulated as the sum of a contribution due to a reference part of the intermolecular potential and a perturbation. Thereby, the equations provide a convenient (low-density) starting point for developing equation-of-state models of fluids or for developing similar approximations for the virial coefficient of (polymeric-)chain fluids. The choice of Barker and Henderson [J. Chem. Phys. 47, 4714 (1967)] and Weeks, Chandler, and Andersen [Phys. Rev. Lett. 25, 149 (1970); J. Chem. Phys. 54, 5237 (1971); and Phys. Rev. A 4, 1597 (1971)] for the reference part of the potential is considered. Our analytic approximations correctly recover the virial coefficient of the inverse-power potential of exponent m in the high-temperature limit and provide accurate estimates of the temperatures for which the virial coefficient equals zero or takes on its maximum value. Our description of the reference contribution to the second virial coefficient follows from an exact mapping onto the second virial coefficient of hard spheres; we propose a simple algebraic equation for the corresponding effective diameter of the hard spheres, which correctly recovers the low- and high-temperature scaling and limits of the reference fluid's second virial coefficient.

Accurate first-order perturbation theory for fluids: uf-theory

We propose a new first-order perturbation theory that provides a near-quantitative description of the thermodynamics of simple fluids. The theory is based on the ansatz that the Helmholtz free energy is bounded below by a first-order Mayer-f expansion. Together with the rigorous upper bound provided by a first-order u-expansion, this brackets the actual free energy between an upper and (effective) lower bound that can both be calculated based on first-order perturbation theory. This is of great practical use. Here, the two bounds are combined into an interpolation scheme for the free energy. The scheme exploits the fact that a first-order Mayer-f perturbation theory is exact in the low-density limit, whereas the accuracy of a first-order u-expansion grows when density increases. This allows an interpolation between the lower "f"-bound at low densities and the upper "u" bound at higher liquid-like densities. The resulting theory is particularly well behaved. Using a density-dependent interpolating function of only two adjustable parameters, we obtain a very accurate representation of the full fluid-phase behavior of a Lennard-Jones fluid. The interpolating function is transferable to other intermolecular potential types, which is here shown for the Mie m-6 family of fluids. The extension to mixtures is simple and accurate without requiring any dependence of the interpolating function on the composition of the mixture.

Prediction of Adsorption Isotherms and Selectivities: Comparison between Classical Density Functional Theory Based on the Perturbed-Chain Statistical Associating Fluid Theory Equation of State and Ideal Adsorbed Solution Theory

This study gives an assessment of the predictive capability of classical density functional theory (DFT) for adsorption processes of pure substances and mixtures of spherical and nonspherical molecular species. A Helmholtz energy functional based on the perturbed-chain statistical associating fluid theory (PC-SAFT) is applied to calculate isotherms and selectivities of multicomponent adsorption. In order to unambiguously assess the accuracy of the DFT model, we conduct molecular simulations. Monte Carlo (MC) simulations are performed in the grand canonical ensemble using the transition matrix. Two types of systems are studied: a model system, where fluid-fluid and solid-fluid interactions are defined as (single-site) Lennard-Jones interactions, and a more realistic methane-n-butane mixture in a graphite-like pore. Differences between a slit-shaped and a cylindrical pore geometry are examined for the model system. Adsorption isotherms and selectivities obtained from DFT calculations and MC simulations are found in very good agreement, particularly at high pressures. Capillary condensation observed along adsorption isotherms containing n-butane was accurately predicted, both, in equilibrium pressure and in density-increase. Comparisons with results from the ideal adsorbed solution theory are presented, confirming powerful predictions of the DFT approach.

Molecular simulation as a computational pharmaceutics tool to predict drug solubility, solubilization processes and partitioning

In this review we will discuss how computational methods, and in particular classical molecular dynamics simulations, can be used to calculate solubility of pharmaceutically relevant molecules and systems. To the extent possible, we focus on the non-technical details of these calculations, and try to show also the added value of a more thorough and detailed understanding of the solubilization process obtained by using computational simulations. Although the main focus is on classical molecular dynamics simulations, we also provide the reader with some insights into other computational techniques, such as the COSMO-method, and also discuss Flory-Huggins theory and solubility parameters. We hope that this review will serve as a valuable starting point for any pharmaceutical researcher, who has not yet fully explored the possibilities offered by computational approaches to solubility calculations.

A Modified Shifted Force Approach to the Wolf Summation

The Wolf method for calculation of electrostatic interactions in molecular simulations is known to describe the energy well, whereas the forces have discontinuities. For a more reliable description of the forces this method can be extended with a shifted force approach. This leads to a good description of the forces and precise molecular dynamics simulation, but the description of the energy becomes poorer. In this study we propose a modification of a shifted force extension to describe the energy as well as the forces in better agreement to reference data as determined from the Ewald summation. We show that vapor-liquid phase equilibria (VLE) calculated with Monte Carlo simulations in the grand canonical ensemble and dynamic properties calculated with molecular dynamics simulations can be calculated reliably using this modification to describe the electrostatic interactions.