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.

A coarse-grain reactive model of RDX: Molecular resolution at the µm scale.

Predictive models for the thermal, chemical, and mechanical response of high explosives at extreme conditions are important for investigating their performance and safety. We introduce a particle-based, reactive model of 1,3,5-trinitro-1,3,5-triazinane (RDX) with molecular resolution utilizing generalized energy-conserving dissipative particle dynamics with reactions. The model is parameterized with respect to the data from atomistic molecular dynamics simulations as well as from quantum mechanical calculations, thus bridging atomic processes to the mesoscales, including microstructures and defects. It accurately captures the response of RDX under a range of thermal loading conditions compared to atomistic simulations. In addition, the Hugoniot response of the CG model in the overdriven regime reasonably matches atomistic simulations and experiments. Exploiting the model's high computational efficiency, we investigate mesoscale systems involving millions of molecules and characterize size-dependent criticality of hotspots in RDX. The combination of accuracy and computational efficiency of our reactive model provides a tool for investigation of mesoscale phenomena, such as the role of microstructures and defects in the shock-to-deflagration transition, through particle-based simulation.

Generalized Energy-Conserving Dissipative Particle Dynamics with Mass Transfer. Part 2: Applications and Demonstrations.

We present the second part of a two-part paper series intended to address a gap in computational capability for coarse-grain particle modeling and simulation, namely, the simulation of phenomena in which diffusion via mass transfer is a contributing mechanism. In part 1, we presented a formulation of a dissipative particle dynamics method to simulate interparticle mass transfer, termed generalized energy-conserving dissipative particle dynamics with mass transfer (GenDPDE-M). In the GenDPDE-M method, the mass of each mesoparticle remains constant following the interparticle mass exchange. In part 2 of this series, further verification and demonstrations of the GenDPDE-M method are presented for mesoparticles with embedded binary mixtures using the ideal gas (IG) and van der Waals (vdW) equation-of-state (EoS). The targeted readership of part 2 is toward practitioners, where applications and practical considerations for implementing the GenDPDE-M method are presented and discussed, including a numerical discretisztion algorithm for the equations-of-motion. The GenDPDE-M method is verified by reproducing the particle distributions predicted by Monte Carlo simulations for the IG and vdW fluids, along with several demonstrations under both equilibrium and non-equilibrium conditions. GenDPDE-M can be generally applied to multi-component mixtures and to other fundamental EoS, such as the Lennard-Jones or Exponential-6 models, as well as to more advanced EoS models such as Statistical Associating Fluid Theory.

Generalized Energy-Conserving Dissipative Particle Dynamics with Mass Transfer. Part 1: Theoretical Foundation and Algorithm.

An extension of the generalized energy-conserving dissipative particle dynamics method (GenDPDE) that allows mass transfer between mesoparticles via a diffusion process is presented. By considering the concept of the mesoparticles as property carriers, the complexity and flexibility of the GenDPDE framework were enhanced to allow for interparticle mass transfer under isoenergetic conditions, notated here as GenDPDE-M. In the formulation, diffusion is described via the theory of mesoscale irreversible processes based on linear relationships between the fluxes and thermodynamic forces, where their fluctuations are described by Langevin-like equations. The mass exchange between mesoparticles is such that the mass of the mesoparticle remains unchanged after the transfer process and requires additional considerations regarding the coupling with other system properties such as the particle internal energy. The proof-of-concept work presented in this article is the first part of a two-part article series. In Part 1, the development of the GenDPDE-M theoretical framework and the derivation of the algorithm are presented in detail. Part 2 of this article series is targeted for practitioners, where applications, demonstrations, and practical considerations for implementing the GenDPDE-M method are presented and discussed.

Generalized Energy-Conserving Dissipative Particle Dynamics with Reactions.

We present an extension of the generalized energy-conserving dissipative particle dynamics method (J. Bonet Avalos, et al., Phys Chem Chem Phys, 2019, 21, 24891-24911) to include chemical reactivity, denoted GenDPDE-RX. GenDPDE-RX provides a means of simulating chemical reactivity at the micro- and mesoscales, while exploiting the attributes of density- and temperature-dependent many-body force fields, which include improved transferability and scalability compared to two-body pairwise models. The GenDPDE-RX formulation considers intra-particle reactivity via a coarse-grain reactor construct. Extent-of-reaction variables assigned to each coarse-grain particle monitor the temporal evolution of the prescribed reaction mechanisms and kinetics assumed to occur within the particle. Descriptions of the algorithm, equations of motion, and numerical discretization are presented, followed by verification of the GenDPDE-RX method through comparison with reaction kinetics theoretical model predictions. Demonstrations of the GenDPDE-RX method are performed using constant-volume adiabatic heating simulations of three different reaction models, including both reversible and irreversible reactions, as well as multistep reaction mechanisms. The selection of the demonstrations is intended to illustrate the flexibility and generality of the method but is inspired by real material systems that span from fluids to solids. Many-body force fields using analytical forms of the ideal gas, Lennard-Jones, and exponential-6 equations of state are used for demonstration, although application to other forms of equation of states is possible. Finally, the flexibility of the GenDPDE-RX framework is addressed with a brief discussion of other possible adaptations and extensions of the method.

Generalized energy-conserving dissipative particle dynamics revisited: Insight from the thermodynamics of the mesoparticle leading to an alternative heat flow model.

Recently we introduced the generalized energy-conserving dissipative particle dynamics method (GenDPDE) [J. Bonet Avalos, M. Lísal, J. P. Larentzos, A. D. Mackie, and J. K. Brennan, Phys. Chem. Chem. Phys. 21, 24891 (2019)]PPCPFQ1463-907610.1039/C9CP04404C, which has been formulated for an emerging class of density- and temperature-dependent coarse-grain models. In the original work, GenDPDE was formulated to ensure a fundamental link is maintained with the underlying physical system at the higher resolution scale. In this paper, we revisit the formulation of the GenDPDE method, and rederive the particle thermodynamics to ensure consistency at the opposing scale extreme, i.e., between the local thermodynamics in the mesoscopic systems and the corresponding macroscopic properties. We demonstrate this consistency by introducing unambiguous, physically meaningful definitions of the heat and work, which lead to the formulation of an alternative heat flow model that is analogous to Fourier's law of heat conduction. We present further analysis of the internal, unresolved degrees-of-freedom of the mesoparticles by considering the thermodynamics of an individual mesoparticle within the GenDPDE framework. Several key outcomes of the analysis include: (i) demonstration that the choice of the independent variables alters the particle thermodynamic description; (ii) demonstration that the mesoscopic thermodynamic transformations introduce additional terms of the order of the size of the local fluctuations, which prevent an unambiguous definition of both the heat and work; (iii) an emphasis on the importance of the choice of the proper estimators of the thermodynamic properties that are embedded in the chosen thermodynamic description; and (iv) a clearly defined path for determining any thermodynamic quantity dressed by the fluctuations. The further insight provided by this deeper analysis is useful for both readers interested in the GenDPDE theoretical framework, as well as readers interested in the practical ramifications of the analysis, namely, the alternative heat flow model.

Heuristics for chemical species identification in dense systems.

A new approach to identify chemical species from molecular dynamics (MD) simulations of reacting materials under extreme temperatures and pressures is presented. The approach is based on bond-distance and vibrational criteria, derived from the examination of atomic behavior during a density functional theory MD simulation of an overdriven shock of the explosive pentaerythritol tetranitrate. For comparison, the trajectory was analyzed using popular bonding criteria commonly used in analysis of reactive MD simulations, including distance, distance-time, and bond-order criteria. Cluster analyses using the new time-dependent bond definition approach presented here and a bond-order approach revealed that species and their corresponding lifetimes were strongly dependent on the chosen approach, indicating significant implications for the development of chemical mechanisms and chemical kinetics models using the results of reactive MD simulations.

Generalised dissipative particle dynamics with energy conservation: density- and temperature-dependent potentials.

We present a generalised, energy-conserving dissipative particle dynamics (DPDE) method appropriate for the non-isothermal simulation of particle interaction force fields that are both density- and temperature-dependent. A detailed derivation is formulated in a bottom-up manner by considering the thermodynamics of small systems with the appropriate consideration of the fluctuations. Connected to the local volume is a local density and corresponding local pressure, which is determined from an equation-of-state based force field that depends also on a particle temperature. Compared to the original DPDE method, the formulation of the generalised DPDE method requires a change in the independent variable from the particle internal energy to the particle entropy. As part of the re-formulation, the terms dressed particle entropy and the corresponding dressed particle temperature are introduced, which depict the many-body contributions in the local volume. The generalised DPDE method has similarities to the energy form of the smoothed dissipative particle dynamics method, yet fundamental differences exist, which are described in the manuscript. The basic dynamic equations are presented along with practical considerations for implementing the generalised DPDE method, including a numerical integration scheme based on the Shardlow-like splitting algorithm. Demonstrations and validation tests are performed using analytical equation-of-states for the van der Waals and Lennard-Jones fluids. Particle probability distributions are analysed, where excellent agreement with theoretical estimates is demonstrated. As further validation of the generalised DPDE method, both equilibrium and non-equilibrium simulation scenarios are considered, including adiabatic flash heating response and vapour-liquid phase separation.

Dissipative particle dynamics with reactions: Application to RDX decomposition.

We present a general, flexible framework for a constant-energy variant of the dissipative particle dynamics method that allows chemical reactions (DPD-RX). In our DPD-RX approach, reaction progress variables are assigned to each particle that monitor the time evolution of an extent-of-reaction associated with the prescribed reaction mechanisms and kinetics assumed to occur within the particle, where chemistry can be modeled using complex or reduced reaction mechanisms. We demonstrate our DPD-RX method by considering thermally initiated unimolecular decomposition of the energetic material, cyclotrimethylene trinitramine (RDX), into a molecular gas mixture. Studies are performed to demonstrate the effect of a spatially averaged particle internal temperature and a local reaction volume term in the chemical kinetics expressions, where both provide implicit mechanisms for capturing condensed phase reactivity. We also present an analysis of the expansion of the product gas mixture during decomposition. Finally, a discussion of other potential applications and extensions of the DPD-RX method is given.

Transferable Reactive Force Fields: Extensions of ReaxFF-lg to Nitromethane.

Transferable ReaxFF-lg models of nitromethane that predict a variety of material properties over a wide range of thermodynamic states are obtained by screening a library of ∼6600 potentials that were previously optimized through the Multiple Objective Evolutionary Strategies (MOES) approach using a training set that included information for other energetic materials composed of carbon, hydrogen, nitrogen, and oxygen. Models that best match experimental nitromethane lattice constants at 4.2 K and 1 atm are evaluated for transferability to high-pressure states at room temperature and are shown to better predict various liquid- and solid-phase structural, thermodynamic, and transport properties as compared to the existing ReaxFF and ReaxFF-lg parametrizations. Although demonstrated for an energetic material, the library of ReaxFF-lg models is supplied to the scientific community to enable new research explorations of complex reactive phenomena in a variety of materials research applications.

Parameterizing complex reactive force fields using multiple objective evolutionary strategies (MOES). Part 1: ReaxFF models for cyclotrimethylene trinitramine (RDX) and 1,1-diamino-2,2-dinitroethene (FOX-7).

ReaxFF (van Duin, A.C.T.; Dasgupta, S.; Lorant, F.; Goddard, W.A. J. Phys. Chem. A, 2001, 105, 9396-9409) reactive potentials are parametrized for cyclotrimethylene trinitramine (RDX) and 1,1-diamino-2,2-dinitroethene (FOX-7) in a novel application combining data envelopment analysis and a modern self-adaptive evolutionary algorithm to optimize multiple objectives simultaneously and map the entire family of solutions. In order to correct the poor crystallographic parameters predicted by ReaxFF using its base parametrization (Strachan, A.; van Duin, A. C. T.; Chakraborty, D.; Dasgupta S.; Goddard, W. A. Phys. Rev. Lett., 2003, 91, 098301), we augmented the existing training set data used for parametrization with additional (SAPT)DFT calculations of RDX and FOX-7 dimer interactions. By adjusting a small subset of the ReaxFF parameters that govern long-range interactions, the evolutionary algorithm approach converges on a family of solutions that best describe crystallographic parameters through simultaneous optimization of the objective functions. Molecular dynamics calculations of RDX and FOX-7 are conducted to assess the quality of the force fields, resulting in parametrizations that improve the overall prediction of the crystal structures.

Parameterizing complex reactive force fields using multiple objective evolutionary strategies (MOES): Part 2: transferability of ReaxFF models to C-H-N-O energetic materials.

The Multiple Objective Evolutionary Strategies (MOES) algorithm was used to parametrize force fields having the form of the reactive models ReaxFF (van Duin, A. C. T.; Dasgupta, S.; Lorant, F.; Goddard, W. A. J. Phys. Chem. A 2001, 105, 9396) and ReaxFF-lg (Liu, L.; Liu, Y.; Zybin, S. V.; Sun, H.; Goddard, W. A. J. Phys. Chem. A 2011, 115, 11016) in an attempt to produce equal or superior ambient state crystallographic structural results for cyclotrimethylene trinitramine (RDX). Promising candidates were then subjected to molecular dynamics simulations of five other well-known conventional energetic materials to assess the degree of transferability of the models. Two models generated through the MOES search were shown to have performance better than or as good as ReaxFF-lg in describing the six energetic systems modeled. This study shows that MOES is an effective and efficient method to develop complex force fields.

Coarse-Grain Model Simulations of Nonequilibrium Dynamics in Heterogeneous Materials.

A suite of computational tools is described for particle-based mesoscale simulations of the nonequilibrium dynamics of energetic solids, including mechanical deformation, phase transitions, and chemical reactivity triggered by shock or thermal loading. The method builds upon our recent advances both in generating coarse-grain models under high strains and in developing a variant of dissipative particle dynamics (DPD) that includes chemical reactions. To describe chemical reactivity, a coarse-grain particle equation-of-state was introduced into the constant-energy DPD variant that rigorously treats complex chemical reactions and the associated chemical energy release. As illustration of these developments, we present simulations of shock compression of an RDX crystal and its thermal decomposition under high temperatures. We also discuss our current efforts toward a highly scalable domain-decomposition implementation that extends applicability to micrometer-size simulations. With appropriate parametrization, the method is applicable to other materials whose dynamic response is driven by microstructural heterogeneities.

Temperature effects on alkaline earth metal ions adsorption on gibbsite: approaches from macroscopic sorption experiments and molecular dynamics simulations.

Two approaches, macroscopic adsorption experiments and molecular dynamics simulations, were employed to study the effect of temperature on alkaline earth metals adsorption on gibbsite surfaces. Increased reaction temperature enhanced the extent of metal ion adsorption for all of the alkaline earth metals studied. Whereas Mg(2+) and Sr(2+) adsorption displayed dependence on ionic strength, Sr(2+) adsorption exhibited less dependence on background ionic strength regardless of temperature. The ionic strength dependence was attributed to outer-sphere complexation reactions. The ionic strength effect on metal ion removal decreased with increasing temperature for both metals. Ba(2+) removal by gibbsite, on the other hand, was not affected by ionic strength. Results from molecular dynamics simulations were in agreement with the findings of the experimental study. The amount of thermal energy required to remove waters of hydration from the metal cation and the ratio of outer-sphere to inner-sphere complexation decreased with increasing ionic radii. It was observed from both macroscopic and molecular approaches that the tendency to form inner-sphere complexes on gibbsite decreased in the order: Ba(2+)>Sr(2+)>Mg(2+) and that the common assumption that alkaline earth metal ions form outer-sphere complexes appears to be dependent on ionic radius and temperature.

Implementation of a Morse potential to model hydroxyl behavior in phyllosilicates.

The accurate molecular simulation of many hydrated chemical systems, including clay minerals and other phyllosilicates and their interfaces with aqueous solutions, requires improved classical force field potentials to better describe structure and vibrational behavior. Classical and ab initio molecular dynamics simulations of the bulk structure of pyrophyllite, talc, and Na-montmorillonite clay phases exhibit dissimilar behavior in the hydroxyl stretch region of power spectra derived from atomic trajectories. The classical simulations, using the CLAYFF force field, include either a standard harmonic potential or a new Morse potential parametrized for both dioctahedral and trioctahedral phases for the O-H bond stretch. Comparisons of classical results with experimental values and with ab initio molecular dynamics simulations indicate improvements in the simulation of hydroxyl orientation relative to the clay octahedral sheet and in the O-H bond stretch in the high frequency region of the power spectrum.

A molecular dynamics study of alkaline earth metal-chloride complexation in aqueous solution.

The relative stability of alkaline earth metals (M2+ = Mg2+, Ca2+, Sr2+, and Ba2+) and their chloride complexes in aqueous solution is examined through molecular dynamics simulations using a flexible SPC water model with an internally consistent set of metal ion force field parameters. For each metal-chloride ion pair in aqueous solution, the free energy profile was calculated via potential of mean force simulations. The simulations provide detailed thermodynamic information regarding the relative stability of the different types of metal-chloride pairs. The free energy profiles indicate that the preference for contact ion pair formation increases with ionic radius and is closely related to the metal hydration free energies. The water residence times within the first hydration shells are in agreement with residence times reported in other computational studies. Calculated association constants suggest an increase in metal-chloride complexation with increasing cation radii that is inconsistent with experimentally observed trends. Possible explanations for this discrepancy are discussed.

Aqueous divalent metal-nitrate interactions: hydration versus ion pairing.

Nitrate aqueous solutions, Mg(NO(3))(2), Ca(NO(3))(2), Sr(NO(3))(2), and Pb(NO(3))(2), are investigated using Raman spectroscopy and free energy profiles from molecular dynamics (MD) simulations. Analysis of the in-plane deformation, symmetric stretch, and asymmetric stretch vibrational modes of the nitrate ions reveal perturbation caused by the metal cations and hydrating water molecules. Results show that Pb(2+) has a strong tendency to form contact ion pairs with nitrate relative to Sr(2+), Ca(2+), and Mg(2+), and contact ion pair formation decreases with decreasing cation size and increasing cation charge density: Pb(2+) > Sr(2+) > Ca(2+) > Mg(2+). In the case of Mg(2+), the Mg(2+)-OH(2) intermolecular modes indicate strong hydration by water molecules and no contact ion pairing with nitrate. Free energy profiles provide evidence for the experimentally observed trend and clarification between solvent-separated, solvent-shared, and contact ion pairs, particularly for Mg(2+) relative to other cations.

Experimental and theoretical methods to investigate extraframework species in a layered material of dodecaniobate anions.

The highly charged dodecaniobate Keggin ions [XNb12O40](-16) (X = Si, Ge) and [XNb12O40](-15) (X = P) serve as building blocks of self-assembled, low-dimensional anionic framework materials. In addition to its high charge, the Keggin ion provides optimal binding geometries that render these materials as attractive metal sorbents and ion exchangers. We describe here the synthesis and single-crystal X-ray structure of K(10-x)[Nb2O2][HxGeNb12O40].11H2O (GeNb12-2d; x = approximately 1-1.5), a phase featuring 2D linkage of [GeNb12O40](-16) Keggin ions interlayered with charge-balancing K(+) cations and water molecules. Thermogravimetry, infrared spectroscopy (IR), 1H MAS NMR, and D2O exchange experiments as well as computational studies were used to describe the location and behavior of these interlayer, extraframework species. To model the basicity of the different types of framework oxygen sites appropriately, atomic-centered partial charges were derived from density functional theory (DFT) calculations to model the electrostatic potential. This model enabled the locations and bonding of K(+) cations associated with the framework, as well as K(+) cations bound predominantly to water in the interlayer space, to be accurately computed via Monte Carlo simulation. The poorest agreement between experimental and simulation results was observed for potassium sites that were associated with disordered portions of the framework, namely, the [Nb2O2](6+) bridge between Keggin ions. Finally, through grand canonical Monte Carlo (GCMC) calculations, saturation water loadings consistent with experimental measurements were computed.

Synthesis, structural characterization, and molecular modeling of dodecaniobate keggin chain materials.

Four new isostructural one-dimensional dodecaniobate Keggin materials, Na12[Ti2O2][TNb12O40] x xH2O and Na10[Nb2O2][TNb12O40] x xH2O with T = (Si or Ge), have been synthesized hydrothermally using a Lindqvist-ion salt, Na7[Nb6O19H] x 15H2O, as the precursor. Their structure, consisting of chains of Keggin ions [TNb12O40]16- linked by [Ti2O2]4+ or [Nb2O2]6+ bridges, was solved ab initio from powder diffraction data. The location of the charge-balancing sodium atoms and the water molecules was further investigated by molecular simulations. These compounds were also characterized by IR and solid-state 1H, 29Si, and 23Na MAS NMR spectroscopies. The structural relationships between these and related phases based on similar Keggin ion building units are discussed.