Direct Molecular Simulations Research Articles

Characteristic Vibrational and Rotational Relaxation Times for Air Species from First-Principles Calculations

We present molecular-scale computational rotational-vibrational relaxation studies for N2, O2, and NO. Characteristic relaxation times for diatom-diatom and diatom-atom interactions are calculated using direct molecular simulation (DMS), with ab initio potential energy surfaces (PESs) as the sole model input. Below approximately 8000 K our N2−N2, O2−O2, and O2−N2 vibrational relaxation times agree well with the Millikan–White (M&W) correlation, but gradually diverge at higher temperatures. Park’s high-temperature correction produces a relatively steeper temperature rise compared to our estimates. DMS further shows that, with increasing temperature, the gap between vibrational and rotational relaxation times shrinks for all species. At T>30,000K their magnitudes become comparable and a clear distinction between both energy modes becomes meaningless. For other interactions, our DMS results differ substantially from the M&W correlation, both in magnitude and temperature dependence. Our predicted N2−O2 vibrational relaxation times are noticeably shorter due to vibration-vibration transfer. For O2−O we observe minimal temperature dependence. Our O2−N and N2−N predictions follow the M&W temperature trend at values roughly one order of magnitude smaller. For NO−NO, N2−O, NO−N, and NO−O we generate partial data due to currently incomplete PES sets. These first-principles-derived relaxation times are useful for informing relaxation models in gas-kinetic and fluid-dynamics simulations of high-enthalpy flows.

High-Temperature Nonequilibrium Air Chemistry from First Principles

We present first-principles calculations for chemically reacting five-species air (N2, N, O2, O, NO) over a range of gas temperatures (T=5000–30,000 K), relying exclusively on ab initio potential energy surfaces (PESs) from the University of Minnesota Computational Chemistry group to describe the forces between atoms. We use these PESs within direct molecular simulations (DMSs) and quasi-classical trajectory (QCT) calculations to determine the coupling of internal energy relaxation to chemical reactions. From DMS we extract the internal energy populations of diatomic species during the quasi-steady-state (QSS) dissociation phase and, for all diatomic species, observe depleted high-energy tails relative to corresponding Boltzmann distributions. A comparison of thermochemical equilibrium rate coefficients (from QCT) with those during QSS (from DMS) helps quantify the macroscopic effects of vibrationally depleted distributions on dissociation. In contrast, Zeldovich exchange reactions are almost unaffected by these vibrationally depleted distributions. Unlike dissociation, they do not exhibit significant vibrational bias and take place at near-thermal rates at all temperatures studied. Furthermore, we quantify the amount of vibrational and rotational energy removed and/or gained in exchange and dissociation reactions. Such macroscopic quantities are of interest for enhancing the fidelity of multitemperature nonequilibrium chemistry models used in computational fluid dynamics codes.

First principles simulation of reacting hypersonic flow over a blunt wedge

This article presents molecular-level analysis of a reactive, near-continuum, Mach 21 nitrogen flow over a blunt wedge using the direct molecular simulation (DMS) method. The flow conditions lead to internal energy excitation and dissociation in the flow field, resulting in thermal and chemical nonequilibrium in the flow. Thermal nonequilibrium in the vibrational mode is observed to extend to the molecular level, where the vibrational energy distributions at various points in the flow field are observed to be non-Boltzmann. Furthermore, this is the first reactive DMS calculation where the wall is assumed to be isothermal and full momentum accommodation of the particles is enforced, hence incorporating viscous wall effects. Since the DMS method uses a quantum mechanically generated interaction potential as its only modeling input, all thermochemical and transport properties of the flow field can directly be attributed to the ab initio potential energy surface. Using the DMS solution as a benchmark, this article assesses the performance of Navier–Stokes computational fluid dynamics solutions using lower fidelity two-temperature models. Two models are chosen as points of comparison: the well-known Park two-temperature model and the recently developed modified Marrone and Treanor model.

Near-continuum, hypersonic oxygen flow over a double cone simulated by direct simulation Monte Carlo informed from quantum chemistry

A large-scale, fully resolved direct simulation Monte Carlo (DSMC) computation of a non-equilibrium, reactive flow of pure oxygen over a double cone is presented. Under the simulated near-continuum conditions, the computational demands are shown to be significant because of the wide range of length scales that must be resolved. Therefore, robust grid adaption capabilities and efficient parallelization of the Stochastic PArallel Rarefied-gas Time-accurate Analyzer (SPARTA) code that is utilized in this work are essential. The thermochemical and transport collision models were selected for efficiency and simplicity. First-principles data, obtained from the highly accurate direct molecular simulation method, were used to inform the collision models’ parameters. Importantly, because SPARTA implements molecular collision models using collision-specific energies, the resulting macroscopic relaxation rates were evaluateda posteriorivia zero-dimensional heat bath simulations. The comparisons of surface properties, namely heat flux and pressure, show very close agreement with previous computational fluid dynamics (CFD) results. Differences with the measurements were found to be similar to the CFD simulations. The unresolved discrepancy with the measurements could be due to inconsistent free stream conditions with the actual experimental data or missing physical phenomena altogether, for example atomic and molecular oxygen electronically excited states, three-dimensional effects, or more complex gas–surface interactions. As shown in this work, the advantages of obtaining a DSMC particle solution for these flows reside in the method's ability to be directly informed from first principles and to seamlessly describe internal energy non-equilibrium for all modes. With the advent of exascale computing and beyond, particle methods will be an increasingly important tool to verify the validity of physical assumptions in reduced-order models via fully resolved, experimental-scale simulations, down to the level of molecular-level distributions.

Calculation of Self, Corrected, and Transport Diffusivities of Isopropyl Alcohol in UiO-66.

The UiO-6x family of metal-organic frameworks has been extensively studied for applications in chemical warfare agent (CWA) capture and destruction. An understanding of intrinsic transport phenomena, such as diffusion, is key to understanding experimental results and designing effective materials for CWA capture. However, the relatively large size of CWAs and their simulants makes diffusion in the small-pored pristine UiO-66 very slow and hence impractical to study directly with direct molecular simulations because of the time scales required. We used isopropanol (IPA) as a surrogate for CWAs to investigate the fundamental diffusion mechanisms of a polar molecule within pristine UiO-66. IPA can form hydrogen bonds with the μ3-OH groups bound to the metal oxide clusters in UiO-66, similar to some CWAs, and can be studied by direct molecular dynamics simulations. We report self, corrected, and transport diffusivities of IPA in pristine UiO-66 as a function of loading. Our calculations highlight the importance of the accurate modeling of the hydrogen bonding interactions on diffusivities, with about an order of magnitude decrease in diffusion coefficients when the hydrogen bonding between IPA and the μ3-OH groups is included. We found that a fraction of the IPA molecules have very low mobility during the course of a simulation, while a small fraction are highly mobile, exhibiting mean square displacements far greater than the ensemble average.

Objective molecular dynamics investigation of dissociation and recombination kinetics in high-temperature nitrogen

In this study, we propose the use of the novel approach of objective molecular dynamics (OMD) simulating far-from-equilibrium gas dynamics problems with chemical reactions. The OMD method has an exact relation to models in continuum mechanics and can be used to improve those models. We provide a detailed molecular dynamics investigation of chemically reacting nitrogen gas in a space-homogeneous adiabatic reactor. The analysis is based on a first-principles derived reactive ReaxFF potential energy surface, which captures the relevant processes of rovibrational relaxation, dissociation, and exchange as well as recombination in a gas evolving under non-equilibrium conditions. We examine the evolution of the internal mode population distribution of all the molecules as well as the rovibrational probability distribution of the pre-collision dissociating and post-collision recombined N2 molecules to investigate the microscopic selectivity of various reactive processes. Subsequently, we make comparisons with results obtained by means of an alternative modeling approach called direct molecular simulation. The current work illustrates the application of the method of OMD to study the compression and expansion kinetics of dissociation-recombination nitrogen mixture relevant to normal shock wave and nozzle expansion.

Can molecular dynamics be used to simulate biomolecular recognition?

There are many problems in biochemistry that are difficult to study experimentally. Simulation methods are appealing due to direct availability of atomic coordinates as a function of time. However, direct molecular simulations are challenged by the size of systems and the time scales needed to describe relevant motions. In theory, enhanced sampling algorithms can help to overcome some of the limitations of molecular simulations. Here, we discuss a problem in biochemistry that offers a significant challenge for enhanced sampling methods and that could, therefore, serve as a benchmark for comparing approaches that use machine learning to find suitable collective variables. In particular, we study the transitions LacI undergoes upon moving between being non-specifically and specifically bound to DNA. Many degrees of freedom change during this transition and that the transition does not occur reversibly in simulations if only a subset of these degrees of freedom are biased. We also explain why this problem is so important to biologists and the transformative impact that a simulation of it would have on the understanding of DNA regulation.

First-principles predictions for shear viscosity of air components at high temperature.

The direct molecular simulation (DMS) method is used to obtain shear viscosity data for non-reacting air and its components by simulating isothermal, plane Poiseuille subsonic flows. Shear viscosity is estimated at several temperatures, from 273 K to 10 000 K, by fitting the DMS velocity profiles using the analytic solution of the Navier-Stokes equations for this simple canonical flow. The ab initio potential energy surfaces (PESs) that describe the various atomic-level interactions are the only input in the simulations. Molecules involved in a collision within the flow can occupy any rovibrational state that is allowed by the effective diatomic potential. For molecular nitrogen, oxygen, and air at standard condition molar composition, the DMS shear viscosity predictions are in excellent agreement with the experimental data that are available up to about 2000 K. The results for pure molecular nitrogen and pure molecular oxygen also agree very well with previously published quasi-classical trajectory (QCT) calculations based on the same PESs. It is further shown that the ab initio shear viscosity data are generally lower than the corresponding values used in popular computational fluid dynamics codes, over a wide temperature range. Finally, Wilke's mixing rule is demonstrated to accurately predict the DMS air viscosity results from the pure molecular components data up to 4000 K.

Simulation of Oxygen Chemical Kinetics Behind Incident and Reflected Shocks via Master Equation

A model for simulating postshock conditions using only state-resolved kinetic data of ab initio accuracy is presented. The quasi-classical trajectory method is used to compute a vibrational-specific kinetic database that describes internal energy transfer and dissociation in a nonionizing oxygen mixture. The kinetic database is implemented in a system of master equations and coupled to conservation laws to simulate a series of conditions, including zero-dimensional adiabatic reservoir, one-dimensional postincident, and one-dimensional postreflected shock relaxation. The present results are in excellent agreement with temperature profiles produced by the direct molecular simulation method at a fraction of cost. For the first time, the state-resolved model is applied to model relaxation behind a reflected shock passing through a thermally nonequilibrium gas. Model validation is made via comparisons to the experiments of Ibraguimova et al. (Journal of Chemical Physics, Vol. 139, No. 3, 2013, Paper 034317) and Streicher et al. (Physics of Fluids, Vol. 33, No. 5, 2021, Paper 056107). It is shown that neglecting relaxation in the postincident shock region may lead to nonnegligible errors in determining initial postreflected shock translational and vibrational temperatures, particularly in cases where the test gas is not diluted with an inert species.

Direct molecular simulation of oxygen dissociation across normal shocks

Direct molecular simulation of oxygen dissociation across normal shocks

Molecular simulation of flows in thermochemical non-equilibrium around a cylinder using ab initio potential energy surfaces for N2 + N and N2 + N2 interactions

We present two-dimensional direct molecular simulation (DMS) results for high-enthalpy nitrogen flows in thermochemical non-equilibrium around a circular cylinder. The simulations are carried out using accurate ab initio potential energy surfaces (PES) to describe N2 + N and N2 + N2 interactions. Select comparisons with the direct simulation Monte Carlo method are presented to demonstrate how the high-fidelity DMS data, both at the level of bulk flow quantities and local molecular distributions, can be used to thoroughly inform or validate simplified reduced-order descriptions. Then, a partially dissociated nitrogen flow around a circular cylinder is obtained from two successive refinements of a well-established ab initio nitrogen PES. The only input in both calculations is the respective PESs, all other simulation parameters being precisely equal. This work, enabled by large scale computing, represents the first attempt at establishing a rigorous methodology for (i) the validation of lower-fidelity, computationally efficient models using ab initio, assumption-free calculations (DMS) as benchmarks and (ii) a systematic assessment of ab initio PES accuracy using entire flow field results.

State-to-State Master Equation and Direct Molecular Simulation Study of Energy Transfer and Dissociation for the N2-N System.

We present a detailed comparison of two high-fidelity approaches for simulating non-equilibrium chemical processes in gases: the state-to-state master equation (StS-ME) and the direct molecular simulation (DMS) methods. The former is a deterministic method, which relies on the pre-computed kinetic database for the N2-N system based on the NASA Ames ab initio potential energy surface (PES) to describe the evolution of the molecules' internal energy states through a system of master equations. The latter is a stochastic interpretation of molecular dynamics relying exclusively on the same ab initio PES. It directly tracks the microscopic gas state through a particle ensemble undergoing a sequence of collisions. We study a mixture of nitrogen molecules and atoms forced into strong thermochemical non-equilibrium by sudden exposure of rovibrationally cold gas to a high-temperature heat bath. We observe excellent agreement between the DMS and StS-ME predictions for the transfer rates of translational into rotational and vibrational energy, as well as of dissociation rates across a wide range of temperatures. Both methods agree down to the microscopic scale, where they predict the same non-Boltzmann population distributions during quasi-steady-state dissociation. Beyond establishing the equivalence of both methods, this cross-validation helped in reinterpreting the NASA Ames kinetic database and resolve discrepancies observed in prior studies. The close agreement found between the StS-ME and DMS methods, whose sole model inputs are the PESs, lends confidence to their use as benchmark tools for studying high-temperature air chemistry.

Consistent kinetic-continuum dissociation model. II. Continuum formulation and verification.

In this article, we implement a recently developed non-equilibrium chemical kinetics model [N. Singh and T. Schwartzentruber, J. Chem. Phys. 152, 224302 (2020)] based on ab initio simulation data and perform verification studies. Direct molecular simulation data are used to verify the predictive capabilities of the model. Using the model, dominant physics, such as the need for a rotational energy equation, and the quantitative role of non-Boltzmann effects are identified. Based on the analysis and reasonable assumptions, a simplified model for implementation into large-scale computational fluid dynamic simulations is proposed. Without incurring additional computational cost, the model can be used in existing flow solvers to analyze hypersonic flows.

Direct Molecular Simulation of Nitrogen Dissociation Under Adiabatic Postshock Conditions

Direct molecular simulations (DMS) of nitrogen dissociation in adiabatic reservoirs covering a wide enthalpy range are presented. These conditions more realistically reproduce the gas state in a hypersonic shock layer than prior isothermal DMS studies. The Minnesota ab initio potential energy surface is used for nitrogen molecule-molecule () and nitrogen atom-molecule () classical trajectory calculations. Profiles of gas parameters (mixture composition, gas temperature, etc.) are reported, and the molecules’ internal energy population distributions during dissociation examined. It is observed that the evolution of the gas mixture under adiabatic conditions can be divided into two phases. Early on, excess translational energy is available for molecules to dissociate, regardless of their internal energy. This causes a sudden drop in the reservoir kinetic temperature and slows down subsequent dissociation. At later stages, the gas settles into a quasi-steady-state (QSS) regime, where dissociation proceeds primarily from higher-lying rovibrational levels near and above the dissociation threshold energy. The dissociation rate becomes limited by depletion of high-lying internal energy levels. Subsequently, adiabatic simulations are compared with prior isothermal DMS calculations performed at similar reservoir temperatures. The same shape is effectively observed for population distributions in both cases. This retroactively justifies the use of isothermal conditions to obtain QSS dissociation rate coefficients.

Mechanical Response of Nanocrystalline Ice-Contained Methane Hydrates: Key Role of Water Ice.

Water ice and gas hydrates can coexist in the permafrost and polar regions on Earth and in the universe. However, the role of ice in the mechanical response of ice-contained methane hydrates is still unclear. Here, we conduct direct million-atom molecular simulations of ice-contained polycrystalline methane hydrates and identify a crossover in the tensile strength and average compressive flow stress due to the presence of ice. The average mechanical shear strengths of hydrate-hydrate bicrystals are about three times as large as those of hydrate-ice bicrystals. The ice content, especially below 70%, shows a significant effect on the mechanical strengths of the polycrystals, which is mainly governed by the proportions of the hydrate-hydrate grain boundaries (HHGBs), the hydrate-ice grain boundaries (HIGBs), and the ice-ice grain boundaries (IIGBs). Quantitative analysis of the microstructure of the water cages in the polycrystals reveals the dissociation and reformation of various water cages due to mechanical deformation. These findings provide molecular insights into the mechanical behavior and microscopic deformation mechanisms of ice-contained methane hydrate systems on Earth and in the universe.

Molecular dynamics study of tilt grain boundary evolution during the growth of beryllium thin films

• Grain boundaries can maintain its type as the epitaxial layer growing. • Large incident angle results in the formation of more defects at the grain boundary. • Incident energy about 5 eV is desired to form improved Beryllium film. Beryllium films fabricated by magnetron sputtering deposition unavoidably contain grain boundaries (GBs), which have a substantial effect on the resulting material properties. The growth dynamics and evolution of various tilt GBs were explored using a direct molecular dynamics vapor deposition simulation. The effects of the incident energy, incident angle and substrate temperature on the film morphologies were also considered. The results show that GBs and dislocations were extended to the epitaxial layer during the growth of the beryllium thin films. The types of GBs were maintained and were closely related to the surface topography of the substrate. An increased incident energy and substrate temperature enabled the formation of good-quality beryllium films. However, large incident angles resulted in the formation of defect structures in the interior of the beryllium films. The low-angle GBs were more stable than the high-angle GBs. Large incident energies (above 10 eV) with large incident angles (above 38°) always accompanied increased numbers of reflected atoms. In brief, during the growth of the beryllium thin films, the GBs were extended to the epitaxial layer, and the types of GBs were maintained. In addition, incident energies about 5 eV with incident angles less than 30° are desired to form improved Be films.

Atomistic Modeling of Metal Nanocluster Motion Caused by Gas Flow Impact

The work is devoted to supercomputer molecular modeling of gas dynamic spraying of nanoparticles on the substrate. The urgency of this problem is related to the development of production technologies for promising nanocoatings and nanomaterials. The observed increase in the power of modern computer and supercomputer systems makes it possible to use mathematical models based on the first principles in numerical experiments. One of such models is the molecular dynamics method. In this paper, a new results of using of direct molecular simulation for calculating of the acceleration of a nickel nanocluster by a nitrogen flow are presented. The data obtained in the calculations allow to optimize the parameters of the accelerating gas system and predict the speed characteristics of the nanocluster near the substrate surface.

Erratum: “Direct molecular simulation of internal energy relaxation and dissociation in oxygen” [Phys. Fluids 31, 076107 (2019)

Erratum: “Direct molecular simulation of internal energy relaxation and dissociation in oxygen” [Phys. Fluids 31, 076107 (2019)

Direct molecular simulation of internal energy relaxation and dissociation in oxygen

A variant of the direct simulation Monte Carlo (DSMC) method, referred to as direct molecular simulation (DMS), is used to study oxygen dissociation from first principles. The sole model input to the DMS calculations consists of 12 potential energy surfaces that govern O2 + O2 and O + O2 collisions, including all spin-spatial degenerate configurations, in the ground electronic state. DMS calculations are representative of the gas evolution behind a strong shock wave, where molecular oxygen excites rotationally and vibrationally before ultimately dissociating and reaching a quasi-steady-state (QSS). Vibrational relaxation time constants are presented for both O2 + O2 and O + O2 collisions and are found to agree closely with experimental data. Compared to O2 + O2 collisions, vibrational relaxation due to O + O2 collisions is found to be ten times faster and to have a weak dependence on temperature. Dissociation rate constants in the QSS dissociation phase are presented for both O2 + O2 and O + O2 collisions and agree (within experimental uncertainty) with rates inferred from shock-tube experiments. Both experiments and simulations indicate that the QSS dissociation rate coefficients for O + O2 interactions are about two times greater than the ones for O2 + O2. DMS calculations predict this to be a result of nonequilibrium (non-Boltzmann) internal energy distributions. Specifically, the increased dissociation rate is caused by faster vibrational relaxation, due to O + O2 collisions, which alters the vibrational energy distribution function in the QSS by populating higher energy states that readily dissociate. Although existing experimental data appear to support this prediction, experiments with lower uncertainty are needed for quantitative validation. The DMS data presented for rovibrational relaxation and dissociation in oxygen could be used to formulate models for DSMC and computational fluid dynamics methods.

Comparison of Potential Energy Surface and Computed Rate Coefficients for Dissociation

Comparisons are made between potential energy surfaces (PESs) for and collisions and between rate coefficients for dissociation that were computed using the quasi-classical trajectory (QCT) method on these PESs. For , Laganà’s empirical London–Eyring–Polanyi–Sato surface is compared with one from NASA Ames Research Center based on ab initio quantum chemistry calculations. For , two ab initio PESs (from NASA Ames and from the University of Minnesota) are compared. These use different methods for computing the ground state electronic energy for but give similar results. Thermal dissociation rate coefficients, for the 10,000–30,000 K temperature range, have been computed using each PES, and the results are in excellent agreement. Quasi-stationary state (QSS) rate coefficients using both PESs have been computed at these temperatures using the direct molecular simulation method (DMS) of Schwartzentruber and coworkers. The QSS rate coefficients are up to a factor of 5 lower than the thermal ones, and the thermal and QSS values bracket the results of shock-tube experiments. It is concluded that the combination of ab initio quantum chemistry PESs and QCT calculations provides an attractive approach for the determination of accurate high-temperature rate coefficients for use in aerothermodynamics modeling.