Three-body dispersion contributions to the thermodynamic properties and effective pair interactions in liquid argon

Insight into the Density-Dependence of Pair Potentials for Predictive Coarse-Grained Models

We investigate the temperature- and density-dependence of effective pair potentials for 1-site coarse-grained (CG) models of two industrial solvents, 1,4-dioxane and tetrahydrofuran. We observe that the calculated pair potentials are much more sensitive to density than to temperature. The generalized-Yvon-Born-Green framework reveals that this striking density-dependence reflects corresponding variations in the many-body correlations that determine the environment-mediated indirect contribution to the pair mean force. Moreover, we demonstrate, perhaps surprisingly, that this density-dependence is not important for accurately modeling the intermolecular structure. Accordingly, we adopt a density-independent interaction potential and transfer the density-dependence of the calculated pair potentials into a configuration-independent volume potential. Furthermore, we develop a single global potential that accurately models the intermolecular structure and pressure-volume equation of state across a very wide range of liquid state points. Consequently, this work provides fundamental insight into the density-dependence of effective pair potentials and also provides a significant step toward developing predictive CG models for efficiently modeling industrial solvents.

Symmetries of many-body systems imply distance-dependent potentials

Considering an interatomic potential U(q), where q=[q_{1},q_{2},⋯,q_{N}]∈R^{3N} is a vector describing positions q_{i}∈R^{3}, it is shown that U can be defined as a function of the interatomic distance variables r_{ij}=|q_{i}-q_{j}| provided the potential U satisfies some symmetry assumptions. Moreover, the potential U can be defined as a function of a proper subset of the distance variables r_{ij}, provided N>5, with the number of distance variables used scaling linearly with the number of atoms N.

Bulk viscosity of gaseous argon from molecular dynamics simulations

The bulk viscosity of dilute argon gas is calculated using molecular dynamics simulations in the temperature range 150-500 K and is found to be proportional to density squared in the investigated range of densities 0.001-1 kg m^{-3}. A comparison of the results obtained using Lennard-Jones and Tang-Toennies models of pair interaction potential reveals that the value of the bulk viscosity coefficient is sensitive to the choice of the pair interaction model. The inclusion of the Axilrod-Teller-Muto three-body interaction in the model does not noticeably affect the values of the bulk viscosity in dilute states, contrary to the previously investigated case of dense fluids.

Melt crystallization mechanism analyzed with dimensional reduction of high-dimensional data representing distribution function geometries

Melt crystallization is essential to many industrial processes, including semiconductor, ice, and food manufacturing. Nevertheless, our understanding of the melt crystallization mechanism remains poor. This is because the molecular-scale structures of melts are difficult to clarify experimentally. Computer simulations, such as molecular dynamics (MD), are often used to investigate melt structures. However, the time evolution of the structural order in a melt during crystallization must be analyzed properly. In this study, dimensional reduction (DR), which is an unsupervised machine learning technique, is used to evaluate the time evolution of structural order. The DR is performed for high-dimensional data representing an atom–atom pair distribution function and the distribution function of the angle formed by three nearest neighboring atoms at each period during crystallization, which are obtained by an MD simulation of a supercooled Lennard–Jones melt. The results indicate that crystallization occurs via the following activation processes: nucleation of a crystal with a distorted structure and reconstruction of the crystal to a more stable structure. The time evolution of the local structures during crystallization is also evaluated with this method. The present method can be applied to studies of the mechanism of crystallization from a disordered system for real materials, even for complicated multicomponent materials.

The Lennard-Jones potential: when (not) to use it

The Lennard-Jones 12-6 potential (LJ) is arguably the most widely used pair potential in molecular simulations. In fact, it is so popular that the question is rarely asked whether it is fit for purpose. In this paper, we argue that, whilst the LJ potential was designed for noble gases such as argon, it is often used for systems where it is not expected to be particularly realistic. Under those circumstances, the disadvantages of the LJ potential become relevant: most important among these is that in simulations the LJ potential is always modified such that it has a finite range. More seriously, there is by now a whole family of different potentials that are all called Lennard-Jones 12-6, and that are all different - and that may have very different macroscopic properties. In this paper, we consider alternatives to the LJ 12-6 potential that could be employed under conditions where the LJ potential is only used as a typical short-ranged potential with attraction. We construct a class of potentials that are, in many respects LJ-like but that are by construction finite ranged, vanishing quadratically at the cut-off distance, and that are designed to be computationally cheap. Below, we present this potential and report numerical data for its thermodynamic and transport properties, for the most important cases (cut-off distance rc = 2σ ("LJ-like") and rc = 1.2σ (a typical "colloidal" potential)).

Compatible observable decompositions for coarse-grained representations of real molecular systems

Coarse-grained (CG) observable expressions, such as pressure or potential energy, are generally different than their fine-grained (FG, e.g., atomistic) counterparts. Recently, we analyzed this so-called "representability problem" in Wagner et al. [J. Chem. Phys. 145, 044108 (2016)]. While the issue of representability was clearly and mathematically stated in that work, it was not made clear how to actually determine CG observable expressions from the underlying FG systems that can only be simulated numerically. In this work, we propose minimization targets for the CG observables of such systems. These CG observables are compatible with each other and with structural observables. Also, these CG observables are systematically improvable since they are variationally minimized. Our methods are local and data efficient because we decompose the observable contributions. Hence, our approaches are called the multiscale compatible observable decomposition (MS-CODE) and the relative entropy compatible observable decomposition (RE-CODE), which reflect two main approaches to the "bottom-up" coarse-graining of real FG systems. The parameterization of these CG observable expressions requires the introduction of new, symmetric basis sets and one-body terms. We apply MS-CODE and RE-CODE to 1-site and 2-site CG models of methanol for the case of pressure, as well as to 1-site methanol and acetonitrile models for potential energy.

Van der Waals Perspective on Coarse-Graining: Progress toward Solving Representability and Transferability Problems

Low-resolution coarse-grained (CG) models provide the necessary efficiency for simulating phenomena that are inaccessible to more detailed models. However, in order to realize their considerable promise, CG models must accurately describe the relevant physical forces and provide useful predictions. By formally integrating out the unnecessary details from an all-atom (AA) model, "bottom-up" approaches can, at least in principle, quantitatively reproduce the structural and thermodynamic properties of the AA model that are observable at the CG resolution. In practice, though, bottom-up approaches only approximate this "exact coarse-graining" procedure. The resulting models typically reproduce the intermolecular structure of AA models at a single thermodynamic state point but often describe other state points less accurately and, moreover, tend to provide a poor description of thermodynamic properties. These two limitations have been coined the "transferability" and "representability" problems, respectively. Perhaps, the simplest and most commonly discussed manifestation of the representability problem regards the tendency of structure-based CG models to dramatically overestimate the pressure. Furthermore, when these models are adjusted to reproduce the pressure, they provide a poor description of the compressibility. More generally, it is sometimes suggested that CG models are fundamentally incapable of reproducing both structural and thermodynamic properties. After all, there is no such thing as a "free lunch"; any significant gain in computational efficiency should come at the cost of significant model limitations. At least in the case of structural and thermodynamic properties, though, we optimistically propose that this may be a false dichotomy. Accordingly, we have recently re-examined the "exact coarse-graining" procedure and investigated the intrinsic consequences of representing an AA model in reduced resolution. These studies clarify the origin and inter-relationship of representability and transferability problems. Both arise as consequences of transferring thermodynamic information from the high resolution configuration space and encoding this information into the many-body potential of mean force (PMF), that is, the potential that emerges from an exact coarse-graining procedure. At least in principle, both representability and transferability problems can be resolved by properly addressing this thermodynamic information. In particular, we have demonstrated that "pressure-matching" provides a practical and rigorous means for addressing the density dependence of the PMF. The resulting bottom-up models accurately reproduce the structure, equilibrium density, compressibility, and pressure equation of state for AA models of molecular liquids. Additionally, we have extended this approach to develop transferable potentials that provide similar accuracy for heptane-toluene mixtures. Moreover, these potentials provide predictive accuracy for modeling concentrations that were not considered in their parametrization. More generally, this work suggests a "van der Waals" perspective on coarse-graining, in which conventional structure-based methods accurately describe the configuration dependence of the PMF, while independent variational principles infer the thermodynamic information that is necessary to resolve representability and transferability problems.

Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. IV. Performance of many-body force fields and tight-binding schemes for the fluid phases of silicon

We extend Expanded Wang-Landau (EWL) simulations beyond classical systems and develop the EWL method for systems modeled with a tight-binding Hamiltonian. We then apply the method to determine the partition function and thus all thermodynamic properties, including the Gibbs free energy and entropy, of the fluid phases of Si. We compare the results from quantum many-body (QMB) tight binding models, which explicitly calculate the overlap between the atomic orbitals of neighboring atoms, to those obtained with classical many-body (CMB) force fields, which allow to recover the tetrahedral organization in condensed phases of Si through, e.g., a repulsive 3-body term that favors the ideal tetrahedral angle. Along the vapor-liquid coexistence, between 3000 K and 6000 K, the densities for the two coexisting phases are found to vary significantly (by 5 orders of magnitude for the vapor and by up to 25% for the liquid) and to provide a stringent test of the models. Transitions from vapor to liquid are predicted to occur for chemical potentials that are 10%-15% higher for CMB models than for QMB models, and a ranking of the force fields is provided by comparing the predictions for the vapor pressure to the experimental data. QMB models also reveal the formation of a gap in the electronic density of states of the coexisting liquid at high temperatures. Subjecting Si to a nanoscopic confinement has a dramatic effect on the phase diagram with, e.g. at 6000 K, a decrease in liquid densities by about 50% for both CMB and QMB models and an increase in vapor densities between 90% (CMB) and 170% (QMB). The results presented here provide a full picture of the impact of the strategy (CMB or QMB) chosen to model many-body effects on the thermodynamic properties of the fluid phases of Si.

Exploring the ability of a multiscale coarse-grained potential to describe the stress-strain response of glassy polystyrene

A new particle-based bottom-up method to develop coarse-grained models of polymers is presented and applied to polystyrene. The multiscale coarse-graining (MS-CG) technique of Izvekov et al. [J. Chem. Phys. 120, 10896 (2004)] is applied to a polymer system to calculate nonbonded interactions. The inverse Boltzmann inversion method was used to parametrize the bonded and bond-angle bending interactions. Molecular dynamics simulations were performed, and the CG model exhibited a significantly lower modulus compared to the atomistic model at low temperature and high strain rate. In an attempt to improve the CG model performance, several other parametrization schemes were used to build other models from this base model. The first of these models included standard frictional forces through use of the constant-temperature dissipative particle dynamics method that improved the modulus, yet was not transferrable to higher temperatures and lower strain rates. Other models were built by increasing the attraction between CG beads through direct manipulation of the nonbonded potential, where an improvement of the stress response was found. For these models, two parametrization protocols that shifted the force to more attractive values were explored. The first protocol involved a uniform shift, while the other protocol shifted the force in a more localized region. The uniformly shifted potential greatly affected the structure of the equilibrium model as compared to the locally shifted potential, yet was more transferrable to different temperatures and strain rates. Further improvements in the coarse-graining protocol to generate models that more satisfactorily capture mechanical properties are suggested.

Many-body effects are essential in a physically motivated CO2 force field

We develop a physically motivated many-body force field for CO(2), incorporating explicit three-body interactions parameterized on the basis of two- and three-body symmetry adapted perturbation theory (SAPT) calculations. The potential is parameterized consistently with, and builds upon, our successful SAPT-based two-body CO(2) model ("Schmidt, Yu, and McDaniel" (SYM) model) [K. Yu, J. G. McDaniel, and J. R. Schmidt, J. Phys Chem B 115, 10054 (2011)]. We demonstrate that three-body interactions are essential to achieve an accurate description of bulk properties, and that previous two-body models have therefore necessarily exploited large error cancellations to achieve satisfactory results. The resulting three-body model exhibits excellent second/third virial coefficients and bulk properties over the phase diagram, yielding a nearly empirical parameter-free model. We show that this explicit three-body model can be converted into a computationally efficient, density/temperature-dependent two-body model that reduces almost exactly to our prior SYM model in the high-density limit.

Representability problems for coarse-grained water potentials

The use of an effective intermolecular potential often involves a compromise between more accurate, complex functional forms and more tractable simple representations. To study this choice in detail, we systematically derive coarse-grained isotropic pair potentials that accurately reproduce the oxygen-oxygen radial distribution function of the TIP4P-Ew water model at state points over density ranges from 0.88 to 1.30 g/cm3 and temperature ranges from 235 to 310 K. Although by construction these effective potentials correctly represent the isothermal compressibility of TIP4P-Ew water, they do not accurately resolve other thermodynamic properties such as the virial pressure, the internal energy, or thermodynamic anomalies. Because at a given state point the pair potential that reproduces the pair structure is unique, we have therefore explicitly demonstrated that it is impossible to simultaneously represent the pair structure and several key equilibrium thermodynamic properties of water with state-point dependent radially symmetric pair potentials. We argue that such representability problems are related to, but different from, more widely acknowledged transferability problems and discuss in detail the implications this has for the modeling of water and other liquids by coarse-grained potentials. Nevertheless, regardless of thermodynamic inconsistencies, the state-point dependent effective potentials for water do generate structural and dynamical anomalies.

Bound-state energies in argon trimers via a variational expansion: The effects from many-body corrections

In this paper we study the bound-state energies and geometries of Ar(3) for J=0, using the distributed Gaussian functions method that provides a configurational description of the different structures contributing to these states. Atom-atom potentials are employed and three-body long-range effects are also included in the computational treatment by adding to the sum of potentials the Axilrod-Teller triple-dipole correction for the whole rotationless energy spectrum. An estimate of the total number of bound states for the Ar trimer is given. With respect to previous calculations, limited to the lower-lying states, our results show slightly larger nonadditive effects and are further able to predict the full range of the bound spectrum. Changes on the geometries of a large part of the vibrationally excited states of Ar(3) when the Axilrod-Teller term is included in the molecular potential are found by the present study.

Depletion interaction in a quasi-two-dimensional colloid assembly

We address several aspects of the character of the depletion interaction in a quasi-two-dimensional (Q2D) colloid system. First, we consider how, given information concerning the pair and triplet correlation functions, the depletion interaction can be efficiently and accurately determined. For this purpose we introduce a method based on the Born-Green equation using the assumption that for the Q2D binary mixtures of interest to us the depletion interaction is accurately represented as a sum of pair potentials. We then verify, by direct calculation, that three-particle contributions to the depletion interaction are negligibly small in the region of thermodynamic state space of interest to us. Second, we develop a representation of the dependence of the depletion interaction in a Q2D colloid system on the thickness of the confining parallel plates. Third, we report the results of extensive simulations of Q2D binary hard-sphere mixtures for a range of cell thickness, large and small particle number densities, and a ratio of sphere diameters q=0.3 .

Nonconformal Interaction Models and Thermodynamics of Polar Fluids

In this work, we develop a simple potential model for polar molecules which represents effectively and accurately the thermodynamics of dilute gases. This potential models dipolar interactions whose nonpolar part is either spherical, as in Stockmayer (SM) molecules, or diatomic, as for 2-center Lennard-Jones molecules (2CLJ). Predictions of the second virial coefficient for SM and polar 2CLJ fluids for various dipole moments and elongations agree very well with results of recent numerical calculations by C. Vega and co-workers (Phys. Chem. Chem Phys. 2002, 4, 3000). The model is used to predict the critical temperature of Stockmayer fluids for variable dipole moment and is applied to HCl as an example of a real polar molecule.

Influence of solvent quality on effective pair potentials between polymers in solution

Solutions of interacting linear polymers are mapped onto a system of "soft" spherical particles interacting via an effective pair potential. This coarse-graining reduces the individual monomer-level description to a problem involving only the center of mass (c.m.) of the polymer coils. The effective pair potentials are derived by inverting the c.m. pair distribution function, generated in Monte Carlo simulations, using the hypernetted chain closure. The method, previously devised for the self-avoiding walk model of polymers in good solvent, is extended to the case of polymers in solvents of variable quality by adding a finite nearest-neighbor monomer-monomer attraction to the previous model and varying the temperature. The resulting effective pair potential is found to depend strongly on temperature and polymer concentration. At low concentration the effective interaction becomes increasingly attractive as the temperature decreases, eventually violating thermodynamic stability criteria. However, as polymer concentration is increased at fixed temperature, the effective interaction reverts to mostly repulsive behavior. These issues help to illustrate some fundamental difficulties encountered when coarse-graining complex systems via effective pair potentials.

Many-body interactions and correlations in coarse-grained descriptions of polymer solutions

We calculate the two-, three-, four-, and five-body (state-independent) effective potentials between the centers of mass (c.m.'s) of self-avoiding walk polymers by Monte Carlo simulations. For full overlap, these coarse-grained n-body interactions oscillate in sign as (-1)(n), and decrease in absolute magnitude with increasing n. We find semiquantitative agreement with a scaling theory, and use this to discuss how the coarse-grained free energy converges when expanded to arbitrary order in the many-body potentials. We also derive effective density dependent two-body potentials that exactly reproduce the pair-correlations between the c.m. of the self avoiding walk polymers. The density dependence of these pair potentials can be largely understood from the effects of the density independent three-body potential. Triplet correlations between the c.m. of the polymers are surprisingly well, but not exactly, described by our coarse-grained effective pair potential picture. In fact, we demonstrate that a pair potential cannot simultaneously reproduce the two- and three-body correlations in a system with many-body interactions. However, the deviations that do occur in our system are very small, and can be explained by the direct influence of three-body potentials.

Analytic dependence of the pressure and energy of an atomic fluid under shear

Nonequilibrium molecular dynamics simulations are reported at different strain rates (gamma;) for a shearing atomic fluid interacting via accurate two- and three-body potentials. We report that the hydrostatic pressure has a strain-rate dependence of gamma;(2), in contrast to the gamma;(3/2) dependence predicted by mode-coupling theory. Our results indicate that the pressure and energy of real fluids may display an analytic dependence on the strain rate. This is in contrast to previous work using either Lennard-Jones or Weeks-Chandler-Anderson potentials that had shown a gamma;(3/2) dependence of pressure and energy.