Calculation of effective interaction potentials from radial distribution functions: A reverse Monte Carlo approach

Exploring the Role of Hydroxy- and Phosphate-Terminated cis-1,4-Polyisoprene Chains in the Formation of Physical Junction Points in Natural Rubber: Insights from Molecular Dynamics Simulations

This study elucidates the pivotal role of terminal structures in cis-1,4-polyisoprene (PI) chains, contributing to the exceptional mechanical properties of Hevea natural rubber (NR). NR's unique networking structure, crucial for crack resistance, elasticity, and strain-induced crystallization, involves two terminal groups, ω and α. The proposed ω terminal structure is dimethyl allyl-(trans-1,4-isoprene)2, and α terminals exist in various forms, including hydroxy, ester, and phosphate groups. Among others, we investigated three types of cis-1,4-PI with different terminal combinations: HPIH (pure PI with H terminal), ωPIα6 (PI with ω and α6 terminals), and ωPIPO4 (PI with ω and PO4 terminals) and revealed significant dynamics variations. Hydrogen bonds between α6 and α6 and PO4 and PO4 residues in ωPIα6 and ωPIPO4 systems induce slower dynamics of hydroxy- and phosphate-terminated PI chains. Associations between α6 and α6 and PO4 and PO4 terminals are markedly stronger than ω and ω, and hydrogen terminals in HPIH and ω PIα6,PO4 systems. Phosphate terminals exhibit a stronger mutual association than hydroxy terminals. Potentials of mean force analysis and cluster-formation-fraction computations reveal stable clusters in ωPIα6 and ωPIPO4 , supporting the formation of polar aggregates (physical junction points). Notably, phosphate terminal groups facilitate large and highly stable phosphate polar aggregates, crucial for the natural networking structure responsible for NR's outstanding mechanical properties compared to synthetic PI rubber. This comprehensive investigation provides valuable insights into the role of terminal groups in cis-1,4-PI melt systems and their profound impact on the mechanical properties of NR.

Development of a bottom-up coarse-grained model for interactions of lipids with TiO 2 nanoparticles

Understanding interactions of inorganic nanoparticles with biomolecules is important in many biotechnology, nanomedicine, and toxicological research, however, the size of typical nanoparticles makes their direct modeling by atomistic simulations unfeasible. Here, we present a bottom-up coarse-graining approach for modeling titanium dioxide (TiO  2 ) nanomaterials in contact with phospholipids that uses the inverse Monte Carlo method to optimize the effective interactions from the structural data obtained in small-scale all-atom simulations of TiO  2 surfaces with lipids in aqueous solution. The resulting coarse-grained models are able to accurately reproduce the structural details of lipid adsorption on different titania surfaces without the use of an explicit solvent, enabling significant computational resource savings and favorable scaling. Our coarse-grained simulations show that small spherical TiO  2 nanoparticles ( r = 2 nm) can only be partially wrapped by a lipid bilayer with phosphoethanolamine headgroups, however, the lipid adsorption increases with the radius of the nanoparticle. The current approach can be used to study the effect of the size and shape of TiO  2 nanoparticles on their interactions with cell membrane lipids, which can be a determining factor in membrane wrapping as well as the recently discovered phenomenon of nanoquarantining, which involves the formation of layered nanomaterial-lipid structures.

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.

A Gauss-Newton method for iterative optimization of memory kernels for generalized Langevin thermostats in coarse-grained molecular dynamics simulations

In molecular dynamics simulations, dynamically consistent coarse-grained (CG) models commonly use stochastic thermostats to model friction and fluctuations that are lost in a CG description. While Markovian, i.e., time-local, formulations of such thermostats allow for an accurate representation of diffusivities/long-time dynamics, a correct description of the dynamics on all time scales generally requires non-Markovian, i.e., non-time-local, thermostats. These thermostats typically take the form of a Generalized Langevin Equation (GLE) determined by a memory kernel. In this work, we use a Markovian embedded formulation of a position-independent GLE thermostat acting independently on each CG degree of freedom. Extracting the memory kernel of this CG model from atomistic reference data requires several approximations. Therefore, this task is best understood as an inverse problem. While our recently proposed approximate Newton scheme allows for the iterative optimization of memory kernels (IOMK), Markovian embedding remained potentially error-prone and computationally expensive. In this work, we present an IOMK-Gauss-Newton scheme (IOMK-GN) based on IOMK that allows for the direct parameterization of a Markovian embedded model.

Reverse Mapping of Coarse Grained Polyglutamine Conformations from PRIME20 Sampling

An inverse coarse-graining protocol is presented for generating and validating atomistic structures of large (bio-) molecules from conformations obtained via a coarse-grained sampling method. Specifically, the protocol is implemented and tested based on the (coarse-grained) PRIME20 protein model (P20/SAMC), and the resulting all-atom conformations are simulated using conventional biomolecular force fields. The phase space sampling at the coarse-grained level is performed with a stochastical approximation Monte Carlo approach. The method is applied to a series of polypeptides, specifically dimers of polyglutamine with varying chain length in aqueous solution. The majority (>70 %) of the conformations obtained from the coarse-grained peptide model can successfully be mapped back to atomistic structures that remain conformationally stable during 10 ns of molecular dynamics simulations. This work can be seen as the first step towards the overarching goal of improving our understanding of protein aggregation phenomena through simulation methods.

Chemically Specific Systematic Coarse-Grained Polymer Model with Both Consistently Structural and Dynamical Properties

The coarse-grained (CG) model serves as a powerful tool for the simulation of polymer systems; its reliability depends on the accurate representation of both structural and dynamical properties. However, strong correlations between structural and dynamical properties on different scales and also a strong memory effect, enforced by chain connectivity between monomers in polymer systems, render developing a chemically specific systematic CG model a formidable task. In this study, we report a systematic CG approach that combines the iterative Boltzmann inversion (IBI) method and the generalized Langevin equation (GLE) dynamics. Structural properties are ensured by using conservative CG potentials derived from the IBI method. To retrieve the correct dynamical properties in the system, we demonstrate that using a combination of a Rouse-type delta function and a time-dependent short-time kernel in the GLE simulation is practically efficient. The former can be used to adjust the long-time diffusion dynamics, and the latter can be reconstructed from an iterative procedure according to the velocity autocorrelation function (ACF) from all-atomistic (AA) simulations. Taking the polystyrene as an example, we show that not only structural properties of radial distribution function, intramolecular bond, and angle distributions can be reproduced but also dynamical properties of mean-square displacement, velocity ACF, and force ACF resulted from our CG model have quantitative agreement with the reference AA model. In addition, reasonable agreements are observed in other collective properties between our GLE-CG model and the AA simulations as well.

Maximum Entropy Theory of Multiscale Coarse-Graining via Matching Thermodynamic Forces: Application to a Molecular Crystal (TATB)

The MSCG/FM (multiscale coarse-graining via force-matching) approach is an efficient supervised machine learning method to develop microscopically informed coarse-grained (CG) models. We present a theory based on the principle of maximum entropy (PME) enveloping the existing MSCG/FM approaches. This theory views the MSCG/FM method as a special case of matching the thermodynamic forces from the extended ensemble described by the set of thermodynamic (relevant) system coordinates. This set may include CG coordinates, the stress tensor, applied external fields, and so forth, and may be characterized by nonequilibrium conditions. Following the presentation of the theory, we discuss the consistent matching of both bonded and nonbonded interactions. The proposed PME formulation is used as a starting point to extend the MSCG/FM method to the constant strain ensemble, which together with the explicit matching of the bonded forces is better suited for coarse-graining anisotropic media at a submolecular resolution. The theory is demonstrated by performing the fine coarse-graining of crystalline 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), a well-known insensitive molecular energetic material, which exhibits highly anisotropic mechanical properties.

Formalizing Coarse-Grained Representations of Anisotropic Interactions at Multimeric Protein Interfaces Using Virtual Sites

Molecular simulations of biomacromolecules that assemble into multimeric complexes remain a challenge due to computationally inaccessible length and time scales. Low-resolution and implicit-solvent coarse-grained modeling approaches using traditional nonbonded interactions (both pairwise and spherically isotropic) have been able to partially address this gap. However, these models may fail to capture the complex anisotropic interactions present at macromolecular interfaces unless higher-order interaction potentials are incorporated at the expense of the computational cost. In this work, we introduce an alternate and systematic approach to represent directional interactions at protein-protein interfaces by using virtual sites restricted to pairwise interactions. We show that virtual site interaction parameters can be optimized within a relative entropy minimization framework by using only information from known statistics between coarse-grained sites. We compare our virtual site models to traditional coarse-grained models using two case studies of multimeric protein assemblies and find that the virtual site models predict pairwise correlations with higher fidelity and, more importantly, assembly behavior that is morphologically consistent with experiments. Our study underscores the importance of anisotropic interaction representations and paves the way for more accurate yet computationally efficient coarse-grained simulations of macromolecular assembly in future research.

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.

Surveying the energy landscape of coarse-grained mappings

Simulations of soft materials often adopt low-resolution coarse-grained (CG) models. However, the CG representation is not unique and its impact upon simulated properties is poorly understood. In this work, we investigate the space of CG representations for ubiquitin, which is a typical globular protein with 72 amino acids. We employ Monte Carlo methods to ergodically sample this space and to characterize its landscape. By adopting the Gaussian network model as an analytically tractable atomistic model for equilibrium fluctuations, we exactly assess the intrinsic quality of each CG representation without introducing any approximations in sampling configurations or in modeling interactions. We focus on two metrics, the spectral quality and the information content, that quantify the extent to which the CG representation preserves low-frequency, large-amplitude motions and configurational information, respectively. The spectral quality and information content are weakly correlated among high-resolution representations but become strongly anticorrelated among low-resolution representations. Representations with maximal spectral quality appear consistent with physical intuition, while low-resolution representations with maximal information content do not. Interestingly, quenching studies indicate that the energy landscape of mapping space is very smooth and highly connected. Moreover, our study suggests a critical resolution below which a "phase transition" qualitatively distinguishes good and bad representations.

Perturbative Expansion in Reciprocal Space: Bridging Microscopic and Mesoscopic Descriptions of Molecular Interactions

Determining the Fourier representation of various molecular interactions is important for constructing density-based field theories from a microscopic point of view, enabling a multiscale bridge between microscopic and mesoscopic descriptions. However, due to the strongly repulsive nature of short-ranged interactions, interparticle interactions cannot be formally defined in Fourier space, which renders coarse-grained (CG) approaches in k-space somewhat ambiguous. In this paper, we address this issue by designing a perturbative expansion of pair interactions in reciprocal space. Our perturbation theory, starting from reciprocal space, elucidates the microscopic origins underlying zeroth-order (long-range attractions) and divergent repulsive interactions from higher order contributions. We propose a systematic framework for constructing a faithful Fourier-space representation of molecular interactions, capturing key structural correlations in various systems, including simple model systems and molecular CG models of liquids. Building upon the Ornstein-Zernike equation, our approach can be combined with appropriate closure relations, and to further improve the closure approximations, we develop a bottom-up parameterization strategy for inferring the bridge function from microscopic statistics. By incorporating the bridge function into the Fourier representation, our findings suggest a systematic, bottom-up approach to performing coarse-graining in reciprocal space, leading to the systematic construction of a bottom-up classical field theory of complex aqueous systems.

Implementation and Validation of an OpenMM Plugin for the Deep Potential Representation of Potential Energy

Machine learning potentials, particularly the deep potential (DP) model, have revolutionized molecular dynamics (MD) simulations, striking a balance between accuracy and computational efficiency. To facilitate the DP model's integration with the popular MD engine OpenMM, we have developed a versatile OpenMM plugin. This plugin supports a range of applications, from conventional MD simulations to alchemical free energy calculations and hybrid DP/MM simulations. Our extensive validation tests encompassed energy conservation in microcanonical ensemble simulations, fidelity in canonical ensemble generation, and the evaluation of the structural, transport, and thermodynamic properties of bulk water. The introduction of this plugin is expected to significantly expand the application scope of DP models within the MD simulation community, representing a major advancement in the field.

Temperature-Transferable Coarse-Grained Models for Volumetric Properties of Poly(lactic Acid)

A new coarse-grained (CG) model, for which each monomer is mapped as one bead at its center of mass, was developed for simulating the volumetric properties of the polylactide (PLA) bulk. The three bonded CG potentials are first parametrized against the strain energies of the dimer, trimer, and tetramer, and the nonbonded CG potentials are then optimized to match the melt densities of the decamer. With the derived CG potentials, molecular dynamics (MD) simulations are found to reproduce thermal expansion and glass transition. By rescaling the dihedral and nonbonded potentials with temperature-independent factors, the glass transition temperature (Tg) is also satisfactorily restored with little modifications on the volumetric expansive coefficients at both rubbery and glassy states. Therefore, the finally optimized CG potentials exhibit excellent temperature transferability, as rationalized by the Simha-Boyer relation. Furthermore, it is confirmed that the dihedral torsions and nonbonded interactions play key roles in glass transition. Also, the simulated bulk moduli and conformational properties in a wide temperature range compare well with the referenced data. The proposed multiscale scheme has great potential in simulating thermo-mechanical properties of PLA and other polymers.

Isotropic active colloids: explicit vs. implicit descriptions of propulsion mechanisms

Modeling the couplings between active particles often neglects the possible many-body effects that control the propulsion mechanism. Accounting for such effects requires the explicit modeling of the molecular details at the origin of activity. Here, we take advantage of a recent two-dimensional model of isotropic active particles whose propulsion originates from the interactions between solute particles in the bath. The colloid catalyzes a chemical reaction in its vicinity, which results in a local phase separation of solute particles, and the density fluctuations of solute particles cause the enhanced diffusion of the colloid. In this paper, we investigate an assembly of such active particles, using (i) an explicit model, where the microscopic dynamics of the solute particles is accounted for; and (ii) an implicit model, whose parameters are inferred from the explicit model at infinite dilution. In the explicit solute model, the long-time diffusion coefficient of the active colloids strongly decreases with density, an effect which is not captured by the derived implicit model. This suggests that classical models, which usually decouple pair interactions from activity, fail to describe collective dynamics in active colloidal systems driven by solute-solute interactions.

CGCompiler: Automated Coarse-Grained Molecule Parametrization via Noise-Resistant Mixed-Variable Optimization

Coarse-grained force fields (CG FFs) such as the Martini model entail a predefined, fixed set of Lennard-Jones parameters (building blocks) to model virtually all possible nonbonded interactions between chemically relevant molecules. Owing to its universality and transferability, the building-block coarse-grained approach has gained tremendous popularity over the past decade. The parametrization of molecules can be highly complex and often involves the selection and fine-tuning of a large number of parameters (e.g., bead types and bond lengths) to optimally match multiple relevant targets simultaneously. The parametrization of a molecule within the building-block CG approach is a mixed-variable optimization problem: the nonbonded interactions are discrete variables, whereas the bonded interactions are continuous variables. Here, we pioneer the utility of mixed-variable particle swarm optimization in automatically parametrizing molecules within the Martini 3 coarse-grained force field by matching both structural (e.g., RDFs) as well as thermodynamic data (phase-transition temperatures). For the sake of demonstration, we parametrize the linker of the lipid sphingomyelin. The important advantage of our approach is that both bonded and nonbonded interactions are simultaneously optimized while conserving the search efficiency of vector guided particle swarm optimization (PSO) methods over other metaheuristic search methods such as genetic algorithms. In addition, we explore noise-mitigation strategies in matching the phase-transition temperatures of lipid membranes, where nucleation and concomitant hysteresis introduce a dominant noise term within the objective function. We propose that noise-resistant mixed-variable PSO methods can both improve and automate parametrization of molecules within building-block CG FFs, such as Martini.

Visualization of Self-Assembly and Hydration of a β-Hairpin through Integrated Small and Wide-Angle Neutron Scattering

Fundamental understanding of the structure and assembly of nanoscale building blocks is crucial for the development of novel biomaterials with defined architectures and function. However, accessing self-consistent structural information across multiple length scales is challenging. This limits opportunities to exploit atomic scale interactions to achieve emergent macroscale properties. In this work we present an integrative small- and wide-angle neutron scattering approach coupled with computational modeling to reveal the multiscale structure of hierarchically self-assembled β hairpins in aqueous solution across 4 orders of magnitude in length scale from 0.1 Å to 300 nm. Our results demonstrate the power of this self-consistent cross-length scale approach and allows us to model both the large-scale self-assembly and small-scale hairpin hydration of the model β hairpin CLN025. Using this combination of techniques, we map the hydrophobic/hydrophilic character of this model self-assembled biomolecular surface with atomic resolution. These results have important implications for the multiscale investigation of aqueous peptides and proteins, for the prediction of ligand binding and molecular associations for drug design, and for understanding the self-assembly of peptides and proteins for functional biomaterials.

Understanding dynamics in coarse-grained models. III. Roles of rotational motion and translation-rotation coupling in coarse-grained dynamics

This paper series aims to establish a complete correspondence between fine-grained (FG) and coarse-grained (CG) dynamics by way of excess entropy scaling (introduced in Paper I). While Paper II successfully captured translational motions in CG systems using a hard sphere mapping, the absence of rotational motions in single-site CG models introduces differences between FG and CG dynamics. In this third paper, our objective is to faithfully recover atomistic diffusion coefficients from CG dynamics by incorporating rotational dynamics. By extracting FG rotational diffusion, we unravel, for the first time reported to our knowledge, a universality in excess entropy scaling between the rotational and translational diffusion. Once the missing rotational dynamics are integrated into the CG translational dynamics, an effective translation-rotation coupling becomes essential. We propose two different approaches for estimating this coupling parameter: the rough hard sphere theory with acentric factor (temperature-independent) or the rough Lennard-Jones model with CG attractions (temperature-dependent). Altogether, we demonstrate that FG diffusion coefficients can be recovered from CG diffusion coefficients by (1) incorporating "entropy-free" rotational diffusion with translation-rotation coupling and (2) recapturing the missing entropy. Our findings shed light on the fundamental relationship between FG and CG dynamics in molecular fluids.

Construction of Coarse-Grained Molecular Dynamics with Many-Body Non-Markovian Memory

We introduce a machine-learning-based coarse-grained molecular dynamics model that faithfully retains the many-body nature of the intermolecular dissipative interactions. Unlike the common empirical coarse-grained models, the present model is constructed based on the Mori-Zwanzig formalism and naturally inherits the heterogeneous state-dependent memory term rather than matching the mean-field metrics such as the velocity autocorrelation function. Numerical results show that preserving the many-body nature of the memory term is crucial for predicting the collective transport and diffusion processes, where empirical forms generally show limitations.

Fast Quasi-Centroid Molecular Dynamics for Water and Ice

We describe how the fast quasi-centroid molecular dynamics (f-QCMD) method can be applied to condensed-phase systems by approximating the quasi-centroid potential of mean force as a sum of inter- and intramolecular corrections to the classical interaction potential. The corrections are found by using a regularized iterative Boltzmann inversion procedure to recover the inter- and intramolecular quasi-centroid distribution functions obtained from a path integral molecular dynamics simulation. The resulting methodology is found to give good agreement with a previously published QCMD dipole absorption spectrum for liquid water and satisfactory agreement for ice. It also gives good agreement with spectra from a recent implementation of CMD that uses a precomputed elevated temperature potential of mean force. Modern centroid molecular dynamics methods, therefore, appear to be reaching a consensus regarding the impact of nuclear quantum effects on the vibrational spectra of water and ice.

Spiers Memorial Lecture: Towards understanding of iontronic systems: electroosmotic flow of monovalent and divalent electrolyte through charged cylindrical nanopores

In many practical applications, ions are the primary charge carrier and must move through either semipermeable membranes or through pores, which mimic ion channels in biological systems. In analogy to electronic devices, the "iontronic" ones use electric fields to induce the charge motion. However, unlike the electrons that move through a conductor, motion of ions is usually associated with simultaneous solvent flow. A study of electroosmotic flow through narrow pores is an outstanding challenge that lies at the interface of non-equilibrium statistical mechanics and fluid dynamics. In this paper, we will review recent works that use dissipative particle dynamics simulations to tackle this difficult problem. We will also present a classical density functional theory (DFT) based on the hypernetted-chain approximation (HNC), which allows us to calculate the velocity of electroosmotic flows inside nanopores containing 1 : 1 or 2 : 1 electrolyte solution. The theoretical results will be compared with simulations. In simulations, the electrostatic interactions are treated using the recently introduced pseudo-1D Ewald summation method. The zeta potentials calculated from the location of the shear plane of a pure solvent are found to agree reasonably well with the Smoluchowski equation. However, the quantitative structure of the fluid velocity profiles deviates significantly from the predictions of the Smoluchowski equation in the case of charged pores with 2 : 1 electrolyte. For low to moderate surface charge densities, the DFT allows us to accurately calculate the electrostatic potential profiles and the zeta potentials inside the nanopores. For pores with 1 : 1 electrolyte, the agreement between theory and simulation is particularly good for large ions, for which steric effects dominate over the ionic electrostatic correlations. The electroosmotic flow is found to depend very strongly on the ionic radii. In the case of pores containing 2 : 1 electrolyte, we observe a reentrant transition in which the electroosmotic flow first reverses and then returns to normal as the surface change density of the pore is increased.

Coarse-Grained Modeling Using Neural Networks Trained on Structural Data

We propose a method of bottom-up coarse-graining, in which interactions within a coarse-grained model are determined by an artificial neural network trained on structural data obtained from multiple atomistic simulations. The method uses ideas of the inverse Monte Carlo approach, relating changes in the neural network weights with changes in average structural properties, such as radial distribution functions. As a proof of concept, we demonstrate the method on a system interacting by a Lennard-Jones potential modeled by a simple linear network and a single-site coarse-grained model of methanol-water solutions. In the latter case, we implement a nonlinear neural network with intermediate layers trained by atomistic simulations carried out at different methanol concentrations. We show that such a network acts as a transferable potential at the coarse-grained resolution for a wide range of methanol concentrations, including those not included in the training set.

Experiments, molecular dynamics simulations, and quantum chemistry calculations on the effect of gemini surfactants' headgroup on the oil-water interfacial tension

The effect of the Gemini surfactant headgroup on the oil-water interfacial tension has yet to be systematically revealed. In this work, anionic Gemini surfactants with different hydrophilic headgroups (carboxylic, sulfuric, and sulfonic) were designed and synthesized. The oil-water interfacial tension was tested. The essential parameters for evaluating the interface characteristics, including the oil-water interfacial layer thickness, the coordination number, and the diffusion coefficient, were calculated employing molecular dynamics simulation. The surface electrostatic potential explained the quantitative mechanism of the hydrophobicity and lipophilicity of three types of Gemini surfactants through quantum chemical calculations. The oil-water interfacial tension difference of the Gemini surfactants was revealed at the electronic level. This paper will provide theoretical guidance for designing Gemini surfactants with a high-efficiency performance to enhance oil recovery.

Role of Terminal Groups of cis-1,4-Polyisoprene Chains in the Formation of Physical Junction Points in Natural Rubber

The terminal structures of cis-1,4-polyisoprene (PI) chains play a vital role in the excellent comprehensive performance of Hevea natural rubber (NR) with properties such as high toughness, tear-resistance, and wet skid resistance. The cis-1,4-polyisoprene chain constituting NR exhibits a distinct composition of terminal groups comprising two distinct types, namely, the ω and α terminal groups. The structures of the ω terminal [dimethyl allyl (DMA)-(trans-1,4-isoprene)2] and six kinds of α end groups of the polymer chain of NR have been explored by utilizing a newly developed 2D NMR method. In the present work, we examine different kinds of PI melt systems, and we choose various combinations of terminal groups: Hydrogen, one DMA unit with two trans isoprene units as ω end groups and ester-terminated isopentene (α1), hydroxy-terminated isopentene (α2), ester-terminated isobutane (α3), hydroxy-terminated isobutane (α4), ester-terminated 1,4-cis-isoprene (α5), and hydroxy-terminated 1,4-cis-isoprene (α6), i.e., HPIH (PI0)-pure PI (Hydrogen terminal), ωPIα1 (PII), ωPIα2 (PIII), ωPIα3 (PIIII), ωPIα4 (PIIV), ωPIα5 (PIV), and ωPIα6 (PIVI). We evaluated dynamic and static properties of PI chains such as the end-to-end vector autocorrelation function (C(t)), its average relaxation time (τ), end-to-end distance (Ree), and radius of gyration (Rg). We also estimated the diffusion coefficients of polyisoprene chains and pair correlation functions [radial distribution functions (RDFs)], potentials of mean force (PMFs) in between end residues, and survival probability (P(τ)) of end groups around the end group by analyzing the equilibrated trajectories of full-atom MD simulations. As per the examination of C(t), rotational relaxation time τ, and RDFs, we discovered that the existence of a strong hydrogen bond in α2-α2, α4-α4, and α6-α6 residues makes the dynamics of hydroxy-terminated polyisoprene chains in ωPIα2,α4,α6 melt systems slower. From the analyses of RDFs and PMFs (W(r)), the association between [α2]-[α2], [α4]-[α4], and [α6]-[α6] terminals in ωPIα2,α4,α6 melt systems is significantly stronger than in [ISO]-[ISO] [Hydrogen terminated 1,4-cis-isoprene:(ISO)] in HPIH and ω-ω, [α1]-[α1], [α3]-[α3], and [α5]-[α5] in ωPIα1,α3,α5 systems. We quantified the fraction of cluster formation of terminal groups of a given size in the seven PI melt systems by employing the criteria of PMFs. It is revealed that no stable cluster exists in the HPIH, ωPIα1, ωPIα3, and ωPIα5 melt systems. Conversely, in the ωPIα2, ωPIα4, and ωPIα6 systems, we perceived stable clusters of [(α2)p] [(α4)p] and [(α6)p] end groups where p (2 ≤ x ≤ 6). These stable clusters validate the presence of physical junction points in between hydroxy-terminated polyisoprene chains through their α2, α4, and α6 terminals. These physical junction points might be crucial for superior properties of NR such as high toughness, crack growth resistance, and strain-induced crystallization.

Phase Transitions of Associative Biomacromolecules

Multivalent proteins and nucleic acids, collectively referred to as multivalent associative biomacromolecules, provide the driving forces for the formation and compositional regulation of biomolecular condensates. Here, we review the key concepts of phase transitions of aqueous solutions of associative biomacromolecules, specifically proteins that include folded domains and intrinsically disordered regions. The phase transitions of these systems come under the rubric of coupled associative and segregative transitions. The concepts underlying these processes are presented, and their relevance to biomolecular condensates is discussed.

Utilizing Machine Learning to Greatly Expand the Range and Accuracy of Bottom-Up Coarse-Grained Models through Virtual Particles

Coarse-grained (CG) models parametrized using atomistic reference data, i.e., "bottom up" CG models, have proven useful in the study of biomolecules and other soft matter. However, the construction of highly accurate, low resolution CG models of biomolecules remains challenging. We demonstrate in this work how virtual particles, CG sites with no atomistic correspondence, can be incorporated into CG models within the context of relative entropy minimization (REM) as latent variables. The methodology presented, variational derivative relative entropy minimization (VD-REM), enables optimization of virtual particle interactions through a gradient descent algorithm aided by machine learning. We apply this methodology to the challenging case of a solvent-free CG model of a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayer and demonstrate that introduction of virtual particles captures solvent-mediated behavior and higher-order correlations which REM alone cannot capture in a more standard CG model based only on the mapping of collections of atoms to the CG sites.

Hierarchical Machine Learning of Low-Resolution Coarse-Grained Free Energy Potentials

A force-matching-based method for supervised machine learning (ML) of coarse-grained (CG) free energy (FE) potentials─known as multiscale coarse-graining via force-matching (MSCG/FM)─is an efficient method to develop microscopically informed CG models that are thermodynamically and statistically equivalent to the reference microscopic models. For low-resolution models, when the coarse-graining is at supramolecular scales, objective-oriented clustering of nonbonded particles is required and the reduced description becomes a function of the clustering algorithm. In the present work, we explore the dependence of the ML of the CG Helmholtz FE potential on the clustering algorithm. We consider coarse-graining based on partitional (k-means, leading to Voronoi diagram) and hierarchical agglomerative (bottom-up) clustering algorithms common in unsupervised ML and develop theory connecting the MSCG/FM learned CG Helmholtz potential and the clustering statistics. By combining the agglomerative clustering and the MSCG/FM learning in a recursive manner, we propose an efficient ML methodology to develop the fine-to-low resolution hierarchies of the CG models. The methodology does not suffer from degrading accuracy or increased computational cost to construct larger hierarchies and as such does not impose an upper size limitation of the CG particles resulting from the extended hierarchies. The utility of the methodology is demonstrated by obtaining the bottom-up agglomerative hierarchy for liquid nitromethane from all-atom molecular dynamics (MD) simulations. For agglomerative hierarchies, we prove the existence of renormalization group transformations that indicate self-similarity and allow for learning the low-resolution MSCG/FM potentials at low computational cost by rescaling and renormalizing the certain finer-resolution members of the hierarchy. The hierarchies of the CG models can be used to carry out simulations under constant-pressure conditions.

Automatic Multiscale Method of Building up a Cross-linked Polymer Reaction System: Bridging SMILES to the Multiscale Molecular Dynamics Simulation

An automatic method is introduced to generate the initial configuration and input file from SMILES for multiscale molecular dynamics (MD) simulation of cross-linked polymer reaction systems. Inputs are a modified version of SMILES of all the components and conditions of coarse-grained (CG) and all-atom (AA) simulations. The overall process comprises the following steps: (1) Modified SMILES inputs of all the components are converted to 3-dimensional coordinates of molecular structures. (2) Molecular structures are mapped to the coarse-grained scale, followed by a CG reaction simulation. (3) CG beads are backmapped to the atomic scale after the CG reaction. (4) An AA productive run is finally performed to analyze volume shrinkage, glass transition, and atomic detail of network structure. The method is applied to two common epoxy resin reactions, that is, the cross-linking process of DGEVA (diglycidyl ether of vanillyl alcohol) and DHAVA (dihydroxyaminopropane of vanillyl alcohol) and that of DGEBA (diglycidyl ether of bisphenol A) and DETA (diethylenetriamine). These components form network structures after the CG cross-linking reaction and are then backmapped to calculate properties in the atomic scale. The result demonstrates that the method can accurately predict volume shrinkage, glass transition, and all-atom structure of cross-linked polymers. The method bridges from SMILES to MD simulation trajectories in an automatic way, which shortens the time of building up cross-linked polymer reaction model and suitable for high-throughput computations.

Predicting surfactant phase behavior with a molecularly informed field theory

HYPOTHESIS

The computational study of surfactants and self-assembly is challenging because 1) models need to reflect chemistry-specific interactions, and 2) self-assembled structures are difficult to equilibrate with conventional molecular dynamics. We propose to overcome these challenges with a multiscale simulation approach where relative entropy minimization transfers chemically-detailed information from all-atom (AA) simulations to coarse-grained (CG) models that can be simulated using field-theoretic methods. Field-theoretic simulations are not limited by intrinsic physical time scales like diffusion and allow for rigorous equilibration via free energy minimization. This approach should enable the study of properties that are difficult to obtain by particle-based simulations.

SIMULATION WORK

We apply this workflow to sodium dodecylsulfate. To ensure chemical fidelity we present an AA force field calibrated against interfacial tension experiments. We generate CG models from AA simulation trajectories and show that particle-based and field-theoretic simulations of the CG model reproduce AA simulations and experimental measurements.

FINDINGS

The workflow captures the complex balance of interactions in a multicomponent system ultimately described by an atomistic model. The resulting CG models can study complex 3D phases like double or alternating gyroids, and reproduce salt effects on properties like aggregation number and shape transitions.

Computational Approaches for Organic Semiconductors: From Chemical and Physical Understanding to Predicting New Materials

While a complete understanding of organic semiconductor (OSC) design principles remains elusive, computational methods─ranging from techniques based in classical and quantum mechanics to more recent data-enabled models─can complement experimental observations and provide deep physicochemical insights into OSC structure-processing-property relationships, offering new capabilities for in silico OSC discovery and design. In this Review, we trace the evolution of these computational methods and their application to OSCs, beginning with early quantum-chemical methods to investigate resonance in benzene and building to recent machine-learning (ML) techniques and their application to ever more sophisticated OSC scientific and engineering challenges. Along the way, we highlight the limitations of the methods and how sophisticated physical and mathematical frameworks have been created to overcome those limitations. We illustrate applications of these methods to a range of specific challenges in OSCs derived from π-conjugated polymers and molecules, including predicting charge-carrier transport, modeling chain conformations and bulk morphology, estimating thermomechanical properties, and describing phonons and thermal transport, to name a few. Through these examples, we demonstrate how advances in computational methods accelerate the deployment of OSCsin wide-ranging technologies, such as organic photovoltaics (OPVs), organic light-emitting diodes (OLEDs), organic thermoelectrics, organic batteries, and organic (bio)sensors. We conclude by providing an outlook for the future development of computational techniques to discover and assess the properties of high-performing OSCs with greater accuracy.

Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamics

Machine-learned coarse-grained (CG) models have the potential for simulating large molecular complexes beyond what is possible with atomistic molecular dynamics. However, training accurate CG models remains a challenge. A widely used methodology for learning bottom-up CG force fields maps forces from all-atom molecular dynamics to the CG representation and matches them with a CG force field on average. We show that there is flexibility in how to map all-atom forces to the CG representation and that the most commonly used mapping methods are statistically inefficient and potentially even incorrect in the presence of constraints in the all-atom simulation. We define an optimization statement for force mappings and demonstrate that substantially improved CG force fields can be learned from the same simulation data when using optimized force maps. The method is demonstrated on the miniproteins chignolin and tryptophan cage and published as open-source code.

SPEADI: Accelerated Analysis of IDP-Ion Interactions from MD-Trajectories

The disordered nature of Intrinsically Disordered Proteins (IDPs) makes their structural ensembles particularly susceptible to changes in chemical environmental conditions, often leading to an alteration of their normal functions. A Radial Distribution Function (RDF) is considered a standard method for characterizing the chemical environment surrounding particles during atomistic simulations, commonly averaged over an entire or part of a trajectory. Given their high structural variability, such averaged information might not be reliable for IDPs. We introduce the Time-Resolved Radial Distribution Function (TRRDF), implemented in our open-source Python package SPEADI, which is able to characterize dynamic environments around IDPs. We use SPEADI to characterize the dynamic distribution of ions around the IDPs Alpha-Synuclein (AS) and Humanin (HN) from Molecular Dynamics (MD) simulations, and some of their selected mutants, showing that local ion-residue interactions play an important role in the structures and behaviors of IDPs.

Integrating Machine Learning in the Coarse-Grained Molecular Simulation of Polymers

Machine learning (ML) is having an increasing impact on the physical sciences, engineering, and technology and its integration into molecular simulation frameworks holds great potential to expand their scope of applicability to complex materials and facilitate fundamental knowledge and reliable property predictions, contributing to the development of efficient materials design routes. The application of ML in materials informatics in general, and polymer informatics in particular, has led to interesting results, however great untapped potential lies in the integration of ML techniques into the multiscale molecular simulation methods for the study of macromolecular systems, specifically in the context of Coarse Grained (CG) simulations. In this Perspective, we aim at presenting the pioneering recent research efforts in this direction and discussing how these new ML-based techniques can contribute to critical aspects of the development of multiscale molecular simulation methods for bulk complex chemical systems, especially polymers. Prerequisites for the implementation of such ML-integrated methods and open challenges that need to be met toward the development of general systematic ML-based coarse graining schemes for polymers are discussed.

Flow-Matching: Efficient Coarse-Graining of Molecular Dynamics without Forces

Coarse-grained (CG) molecular simulations have become a standard tool to study molecular processes on time and length scales inaccessible to all-atom simulations. Parametrizing CG force fields to match all-atom simulations has mainly relied on force-matching or relative entropy minimization, which require many samples from costly simulations with all-atom or CG resolutions, respectively. Here we present flow-matching, a new training method for CG force fields that combines the advantages of both methods by leveraging normalizing flows, a generative deep learning method. Flow-matching first trains a normalizing flow to represent the CG probability density, which is equivalent to minimizing the relative entropy without requiring iterative CG simulations. Subsequently, the flow generates samples and forces according to the learned distribution in order to train the desired CG free energy model via force-matching. Even without requiring forces from the all-atom simulations, flow-matching outperforms classical force-matching by an order of magnitude in terms of data efficiency and produces CG models that can capture the folding and unfolding transitions of small proteins.

Machine learning assisted coarse-grained molecular dynamics modeling of meso-scale interfacial fluids

A hallmark of meso-scale interfacial fluids is the multi-faceted, scale-dependent interfacial energy, which often manifests different characteristics across the molecular and continuum scale. The multi-scale nature imposes a challenge to construct reliable coarse-grained (CG) models, where the CG potential function needs to faithfully encode the many-body interactions arising from the unresolved atomistic interactions and account for the heterogeneous density distributions across the interface. We construct the CG models of both single- and two-component polymeric fluid systems based on the recently developed deep coarse-grained potential [Zhang et al., J. Chem. Phys. 149, 034101 (2018)] scheme, where each polymer molecule is modeled as a CG particle. By only using the training samples of the instantaneous force under the thermal equilibrium state, the constructed CG models can accurately reproduce both the probability density function of the void formation in bulk and the spectrum of the capillary wave across the fluid interface. More importantly, the CG models accurately predict the volume-to-area scaling transition for the apolar solvation energy, illustrating the effectiveness to probe the meso-scale collective behaviors encoded with molecular-level fidelity.

Neural network potentials for chemistry: concepts, applications and prospects

Artificial Neural Networks (NN) are already heavily involved in methods and applications for frequent tasks in the field of computational chemistry such as representation of potential energy surfaces (PES) and spectroscopic predictions. This perspective provides an overview of the foundations of neural network-based full-dimensional potential energy surfaces, their architectures, underlying concepts, their representation and applications to chemical systems. Methods for data generation and training procedures for PES construction are discussed and means for error assessment and refinement through transfer learning are presented. A selection of recent results illustrates the latest improvements regarding accuracy of PES representations and system size limitations in dynamics simulations, but also NN application enabling direct prediction of physical results without dynamics simulations. The aim is to provide an overview for the current state-of-the-art NN approaches in computational chemistry and also to point out the current challenges in enhancing reliability and applicability of NN methods on a larger scale.

Understanding dynamics in coarse-grained models. II. Coarse-grained diffusion modeled using hard sphere theory

The first paper of this series [J. Chem. Phys. 158, 034103 (2023)] demonstrated that excess entropy scaling holds for both fine-grained and corresponding coarse-grained (CG) systems. Despite its universality, a more exact determination of the scaling relationship was not possible due to the semi-empirical nature. In this second paper, an analytical excess entropy scaling relation is derived for bottom-up CG systems. At the single-site CG resolution, effective hard sphere systems are constructed that yield near-identical dynamical properties as the target CG systems by taking advantage of how hard sphere dynamics and excess entropy can be analytically expressed in terms of the liquid packing fraction. Inspired by classical equilibrium perturbation theories and recent advances in constructing hard sphere models for predicting activated dynamics of supercooled liquids, we propose a new approach for understanding the diffusion of molecular liquids in the normal regime using hard sphere reference fluids. The proposed "fluctuation matching" is designed to have the same amplitude of long wavelength density fluctuations (dimensionless compressibility) as the CG system. Utilizing the Enskog theory to derive an expression for hard sphere diffusion coefficients, a bridge between the CG dynamics and excess entropy is then established. The CG diffusion coefficient can be roughly estimated using various equations of the state, and an accurate prediction of accelerated CG dynamics at different temperatures is also possible in advance of running any CG simulation. By introducing another layer of coarsening, these findings provide a more rigorous method to assess excess entropy scaling and understand the accelerated CG dynamics of molecular fluids.

Equilibrium states corresponding to targeted hyperuniform nonequilibrium pair statistics

The Zhang-Torquato conjecture [G. Zhang and S. Torquato, Phys. Rev. E, 2020, 101, 032124.] states that any realizable pair correlation function g₂(r) or structure factor S(k) of a translationally invariant nonequilibrium system can be attained by an equilibrium ensemble involving only (up to) effective two-body interactions. To further test and study this conjecture, we consider two singular nonequilibrium models of recent interest that also have the exotic hyperuniformity property: a 2D "perfect glass" and a 3D critical absorbing-state model. We find that each nonequilibrium target can be achieved accurately by equilibrium states with effective one- and two-body potentials, lending further support to the conjecture. To characterize the structural degeneracy of such a nonequilibrium-equilibrium correspondence, we compute higher-order statistics for both models, as well as those for a hyperuniform 3D uniformly randomized lattice (URL), whose higher-order statistics can be very precisely ascertained. Interestingly, we find that the differences in the higher-order statistics between nonequilibrium and equilibrium systems with matching pair statistics, as measured by the "hole" probability distribution, provide measures of the degree to which a system is out of equilibrium. We show that all three systems studied possess the bounded-hole property and that holes near the maximum hole size in the URL are much rarer than those in the underlying simple cubic lattice. Remarkably, upon quenching, the effective potentials for all three systems possess local energy minima (i.e., inherent structures) with stronger forms of hyperuniformity compared to their target counterparts. Our methods are expected to facilitate the self-assembly of tunable hyperuniform soft-matter systems.

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.

Stability, Speed, and Constraints for Structural Coarse-Graining in VOTCA

Structural coarse-graining involves the inverse problem of deriving pair potentials that reproduce target radial distribution functions. Despite its clear mathematical formulation, there are open questions about the existing methods concerning speed, stability, and physical representability of the resulting potentials. In this work, we make progress on several aspects of iterative methods used to solve the inverse problem. Based on integral equation theory, we derive fast Gauss-Newton schemes applicable to very general systems, including molecules with bonds and mixtures. Our methods are similar to inverse Monte Carlo in terms of convergence speed and have a similar cost per iteration as iterative Boltzmann inversion. We investigate stability problems in our schemes and in the inverse Monte Carlo method and propose modifications to fix them. Furthermore, we establish how the pair potential can be constrained at each iteration to reproduce the pressure, Kirkwood-Buff integral, or the enthalpy of vaporization. We demonstrate the potential of our approach in deriving coarse-grained force fields for nine different solvents and their mixtures. All methods described are implemented in the free and open VOTCA software framework for systematic coarse-graining.

Transferable Force Fields from Experimental Scattering Data with Machine Learning Assisted Structure Refinement

Deriving transferable pair potentials from experimental neutron and X-ray scattering measurements has been a longstanding challenge in condensed matter physics. State-of-the-art scattering analysis techniques estimate real-space microstructure from reciprocal-space total scattering data by refining pair potentials to obtain agreement between simulated and experimental results. Prior attempts to apply these potentials with molecular simulations have revealed inaccurate predictions of thermodynamic fluid properties. In this Letter, a machine learning assisted structure-inversion method applied to neutron scattering patterns of the noble gases (Ne, Ar, Kr, and Xe) is shown to recover transferable pair potentials that accurately reproduce both microstructure and vapor-liquid equilibria from the triple to critical point. Therefore, it is concluded that a single neutron scattering measurement is sufficient to predict macroscopic thermodynamic properties over a wide range of states and provide novel insight into local atomic forces in dense monatomic systems.

Realizability of iso-g2 processes via effective pair interactions

An outstanding problem in statistical mechanics is the determination of whether prescribed functional forms of the pair correlation function g2( r) [or equivalently, structure factor S( k)] at some number density ρ can be achieved by many-body systems in d-dimensional Euclidean space. The Zhang–Torquato conjecture states that any realizable set of pair statistics, whether from a nonequilibrium or equilibrium system, can be achieved by equilibrium systems involving up to two-body interactions. To further test this conjecture, we study the realizability problem of the nonequilibrium iso- g2 process, i.e., the determination of density-dependent effective potentials that yield equilibrium states in which g2 remains invariant for a positive range of densities. Using a precise inverse algorithm that determines effective potentials that match hypothesized functional forms of g2( r) for all r and S( k) for all k, we show that the unit-step function g2, which is the zero-density limit of the hard-sphere potential, is remarkably realizable up to the packing fraction ϕ = 0.49 for d = 1. For d = 2 and 3, it is realizable up to the maximum “terminal” packing fraction ϕ c = 1/2 d, at which the systems are hyperuniform, implying that the explicitly known necessary conditions for realizability are sufficient up through ϕ c. For ϕ near but below ϕ c, the large- r behaviors of the effective potentials are given exactly by the functional forms exp[ − κ( ϕ) r] for d = 1, r−1/2 exp[ − κ( ϕ) r] for d = 2, and r−1 exp[ − κ( ϕ) r] (Yukawa form) for d = 3, where κ−1( ϕ) is a screening length, and for ϕ = ϕ c, the potentials at large r are given by the pure Coulomb forms in the respective dimensions as predicted by Torquato and Stillinger [Phys. Rev. E 68, 041113 (2003)]. We also find that the effective potential for the pair statistics of the 3D “ghost” random sequential addition at the maximum packing fraction ϕ c = 1/8 is much shorter ranged than that for the 3D unit-step function g2 at ϕ c; thus, it does not constrain the realizability of the unit-step function g2. Our inverse methodology yields effective potentials for realizable targets, and, as expected, it does not reach convergence for a target that is known to be non-realizable, despite the fact that it satisfies all known explicit necessary conditions. Our findings demonstrate that exploring the iso- g2 process via our inverse methodology is an effective and robust means to tackle the realizability problem and is expected to facilitate the design of novel nanoparticle systems with density-dependent effective potentials, including exotic hyperuniform states of matter.

The Influence of Carbides on Atomic-Scale Mechanical Properties of Carbon Steel: A Molecular Dynamics Study

Pearlite is an important structure in carbon steel; however, the influence mechanism of carbides in pearlite on its mechanical properties and microstructure evolution has not yet been fully elucidated. In this work, a ferrite-carbide composite model with various carbide types was constructed to investigate the influence of carbide types via a uniaxial compression deformation using classical molecular dynamics simulations. It was found that the carbide type had little effect on the compressive elastic modulus, but a more obvious effect on the yield strain, yield stress, and flow stress. The maximum compressive elastic modulus was in the Fe2C model, with 300.32 GPa, while the minimum was found in the Fe4C model at 285.16 GPa; the error was 5.32%. There were significant differences in the yield stress, yield strain, and flow stress of the ferrite-carbide model according to the stress-strain curve. Secondly, the type of carbide used affected its elastic constant, especially the bulk modulus and Cauchy pressure. The maximum bulk modulus of the Fe4C model was 199.01 GPa, the minimum value of the Fe3C model was 146.03 GPa, and the difference was 52.98 GPa. The Cauchy pressure calculation results were consistent with the yield strain trend. Additionally, the effective elastic moduli of the composite system were used to verify the accuracy of the calculation results of this work. Thirdly, ferrite-carbide interfaces could act as a resource for dislocation emission. The initial stacking fault forms at ferrite-carbide interfaces and expands into ferrite. The dislocation type and segment in the ferrite-carbide model were significantly different due to the type of carbide used.

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.

Precise determination of pair interactions from pair statistics of many-body systems in and out of equilibrium

The determination of the pair potential v(r) that accurately yields an equilibrium state at positive temperature T with a prescribed pair correlation function g_{2}(r) or corresponding structure factor S(k) in d-dimensional Euclidean space R^{d} is an outstanding inverse statistical mechanics problem with far-reaching implications. Recently, Zhang and Torquato [Phys. Rev. E 101, 032124 (2020)2470-004510.1103/PhysRevE.101.032124] conjectured that any realizable g_{2}(r) or S(k) corresponding to a translationally invariant nonequilibrium system can be attained by a classical equilibrium ensemble involving only (up to) effective pair interactions. Testing this conjecture for nonequilibrium systems as well as for nontrivial equilibrium states requires improved inverse methodologies. We have devised an optimization algorithm to precisely determine effective pair potentials that correspond to pair statistics of general translationally invariant disordered many-body equilibrium or nonequilibrium systems at positive temperatures. This methodology utilizes a parameterized family of pointwise basis functions for the potential function whose initial form is informed by small-, intermediate- and large-distance behaviors dictated by statistical-mechanical theory. Subsequently, a nonlinear optimization technique is utilized to minimize an objective function that incorporates both the target pair correlation function g_{2}(r) and structure factor S(k) so that the small intermediate- and large-distance correlations are very accurately captured. To illustrate the versatility and power of our methodology, we accurately determine the effective pair interactions of the following four diverse target systems: (1) Lennard-Jones system in the vicinity of its critical point, (2) liquid under the Dzugutov potential, (3) nonequilibrium random sequential addition packing, and (4) a nonequilibrium hyperuniform "cloaked" uniformly randomized lattice. We found that the optimized pair potentials generate corresponding pair statistics that accurately match their corresponding targets with total L_{2}-norm errors that are an order of magnitude smaller than that of previous methods. The results of our investigation lend further support to the Zhang-Torquato conjecture. Furthermore, our algorithm will enable one to probe systems with identical pair statistics but different higher-body statistics, which will shed light on the well-known degeneracy problem of statistical mechanics.

Modelling Sorption and Transport of Gases in Polymeric Membranes across Different Scales: A Review

Professor Giulio C. Sarti has provided outstanding contributions to the modelling of fluid sorption and transport in polymeric materials, with a special eye on industrial applications such as membrane separation, due to his Chemical Engineering background. He was the co-creator of innovative theories such as the Non-Equilibrium Theory for Glassy Polymers (NET-GP), a flexible tool to estimate the solubility of pure and mixed fluids in a wide range of polymers, and of the Standard Transport Model (STM) for estimating membrane permeability and selectivity. In this review, inspired by his rigorous and original approach to representing membrane fundamentals, we provide an overview of the most significant and up-to-date modeling tools available to estimate the main properties governing polymeric membranes in fluid separation, namely solubility and diffusivity. The paper is not meant to be comprehensive, but it focuses on those contributions that are most relevant or that show the potential to be relevant in the future. We do not restrict our view to the field of macroscopic modelling, which was the main playground of professor Sarti, but also devote our attention to Molecular and Multiscale Hierarchical Modeling. This work proposes a critical evaluation of the different approaches considered, along with their limitations and potentiality.

Carbon Nanodots from an In Silico Perspective

Carbon nanodots (CNDs) are the latest and most shining rising stars among photoluminescent (PL) nanomaterials. These carbon-based surface-passivated nanostructures compete with other related PL materials, including traditional semiconductor quantum dots and organic dyes, with a long list of benefits and emerging applications. Advantages of CNDs include tunable inherent optical properties and high photostability, rich possibilities for surface functionalization and doping, dispersibility, low toxicity, and viable synthesis (top-down and bottom-up) from organic materials. CNDs can be applied to biomedicine including imaging and sensing, drug-delivery, photodynamic therapy, photocatalysis but also to energy harvesting in solar cells and as LEDs. More applications are reported continuously, making this already a research field of its own. Understanding of the properties of CNDs requires one to go to the levels of electrons, atoms, molecules, and nanostructures at different scales using modern molecular modeling and to correlate it tightly with experiments. This review highlights different in silico techniques and studies, from quantum chemistry to the mesoscale, with particular reference to carbon nanodots, carbonaceous nanoparticles whose structural and photophysical properties are not fully elucidated. The role of experimental investigation is also presented. Hereby, we hope to encourage the reader to investigate CNDs and to apply virtual chemistry to obtain further insights needed to customize these amazing systems for novel prospective applications.

Using molecular simulation to understand the skin barrier

Skin's effectiveness as a barrier to permeation of water and other chemicals rests almost entirely in the outermost layer of the epidermis, the stratum corneum (SC), which consists of layers of corneocytes surrounded by highly organized lipid lamellae. As the only continuous path through the SC, transdermal permeation necessarily involves diffusion through these lipid layers. The role of the SC as a protective barrier is supported by its exceptional lipid composition consisting of ceramides (CERs), cholesterol (CHOL), and free fatty acids (FFAs) and the complete absence of phospholipids, which are present in most biological membranes. Molecular simulation, which provides molecular level detail of lipid configurations that can be connected with barrier function, has become a popular tool for studying SC lipid systems. We review this ever-increasing body of literature with the goals of (1) enabling the experimental skin community to understand, interpret and use the information generated from the simulations, (2) providing simulation experts with a solid background in the chemistry of SC lipids including the composition, structure and organization, and barrier function, and (3) presenting a state of the art picture of the field of SC lipid simulations, highlighting the difficulties and best practices for studying these systems, to encourage the generation of robust reproducible studies in the future. This review describes molecular simulation methodology and then critically examines results derived from simulations using atomistic and then coarse-grained models.