A pressure-transferable coarse-grained potential for modeling the shock Hugoniot of polyethylene

Accessing the electronic structure of liquid crystalline semiconductors with bottom-up electronic coarse-graining

Understanding the relationship between multiscale morphology and electronic structure is a grand challenge for semiconducting soft materials. Computational studies aimed at characterizing these relationships require the complex integration of quantum-chemical (QC) calculations, all-atom and coarse-grained (CG) molecular dynamics simulations, and back-mapping approaches. However, these methods pose substantial computational challenges that limit their application to the requisite length scales of soft material morphologies. Here, we demonstrate the bottom-up electronic coarse-graining (ECG) of morphology-dependent electronic structure in the liquid-crystal-forming semiconductor, 2-(4-methoxyphenyl)-7-octyl-benzothienobenzothiophene (BTBT). ECG is applied to construct density functional theory (DFT)-accurate valence band Hamiltonians of the isotropic and smectic liquid crystal (LC) phases using only the CG representation of BTBT. By bypassing the atomistic resolution and its prohibitive computational costs, ECG enables the first calculations of the morphology dependence of the electronic structure of charge carriers across LC phases at the ∼20 nm length scale, with robust statistical sampling. Kinetic Monte Carlo (kMC) simulations reveal a strong morphology dependence on zero-field charge mobility among different LC phases as well as the presence of two-molecule charge carriers that act as traps and hinder charge transport. We leverage these results to further evaluate the feasibility of developing mesoscopic, field-based ECG models in future works. The fully CG approach to electronic property predictions in LC semiconductors opens a new computational direction for designing electronic processes in soft materials at their characteristic length scales.

Rigorous Progress in Coarse-Graining

Low-resolution coarse-grained (CG) models provide remarkable computational and conceptual advantages for simulating soft materials. In principle, bottom-up CG models can reproduce all structural and thermodynamic properties of atomically detailed models that can be observed at the resolution of the CG model. This review discusses recent progress in developing theory and computational methods for achieving this promise. We first briefly review variational approaches for parameterizing interaction potentials and their relationship to machine learning methods. We then discuss recent approaches for simultaneously improving both the transferability and thermodynamic properties of bottom-up models by rigorously addressing the density and temperature dependence of these potentials. We also briefly discuss exciting progress in modeling high-resolution observables with low-resolution CG models. More generally, we highlight the essential role of the bottom-up framework not only for fundamentally understanding the limitations of prior CG models but also for developing robust computational methods that resolve these limitations in practice.

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.

Derived Coarse-Grained Potentials for Semicrystalline Polymers with a Blended Multistate Iterative Boltzmann Inversion Method

In this article, we employ the multistate iterative Boltzmann inversion (MS-IBI) method to develop coarse-grained potentials capable of representing molecular structure in both the amorphous and crystalline phases of semicrystalline polymers with improved accuracy while allowing for tunable control over the dynamics governing the α-relaxation process. A unique feature of this method is that the potentials are blended using the product of the target structural distributions, for example, the radial density function, for each phase and a weighting factor. To demonstrate this approach, a family of potentials for polyethylene is developed where the weighting factor of the crystalline phase ranges is varied from zero, incorporating information only from the amorphous phase, to unity, where the model is trained from only the crystalline phase. The most accurate representation of structural distributions was obtained when the crystalline phases is weighted at 50%. However, we show that when the crystalline phase is weighted at 90%, the model more accurately represents dynamics of the α-relaxation process, with realistic predicted values of activation energy and diffusion rates, with relatively minor impact on accuracy in structure.

Local density dependent potentials for an underlying van der Waals equation of state: A simulation and density functional theory analysis

There is an ever increasing use of local density dependent potentials in the mesoscale modeling of complex fluids. Questions remain, though, about the dependence of the thermodynamic and structural properties of such systems on the cutoff distance used to calculate these local densities. These questions are particularly acute when it comes to the stability and structure of the vapor/liquid interface. In this article, we consider local density dependent potentials derived from an underlying van der Waals equation of state. We use simulation and density functional theory to examine how the bulk thermodynamic and interfacial properties vary with the cutoff distance, rc, used to calculate the local densities. We show quantitatively how the simulation results for bulk thermodynamic properties and vapor-liquid equilibrium approach the van der Waals limit as rc increases and demonstrate a scaling law for the radial distribution function in the large rc limit. We show that the vapor-liquid interface is stable with a well-defined surface tension and that the interfacial density profile is oscillatory, except for temperatures close to critical. Finally, we show that in the large rc limit, the interfacial tension is proportional to rc and, therefore, unlike the bulk thermodynamic properties, does not approach a constant value as rc increases. We believe that these results give new insights into the properties of local density dependent potentials, in particular their unusual interfacial behavior, which is relevant for modeling complex fluids in soft matter.

Gaussian representation of coarse-grained interactions of liquids: Theory, parametrization, and transferability

Coarse-grained (CG) interactions determined via bottom-up methodologies can faithfully reproduce the structural correlations observed in fine-grained (atomistic resolution) systems, yet they can suffer from limited extensibility due to complex many-body correlations. As part of an ongoing effort to understand and improve the applicability of bottom-up CG models, we propose an alternative approach to address both accuracy and transferability. Our main idea draws from classical perturbation theory to partition the hard sphere repulsive term from effective CG interactions. We then introduce Gaussian basis functions corresponding to the system's characteristic length by linking these Gaussian sub-interactions to the local particle densities at each coordination shell. The remaining perturbative long-range interaction can be treated as a collective solvation interaction, which we show exhibits a Gaussian form derived from integral equation theories. By applying this numerical parametrization protocol to CG liquid systems, our microscopic theory elucidates the emergence of Gaussian interactions in common phenomenological CG models. To facilitate transferability for these reduced descriptions, we further infer equations of state to determine the sub-interaction parameter as a function of the system variables. The reduced models exhibit excellent transferability across the thermodynamic state points. Furthermore, we propose a new strategy to design the cross-interactions between distinct CG sites in liquid mixtures. This involves combining each Gaussian in the proper radial domain, yielding accurate CG potentials of mean force and structural correlations for multi-component systems. Overall, our findings establish a solid foundation for constructing transferable bottom-up CG models of liquids with enhanced extensibility.

Mechanisms of Shock Dissipation in Semicrystalline Polyethylene

Semicrystalline polymers are lightweight, multiphase materials that exhibit attractive shock dissipation characteristics and have potential applications as protective armor for people and equipment. For shocks of 10 GPa or less, we analyzed various mechanisms for the storage and dissipation of shock wave energy in a realistic, united atom (UA) model of semicrystalline polyethylene. Systems characterized by different levels of crystallinity were simulated using equilibrium molecular dynamics with a Hugoniostat to ensure that the resulting states conform to the Rankine-Hugoniot conditions. To determine the role of structural rearrangements, order parameters and configuration time series were collected during the course of the shock simulations. We conclude that the major mechanisms responsible for the storage and dissipation of shock energy in semicrystalline polyethylene are those associated with plastic deformation and melting of the crystalline domain. For this UA model, plastic deformation occurs primarily through fine crystallographic slip and the formation of kink bands, whose long period decreases with increasing shock pressure.

Enhancing pressure consistency and transferability of structure-based coarse-graining

Coarse-graining, which models molecules with coarse-grained (CG) beads, allows molecular dynamics simulations to be applied to systems with large length and time scales while preserving the essential molecular structure. However, CG models generally have insufficient representability and transferability. A commonly used method to resolve this problem is multi-state iterative Boltzmann inversion (MS-IBI) with pressure correction, which matches both the structural properties and pressures at different thermodynamic states between CG and all-atom (AA) simulations. Nevertheless, this method is usually effective only in a narrow pressure range. In this paper, we propose a modified CG scheme to overcome this limitation. We find that the fundamental reason for this limitation is that CG beads at close distances are ellipsoids rather than isotropically compressed spheres, as described in conventional CG models. Hence, we propose a method to compensate for such differences by slightly modifying the radial distribution functions (RDFs) derived from AA simulations and using the modified RDFs as references for pressure-corrected MS-IBI. We also propose a method to determine the initial non-bonded potential using both the target RDF and pressure. Using n-dodecane as a case study, we demonstrate that the CG model developed using our scheme reproduces the RDFs and pressures over a wide range of pressure states, including three reference low-pressure states and two test high-pressure states. The proposed scheme allows for accurate CG simulations of systems in which pressure or density varies with time and/or position.

Simulating Polymerization by Boltzmann Inversion Force Field Approach and Dynamical Nonequilibrium Reactive Molecular Dynamics

The radical polymerization process of acrylate compounds is, nowadays, numerically investigated using classical force fields and reactive molecular dynamics, with the aim to probe the gel-point transition as a function of the initial radical concentration. In the present paper, the gel-point transition of the 1,6-hexanediol dimethacrylate (HDDMA) is investigated by a coarser force field which grants a reduction in the computational costs, thereby allowing the simulation of larger system sizes and smaller radical concentrations. Hence, the polymerization is investigated using reactive classical molecular dynamics combined with a dynamical approach of the nonequilibrium molecular dynamics (D-NEMD). The network structures in the polymerization process are probed by cluster analysis tools, and the results are critically compared with the similar all-atom system, showing a good agreement.

Bottom-up Coarse-Graining: Principles and Perspectives

Large-scale computational molecular models provide scientists a means to investigate the effect of microscopic details on emergent mesoscopic behavior. Elucidating the relationship between variations on the molecular scale and macroscopic observable properties facilitates an understanding of the molecular interactions driving the properties of real world materials and complex systems (e.g., those found in biology, chemistry, and materials science). As a result, discovering an explicit, systematic connection between microscopic nature and emergent mesoscopic behavior is a fundamental goal for this type of investigation. The molecular forces critical to driving the behavior of complex heterogeneous systems are often unclear. More problematically, simulations of representative model systems are often prohibitively expensive from both spatial and temporal perspectives, impeding straightforward investigations over possible hypotheses characterizing molecular behavior. While the reduction in resolution of a study, such as moving from an atomistic simulation to that of the resolution of large coarse-grained (CG) groups of atoms, can partially ameliorate the cost of individual simulations, the relationship between the proposed microscopic details and this intermediate resolution is nontrivial and presents new obstacles to study. Small portions of these complex systems can be realistically simulated. Alone, these smaller simulations likely do not provide insight into collectively emergent behavior. However, by proposing that the driving forces in both smaller and larger systems (containing many related copies of the smaller system) have an explicit connection, systematic bottom-up CG techniques can be used to transfer CG hypotheses discovered using a smaller scale system to a larger system of primary interest. The proposed connection between different CG systems is prescribed by (i) the CG representation (mapping) and (ii) the functional form and parameters used to represent the CG energetics, which approximate potentials of mean force (PMFs). As a result, the design of CG methods that facilitate a variety of physically relevant representations, approximations, and force fields is critical to moving the frontier of systematic CG forward. Crucially, the proposed connection between the system used for parametrization and the system of interest is orthogonal to the optimization used to approximate the potential of mean force present in all systematic CG methods. The empirical efficacy of machine learning techniques on a variety of tasks provides strong motivation to consider these approaches for approximating the PMF and analyzing these approximations.

Molecular mechanism of ultrasound interaction with a blood brain barrier model

The brain is strictly protected by the blood brain barrier preventing the crossing of therapeutics to treat brain diseases. The high and low intensity focused ultrasound methods have been used to temporarily open the blood brain barrier, facilitating the transport of drugs. The methods are very promising because the opening is transient, localized, and noninvasive. However, the molecular mechanism of the opening is unknown, and this limits the development and application of these methods. With this in mind, we carry out a molecular dynamics simulation study to understand the interaction of ultrasound with the cell membrane and the tight junction. Our minimal blood brain barrier model is composed of two lipid bilayers, mimicking two portions of neighboring cells, connected together by a tight junction formed by a pair of two cis-dimers of the claudin-5 protein. Using an experimental ultrasound frequency of 50 MHz, simulations show that at low intensities, ultrasound does not impact the structure of the cell membranes and tight junction, implying that the direct interaction of ultrasound with the blood brain barrier is not responsible for the experimentally observed opening. At high intensities, the ultrasound pulls the monolayers of individual cell membrane lipid bilayers apart, creating air compartments inside the bilayers. This reduces the free energy barrier for the translocation of drugs across the lipid bilayer and enhances drug permeability. At very high intensities, the two monolayers are largely separated, resulting in cell damage and implying that the blood brain barrier is primarily opened at the experimentally observed damaged areas.

Effectiveness of coarse graining degree and speedup on the dynamic properties of homopolymer

Evaluation of effective coarse graining (CG) degree and reasonable speedup relative to all-atomistic (AA) model was conducted to provide a basis for building appropriate larger-scale model. The reproducibility of atomistic conformation and temperature transferability both act as the analysis criteria to resolve the maximum acceptable CG degree. Taking short- and long time spans into account simultaneously in the estimation of computational speedup, a dynamic scaling factor is accessible in fitting mean squared displacement ratio of CG to AA as an exponential function. Computing loss in parallel running is an indispensable component in acceleration, which was also added in the evaluation. Subsequently, a quantified prediction of CG speedup arises as a multiplication of dynamic scaling factor, computing loss, time step, and the square of reduction in the number of degrees of freedom. Polyethylene oxide was adopted as a reference system to execute the direct Boltzmann inversion and iterative Boltzmann inversion. Bonded and non-bonded potentials were calculated in CG models with 1~4 monomers per bead. The effective CG degree was determined as two at the most with a speedup of four orders magnitude over AA in this study. Determination of effectiveness CG degree and the corresponding speedup prediction provide available tools in larger spatiotemporal-scale calculations.

Gruneisen parameters of bead-spring chains: MD simulation and theory

Molecular Dynamics (MD) simulations were carried out in a microcanonical ensemble to compute the Gruneisen parameter (denoted as γ) of a liquid of bead-spring chains having 10 beads/chain. γ was studied over a wide range of temperatures below and above the glass transition temperature. We found that the Gruneisen parameter varied in the range of 2.1-3.1 and was significantly higher than typically observed experimentally in real polymers. In the glass, a theory was developed for γ using a cell model in which the beads are harmonically bound to their respective cell centers. The resulting Gruneisen parameter is predicted to increase slightly with temperature. Above the glass transition temperature, we employed the generalized Flory dimer equation-of-state and the polymer reference interaction model theory to calculate γ. In these calculations, we found that γ decreased with temperature in the liquid. The theoretical predictions for γ were found to be in good qualitative agreement with our MD simulations, without any adjustable parameters, both above and below T_g. In experiments on real polymers, γ undergoes a sharp discontinuity at the glass transition. By contrast, in our MD simulations, γ varies smoothly over a broad transition region.

Bottom-up coarse-grained models for external fields and interfaces

Bottom-up coarse-grained (CG) models accurately describe the structure of homogeneous systems but sometimes provide limited transferability and a poor description of thermodynamic properties. Consequently, inhomogeneous systems present a severe challenge for bottom-up models. In this work, we examine bottom-up CG models for interfaces and inhomogeneous systems. We first analyze the effect of external fields upon the many-body potential of mean force. We also demonstrate that the multiscale CG (MS-CG) variational principle for modeling the external field corresponds to a generalization of the first Yvon-Born-Green equation. This provides an important connection with liquid state theory, as well as physical insight into the structure of interfaces and the resulting MS-CG models. We then develop and assess MS-CG models for a film of liquid methanol that is adsorbed on an attractive wall and in coexistence with its vapor phase. While pair-additive potentials provide unsatisfactory accuracy and transferability, the inclusion of local-density (LD) potentials dramatically improves the accuracy and transferability of the MS-CG model. The MS-CG model with LD potentials quite accurately describes the wall-liquid interface, the bulk liquid density, and the liquid-vapor interface while simultaneously providing a much improved description of the vapor phase. This model also provides an excellent description of the pair structure and pressure-density equation of state for the bulk liquid. Thus, LD potentials hold considerable promise for transferable bottom-up models that accurately describe the structure and thermodynamic properties of both bulk and interfacial systems.

Temperature and Phase Transferable Bottom-up Coarse-Grained Models

Despite the high fidelity of bottom-up coarse-grained (CG) approaches to recapitulate the structural correlations in atomistic simulations, the general use of bottom-up CG methods is limited because of the nontransferable nature of these CG models under different thermodynamic conditions. Because bottom-up CG potentials usually correspond to configuration-dependent free energies of the system, recent studies have focused on adjusting enthalpic or entropic contributions to account for issues with transferability. However, these approaches can require a manual adjustment of the CG interaction a priori and are usually limited to constant volume ensembles. To overcome these limitations, we construct temperature and phase transferable CG models under constant pressure by developing the ultra-coarse-graining (UCG) methodology in the mean-field limit. In the mean-field ansatz, an embedded semi-global order parameter recapitulates global changes to the system by automatically adjusting the effective CG interactions, thus bridging free energy decompositions with UCG theory. The method presented is designed to faithfully capture structural correlations under different thermodynamic conditions, using a single UCG model. Specifically, we test the applicability of the developed theory in three distinct cases: (1) different temperatures at constant pressure in liquids, (2) different temperatures across thermodynamic phases, and (3) liquid/vapor interfaces. We demonstrate that the systematic construction of both temperature and phase transferable bottom-up CG models is possible using this generalized UCG theory. Based on our findings, this approach significantly extends the transferability and applicability of the bottom-up CG theory and method.

Material Point Method Simulation of the Equation of State of Polymer-Bonded Explosive under Impact Loading at Mesoscale

Mesoscale simulation using the material point method (MPM) was conducted to study the pressure–volume (PV) variations of Octahydro-1,3,5,7-Tetranitro-1,2,3,5-Tetrazocine (HMX)/Estane polymer-bonded explosive (PBX) under impact loading. The PV isotherms and Hugoniot data were calculated for the different porosities and binder volume fractions. The PV isotherms were used to determine the parameters for the Birch– Murnaghan equation of state (EOS) for the PBX. From the EOS, the isothermal bulk modulus (K0) and its pressure derivative (K′0) were calculated. Additionally, the pseudo particle velocity and pseudo shock velocity variations were used to obtain the bulk wave speed c and dimensionless coefficient s for the Mie–Grüneisen EOS. The simulations provide an alternative approach for determining an EOS that is consistent with experimental observations.

Coarse-graining of polyisoprene melts using inverse Monte Carlo and local density potentials

Bottom-up coarse-graining of polymers is commonly performed by matching structural order parameters such as distribution of bond lengths, bending and dihedral angles, and pair distribution functions. In this study, we introduce the distribution of nearest-neighbors as an additional order parameter in the concept of local density potentials. We describe how the inverse-Monte Carlo method provides a framework for forcefield development that is capable of overcoming challenges associated with the parameterization of interaction terms in polymer systems. The technique is applied on polyisoprene melts as a prototype system. We demonstrate that while different forcefields can be developed that perform equally in terms of matching target distributions, the inclusion of nearest-neighbors provides a straightforward route to match both thermodynamic and conformational properties. We find that several temperature state points can also be addressed, provided that the forcefield is refined accordingly. Finally, we examine both the single-particle and the collective dynamics of the coarse-grain models, demonstrating that all forcefields present a similar acceleration relative to the atomistic systems.

Analysis of local density potentials

Low resolution coarse-grained (CG) models are widely adopted for investigating phenomena that cannot be effectively simulated with all-atom (AA) models. Since the development of the many-body dissipative particle dynamics method, CG models have increasingly supplemented conventional pair potentials with one-body potentials of the local density (LD) around each site. These LD potentials appear to significantly extend the transferability of CG models, while also enabling more accurate descriptions of thermodynamic properties, interfacial phenomena, and many-body correlations. In this work, we systematically examine the properties of LD potentials. We first derive and numerically demonstrate a nontrivial transformation of pair and LD potentials that leaves the total forces and equilibrium distribution invariant. Consequently, the pair and LD potentials determined via bottom-up methods are not unique. We then investigate the sensitivity of CG models for glycerol to the weighting function employed for defining the local density. We employ the multiscale coarse-graining (MS-CG) method to simultaneously parameterize both pair and LD potentials. When employing a short-ranged Lucy function that defines the local density from the first solvation shell, the MS-CG model accurately reproduces the pair structure, pressure-density equation of state, and liquid-vapor interfacial profile of the AA model. The accuracy of the model generally decreases as the range of the Lucy function increases further. The MS-CG model provides similar accuracy when a smoothed Heaviside function is employed to define the local density from the first solvation shell. However, the model performs less well when this function acts on either longer or shorter length scales.

Interaction mechanism between the focused ultrasound and lipid membrane at the molecular level

Focused ultrasound (FUS) has a wide range of medical applications. Nowadays, the diagnostic and therapeutic ultrasound procedures are routinely used; effects of ultrasound on biological systems at the molecular level are, however, not fully understood. Experimental results on the interaction of the cell membrane, a simplest but important system component, with ultrasound are controversial. Molecular dynamics (MD) simulations could provide valuable insights, but there is no single study on the mechanism of the FUS induced structural changes in cell membranes. With this in mind, we develop a simple method to include FUS into a standard MD simulation. Adopting the 1,2-dioleoyl-sn-glycero-3-phosphocholine lipid membrane as a representative model described by the MARTINI coarse-grained force field, and using experimental values of the ultrasound frequency and intensity, we show that the heat and bubble cavitation are not the primary direct mechanisms that cause structural changes in the membrane. The spatial pressure gradients between the focused and free regions and between the parallel and perpendicular directions to the membrane are the origin of the mechanism. These gradients force lipids to move out of the focused region, forming a lipid flow along the membrane diagonal. Lipids in the free region move in the opposite direction due to the conservation of the total momentum. These opposite motions create wrinkles along the membrane diagonal at low FUS intensities and tear up the membrane at high FUS intensities. Once the membrane is torn up, it is not easy to reform. The implication of our findings in the FUS-induced drug delivery is discussed in some detail.

Extending the range and physical accuracy of coarse-grained models: Order parameter dependent interactions

Order parameters (i.e., collective variables) are often used to describe the behavior of systems as they capture different features of the free energy surface. Yet, most coarse-grained (CG) models only employ two- or three-body non-bonded interactions between the CG particles. In situations where these interactions are insufficient for the CG model to reproduce the structural distributions of the underlying fine-grained (FG) model, additional interactions must be included. In this paper, we introduce an approach to expand the basis sets available in the multiscale coarse-graining (MS-CG) methodology by including order parameters. Then, we investigate the ability of an additive local order parameter (e.g., density) and an additive global order parameter (i.e., distance from a hard wall) to improve the description of CG models in interfacial systems. Specifically, we study methanol liquid-vapor coexistence, acetonitrile liquid-vapor coexistence, and acetonitrile liquid confined by hard-wall plates, all using single site CG models. We find that the use of order parameters dramatically improves the reproduction of structural properties of interfacial CG systems relative to the FG reference as compared with pairwise CG interactions alone.

Transferable Coarse-Grained Models of Liquid-Liquid Equilibrium Using Local Density Potentials Optimized with the Relative Entropy

Bottom-up coarse-grained (CG) models are now regularly pursued to enable large length and time scale molecular simulations of complex, often macromolecular systems. However, predicting fluid phase equilibria using such models remains fundamentally challenging. A major problem stems from the typically low transferability of CG models beyond the densities and/or compositions at which they are parametrized, which is necessary if they are to describe distinct structural and thermodynamic properties unique to each phase. CG model transferability is compounded by the representation of the inherently multibody coarse interactions using pair potentials that neglect higher order effects. Here, we propose to construct transferable single site CG models of liquid mixtures by supplementing traditional CG pair interactions with local density potentials, which constitute a computationally inexpensive mean-field approach to describe many-body effects, in that site energies are modulated by the local solution environment. To illustrate the approach, we use intra- and interspecies local density potentials to develop CG models of benzene-water solutions that show impressive transferability in structural metrics (pair correlation functions, density profiles) throughout composition space, in contrast to pair-only CG representations. While further refinement may be necessary to represent more complex thermodynamic properties, like the liquid-liquid interfacial tension, the generality and improvement offered by the local density approach are highly encouraging for enabling complex phase equilibrium modeling using CG models.