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At least 451 records · Page 25

Molecular-gas-dynamics simulations of turbulent Couette flow over a mean-free-path-scale permeable substrate

Here we report flow statistics and visualizations from molecular-gas-dynamics simulations using the direct simulation Monte Carlo (DSMC) method for turbulent Couette flow in a minimal domain where the lower wall is replaced by an idealized permeable fibrous substrate representative of thermal-protection-system materials for which the Knudsen number is O(10 -1 ). Comparisons are made with smooth-wall DSMC simulations and smooth-wall direct numerical simulations (DNS) of the Navier-Stokes equations for the same conditions. Roughness, permeability, and noncontinuum effects are assessed. In the range of Reynolds numbers considered herein, the scalings of the skin friction on the permeable substrate and of the mean flow within the substrate suggest that they are dominated by viscous effects. While the regenerative cycle characteristic of smooth-wall turbulence remains intact for all cases considered, we observe that the near-wall velocity fluctuations are modulated by the permeable substrate with a wavelength equal to the pore spacing. Additionally, the flow within the substrate shows significant rarefaction effects, resulting in an apparent permeability that is 13% larger than the intrinsic permeability. In contrast, the smooth-wall DSMC and DNS simulations exhibit remarkably good agreement for the statistics examined, despite the Knudsen number based on the viscous length scale being as large as O(10 -1 ). This latter result is at variance with classical estimates for the breakdown of the continuum assumption and calls for further investigations into the interaction of noncontinuum effects and turbulence.

42 ENGINEERING↗

REACTER 2.0: Quantum-Informed Reaction Constraints and Automated Interaction Typing

REACTER is a heuristic method for modeling chemical reactions in classical molecular dynamics simulations, implemented in LAMMPS as fix bond/react. The authors recently extended LAMMPS to support alphanumeric labels for atom types, bond types etc., which enables the pre- and post-reaction templates required by the REACTER protocol to be portable between different simulations and greatly simplifies the task of creating simulation-ready reaction templates. To further increase the generality of reaction templates, support for wildcard characters within atom types has been added, along with the automatic assignment of interaction types for new bonds, angles, etc. based on the involved atom types. In some cases, this feature can express a class of reactions with one pair of reaction templates, where previously dozens may have been required. Advanced reaction constraints have also been added, including an Arrhenius constraint to enforce an effective activation energy, a root-mean-square-deviation option for complex geometrical constraints, as well as a custom constraint that leverages LAMMPS’ powerful built-in variable framework. Other new features include variable support for various inputs (e.g., to allow reaction rates or cutoffs to be dependent on overall conversion), on-the-fly update of molecule IDs, and the ability to create new atoms positioned with respect to the reaction site. The new features are applied to modeling polymeric, thermosetting and composite materials, and advanced applications of the new reaction constraints are demonstrated. For example, REACTER is shown to accurately reproduce mechanically-induced bond breaking, as characterized by third-order DFT-based tight-binding (DFTB3) simulations, via a constraint on the total potential energy of the involved atoms.

polymer simulations↗

In Silico Insights into Protein–Protein Interaction Disruptive Mutations in the PCSK9-LDLR Complex

Gain-of-function mutations in PCSK9 (proprotein convertase subtilisin/kexin type 9) lead to reduced uptake of LDL (low density lipoprotein) cholesterol and, therefore, increased plasma LDL levels. However, the mechanism by which these mutants reduce LDL reuptake is not fully understood. Here, we have used molecular dynamics simulations, MM/PBSA (Molecular Mechanics/Poisson–Boltzmann Surface Area) binding affinity calculations, and residue interaction networks, to investigate the protein–protein interaction (PPI) disruptive effects of two of PCSK9's gain-of-function mutations, Ser127Arg and Asp374Tyr on the PCSK9 and LDL receptor complex. In addition to these PPI disruptive mutants, a third, non-interface mutation (Arg496Trp) is included as a positive control. Our results indicate that Ser127Arg and Asp374Tyr confer significantly improved binding affinity, as well as different binding modes, when compared to the wild-type. These PPI disruptive mutations lie between the EGF(A) (epidermal growth factor precursor homology domain A) of the LDL receptor and the catalytic domain of PCSK9 (Asp374Tyr) and between the prodomain of PCSK9 and the β-propeller of the LDL receptor (Ser127Arg). The interactions involved in these two interfaces result in an LDL receptor that is sterically inhibited from entering its closed conformation. This could potentially implicate the prodomain as a target for small molecule inhibitors.

59 BASIC BIOLOGICAL SCIENCES↗

fp-tools

The output of a molecular dynamics simulation is a data file containing properties of the motion of the simulated particles as a function of time (e.g., positions, velocities). From this output, scientists can extract various properties which give insight into the physics of the system; for example, the radial distribution function can be computed from the particle positions, which gives insight into how close the system is to melting or freezing. Many publicly available codes to perform molecular dynamics simulations exist and have been well adopted by the scientific community (e.g., LAMMPS, VASP). However, it remains standard practice for scientists to write their own post-processing scripts to extract various properties of interest from the molecular dynamics simulation data. Since in many cases scientists are interested in the same set of “textbook” properties, there is a large duplication of effort in writing these post-processing scripts. Our proposed code, FP-Tools, is a C++ toolkit designed to help scientists extract and analyze quantities of interest from the output of a molecular dynamics simulation, eliminating the need for them to write these codes themselves and thus reducing this duplication of effort. The quantities which are computed by our code are well documented in the literature (either in publications or textbooks), and the algorithms we implement to compute these properties are also well known in the field. We are not introducing new science or methods here; rather, our primary goal is to provide a useful tool to the community in the form of a well-documented, easy to use package.

Hartman, Leah↗

Assessing the Effect of Explicit Polarizability on Models of Carbon Dioxide Solvation in Ionic Liquids

Ionic liquids are an important possible carbon capture material because of their anomalously high sorption selectivity for carbon dioxide over other gases common in air. Many research groups have investigated the molecular origins of this property and provided important insights, including using 1D and 2D-IR spectroscopy. Molecular dynamics simulations have been indispensable to the interpretation of these experiments. In prior molecular dynamics simulation work, charge-scaled force fields have typically been used to provide a mean-field treatment of effects vital to ionic liquid systems such as charge transfer and polarization. Here, we compare models of carbon dioxide solvated in ionic liquids with explicit polarization to models of the same with implicit polarizability through charge-scaling. We calculate structural, dynamical, and spectroscopic properties, and make comparisons to the same items measured in experiment. In this study, we focus on two ionic liquids: 1-butyl-3- methylimidazolium (BMIM + ) paired with bis(trifluoromethane sulfonyl imide) (Tf 2 N − ) and 1-butyl-3-methylimidazolium (BMIM+) paired with hexafluorophosphate (PF 6 − ). We find that many structural, dynamical, and spectroscopic properties are changed when polarization is modeled explicitly. We also find that explicit polarizability softens local ion cages around the carbon dioxide and that the long-time diffusion of the carbon dioxide is gated by the reorganization of the ionic liquid molecules. Comparisons to experiment show modest improvement of many observables compared with experiment for the explicitly polarizable model over the charge-scaled model. Overall, our results show that charge-scaled force fields are likely sufficient to compute spectroscopic properties of carbon dioxide in ionic liquids and suggest some interpretive rules for understanding their structural and dynamical properties. Those using charge-scaled force fields should generally assume that the ion cages around solutes such as carbon dioxide are too stiff and cation-rich in their models and adjust their interpretations and predictions accordingly.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

GLUE Code: A framework handling communication and interfaces between scales

Many scientific applications are inherently multiscale in nature. Such complex physical phenomena often require simultaneous execution and coordination of simulations spanning multiple time and length scales. This is possible by combining expensive small-scale simulations (such as molecular dynamics simulations) with larger scale simulations (such continuum limit/hydro solvers) to allow for considerably larger systems using task and data parallelism. However, the granularity of the tasks can be very large and often leads to load imbalance. Traditionally, we use approximations to streamline the computation of the more costly interactions and this introduces trade-offs between simulation cost and accuracy. In recent years, the available computational power and the advances in machine learning have made computing these scale-bridging interactions and multiscale simulations more feasible. One driving application has been plasma modeling in inertial confinement fusion (ICF), which is fundamentally multiscale in nature. This requires deep understanding of how to extrapolate microscopic information into macroscopically relevant scales. For example, in ICF one needs an accurate understanding of the connection between experimental observables and the underlying microphysics. The properties of the larger scales are often affected by the microscale behavior incorporated usually into the equations of state and ionic and electronic transport coefficients (Liboff, 1959; Rinderknecht et al., 2014; Rosenberg et al., 2015; Ross et al., 2017). Instead of incorporating this information using reliable molecular dynamics (MD) simulations, one often needs to use theoretical models, due to the inability of MD to reach engineering scales (Glosli et al., 2007; Marinak et al., 1998). One approach to resolve this issue is by coupling two MD simulations of different scales via force interpolation, e.g., the AdResS method (Krekeler et al., 2018; Nagarajan et al., 2013). Another approach, which we will pursue in the scope of this work, is by enabling scale bridging between MD simulations and meso/macro-scale models through the development and support of application programming interfaces that these different applications can interact through.

54 ENVIRONMENTAL SCIENCES↗

Molecular design and fabrication of PIM-1/polyphosphazene blend membranes with high performance for CO 2 /N 2 separation

New polymeric blend membranes for CO 2 separation were synthesized based on insights from molecular dynamics simulation. A molecular-level structure-property relationship in polymers of intrinsic microporosity (PIM) based blend membranes, was investigated in detail computationally. Calculated local density profiles and energy of interaction of the blend membranes, composed of PIM-1 and various polyphosphazenes, showed that using the polyphosphazene with a higher concentration of ether side chains can improve the compatibility with PIM-1. Furthermore, based on the findings of computational studies, blend membranes were experimentally fabricated from PIM-1 and polyphosphazenes with various polyether side chain concentrations. Polyether concentration in polyphosphazenes was correlated with the film properties and gas transport performance of the blend membranes. Blend membranes showed very high CO 2 permeability (3100-5300 barrer) and improved CO 2 /N 2 selectivity (24-28), outperforming all other PIM-based blend membranes reported to date. Moreover, the CO 2 permeability performance of the blend membranes was tested 566 hours under real post-combustion flue gas from a coal-fired power plant, including CO 2 , N 2 , H 2 O, O 2 , SO x and NO x .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A data-driven multiscale model for reactive wetting simulations

Here, we describe a data-driven, multiscale technique to model reactive wetting of a silver–aluminum alloy on a Kovar™ (Fe-Ni-Co alloy) surface. We employ molecular dynamics simulations to elucidate the dependence of surface tension and wetting angle on the drop’s composition and temperature. A design of computational experiments is used to efficiently generate training data of surface tension and wetting angle from a limited number of molecular dynamics simulations. The simulation results are used to parameterize models of the material’s wetting properties and compute the uncertainty in the models due to limited data. The data-driven models are incorporated into an engineering-scale (continuum) model of a silver–aluminum sessile drop on a Kovar™ substrate. Model predictions of the wetting angle are compared with experiments of pure silver spreading on Kovar™ to quantify the model-form errors introduced by the limited training data versus the simplifications inherent in the molecular dynamics simulations. The paper presents innovations in the determination of “convergence” of noisy MD simulations before they are used to extract the wetting angle and surface tension, and the construction of their models which approximate physio-chemical processes that are left unresolved by the engineering-scale model. Together, these constitute a multiscale approach that integrates molecular-scale information into continuum scale models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Driving and characterizing nucleation of urea and glycine polymorphs in water

Crystal nucleation is relevant across the domains of fundamental and applied sciences. However, in many cases, its mechanism remains unclear due to a lack of temporal or spatial resolution. To gain insights into the molecular details of nucleation, some form of molecular dynamics simulations is typically performed; these simulations, in turn, are limited by their ability to run long enough to sample the nucleation event thoroughly. To overcome the timescale limits in typical molecular dynamics simulations in a manner free of prior human bias, here, we employ the machine learning-augmented molecular dynamics framework “reweighted autoencoded variational Bayes for enhanced sampling (RAVE).” We study two molecular systems—urea and glycine—in explicit all-atom water, due to their enrichment in polymorphic structures and common utility in commercial applications. From our simulations, we observe multiple back-and-forth nucleation events of different polymorphs from homogeneous solution; from these trajectories, we calculate the relative ranking of finite-sized polymorph crystals embedded in solution, in terms of the free-energy difference between the finite-sized crystal polymorph and the original solution state. We further observe that the obtained reaction coordinates and transitions are highly nonclassical.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of Solvent on the Local Structure, Dynamics, and Vibrational Density of States in Sn-BEA Zeolite

Lewis acid zeolites are attractive catalysts for epoxidation and biomass valorization, as they are highly active and selective in the liquid phase and can operate at or near ambient conditions. While a rich experimental literature exists on liquid-phase Lewis acid zeolite catalysis, our understanding of the molecular organization and solvent dynamics in the vicinity of Lewis acid sites with differing metal site speciation remains limited. In this work, we investigate the molecular coordination and diffusion of two common solvents (methanol and water) around the closed and open Sn-BEA zeolite active sites using molecular dynamics simulations with a machine-learned interatomic potential trained on ab initio molecular dynamics trajectories. Molecular dynamics simulations reveal that introducing active sites significantly enhances local order in the first and second solvation shells compared to the pure silica case. For methanol, both closed and open active sites are singly coordinated, while more than two water molecules coordinate the open site. In contrast to methanol, we observed that water molecules dissociate, leading to the formation of additional Sn-OH and silanol groups away from the active site. The diffusion coefficients of water and methanol are functions of the solvent population in the pore. Here, our work provides insights into how active site speciation in Lewis acid zeolites affects solvent coordination, diffusion, and vibrational signature. This information is foundational for catalyst design and optimization of liquid-phase catalytic processes in zeolites. It also demonstrates the suitability of machine-learned interatomic potentials for modeling reactive systems, enabling sufficiently long trajectories for appropriate statistical averaging.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Adaptive Conformer Sampling for Property Prediction Using the Conductor-like Screening Model for Real Solvents

The valorization of lignocellulose-derived bioproducts requires effective separation from excessive water. Liquid–liquid extraction is a promising low-energy separation technology, but effective extraction requires solvent selection based on the thermodynamic properties of the bioproduct and solvent components. We propose a computational framework for predicting such properties by developing an adaptive conformer selection approach for use with COSMO-RS (conductor-like screening model for real solvents) calculations. In this framework, molecular dynamics simulations are used to generate many molecular structures (conformers) at representative temperatures in varying solvent environments. Conformers are then clustered based on structural metrics in a low-dimensional space and selected using a mixed-integer quadratic programming problem to iteratively insert a sampled conformer. At each iteration, we determine bioproduct properties using COSMO-RS. Here, we demonstrate the capability of the proposed framework on representative bioproducts to show convergence of the adaptive sampling toward experimentally measured properties with fewer calculations than required by random conformer sampling, enabling the improved screening of solvent systems for liquid-phase separation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fouling behavior of zwitterionic membranes compared to polyamide membranes

Membrane fouling remains a critical bottleneck for reverse osmosis (RO) desalination, driving energy consumption and reducing membrane lifetime. Here, we employ all-atom molecular dynamics simulations to investigate the antifouling behavior of random zwitterionic amphiphilic copolymer (r-ZAC) membranes composed of sulfobetaine methacrylate (SBMA) and allyl methacrylate (AMA), benchmarked against conventional polyamide (PA) RO membranes. Structural and dynamical analyses—including radial distribution functions, coordination numbers, tetrahedral order parameters, vector orientation, and residence-time correlation functions—reveal that r-ZAC surfaces sustain tightly bound, long-lived hydration layers with preserved tetrahedrality and anisotropic water orientation, in sharp contrast to the weak and disordered hydration of PA. Steered molecular dynamics simulations demonstrate that r-ZAC membranes impose substantial free-energy barriers to foulant approach (alginate ≈ 90 kcal/mol, sucrose ≈ 35 kcal/mol, humic acid ≈ 15 kcal/mol), whereas PA membranes exhibit negligible barriers (< 1 kcal/mol) and thermodynamically favorable adsorption. Detailed foulant–surface interaction analyses show that zwitterionic hydration and electrostatic heterogeneity in r-ZAC suppress adhesion, except in the case of amphiphilic humic acid, which exploits multiple binding modes. Together, these results establish molecular-level design principles for antifouling membranes: the combination of zwitterionic hydration, structured interfacial water, and controlled amphiphilic balance in r-ZAC membranes provides superior resistance to organic fouling relative to PA.

Cross-linked polyamide↗

Computational Nanomechanics of Carbon Nanotubes and Composites

Nanomechanics of individual carbon and boron-nitride nanotubes and their application as reinforcing fibers in polymer composites has been reviewed with interplay of theoretical modeling, computer simulations and experimental observations. The emphasis in this work is on elucidating the multi-length scales of the problems involved, and of different simulation techniques that are needed to address specific characteristics of individual nanotubes and nanotube polymer-matrix interfaces. Classical molecular dynamics simulations are shown to be sufficient to describe the generic behavior such as strength and stiffness modulus but are inadequate to describe elastic limit and nature of plastic buckling at large strength. Quantum molecular dynamics simulations are shown to bring out explicit atomic nature dependent behavior of these nanoscale materials objects that are not accessible either via continuum mechanics based descriptions or through classical molecular dynamics based simulations. As examples, we discus local plastic collapse of carbon nanotubes under axial compression and anisotropic plastic buckling of boron-nitride nanotubes. Dependence of the yield strain on the strain rate is addressed through temperature dependent simulations, a transition-state-theory based model of the strain as a function of strain rate and simulation temperature is presented, and in all cases extensive comparisons are made with experimental observations. Mechanical properties of nanotube-polymer composite materials are simulated with diverse nanotube-polymer interface structures (with van der Waals interaction). The atomistic mechanisms of the interface toughening for optimal load transfer through recycling, high-thermal expansion and diffusion coefficient composite formation above glass transition temperature, and enhancement of Young's modulus on addition of nanotubes to polymer are discussed and compared with experimental observations.

Srivastava, Deepak↗

Molecular Dynamics Free Energy Simulations Reveal the Mechanism for the Antiviral Resistance of the M66I HIV-1 Capsid Mutation

While drug resistance mutations can often be attributed to the loss of direct or solvent-mediated protein−ligand interactions in the drug-mutant complex, in this study we show that a resistance mutation for the picomolar HIV-1 capsid (CA)-targeting antiviral (GS-6207) is mainly due to the free energy cost of the drug-induced protein side chain reorganization in the mutant protein. Among several mutations, M66I causes the most suppression of the GS-6207 antiviral activity (up to ~84,000-fold), and only 83- and 68-fold reductions for PF74 and ZW-1261, respectively. To understand the molecular basis of this drug resistance, we conducted molecular dynamics free energy simulations to study the structures, energetics, and conformational free energy landscapes involved in the inhibitors binding at the interface of two CA monomers. To minimize the protein−ligand steric clash, the I66 side chain in the M66I−GS-6207 complex switches to a higher free energy conformation from the one adopted in the apo M66I. In contrast, the binding of GS-6207 to the wild-type CA does not lead to any significant M66 conformational change. Based on an analysis that decomposes the absolute binding free energy into contributions from two receptor conformational states, it appears that it is the free energy cost of side chain reorganization rather than the reduced protein−ligand interaction that is largely responsible for the drug resistance against GS-6207.

Sun, Qinfang (ORCID:0000000173621543)↗

Graph-based quantum response theory and shadow Born–Oppenheimer molecular dynamics

Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born–Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. Further, the proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.

74 ATOMIC AND MOLECULAR PHYSICS↗

Shock-induced chemistry and high strain-rate viscoelastic behavior of a phenolic polymer

We use impact experiments and a finite element model (up to 1.2 GPa), and molecular dynamics simulations (up to 60 GPa), to examine the behavior of a phenolic polymer under shock compression, spanning both nonreactive and reactive regimes. In the nonreactive regime, relaxation following compression at strain rates of ∼105 s−1 can be explained by viscoelasticity observed at ordinary laboratory rates (≲1 s−1) by accounting for the temperature dependence of the phenolic β-transition. Reasonable agreement is found between the measured shock Hugoniot up to 1.2 GPa and molecular dynamics simulation for cross-linked structures of comparable density. We also observed a first-order mechanical transition near 0.36 GPa shock stress and estimated a spall strength of 0.102 GPa and Hugoniot elastic limit of 1–2 GPa. The shock stress is found to vary up to 24% among phenolics made with different resin and/or cure processes. Finally, molecular dynamics simulations are used to identify a reactive regime at shock pressures ≳20 GPa that is characterized by chemically driven, rate-dependent relaxation processes, including dehydrogenation and dehydration reactions that promote the formation of a dense, highly cross-linked carbonaceous solid and the release of light volatiles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

CTRAMER: An open-source software package for correlating interfacial charge transfer rate constants with donor/acceptor geometries in organic photovoltaic materials

In this paper, we present CTRAMER (Charge-Transfer RAtes from Molecular dynamics, Electronic structure, and Rate theory)—an opensource software package for calculating interfacial charge-transfer (CT) rate constants in organic photovoltaic (OPV) materials based on ab initio calculations and molecular dynamics simulations. The software is based on identifying representative donor/acceptor geometries within interfacial structures obtained from molecular dynamics simulation of donor/acceptor blends and calculating the corresponding Fermi’s golden rule CT rate constants within the framework of the linearized-semiclassical approximation. While the methods used are well established, the integration of these state-of-the-art tools originating from different disciplines to study photoinduced CT processes with explicit treatment of the environment, in our opinion, makes this package unique and innovative. The software also provides tools for investigating other observables of interest. After outlining the features and implementation details, the usage and performance of the software are demonstrated with results from an example OPV system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Optimization of Thermal Conductance at Interfaces Using Machine Learning Algorithms

We report optimization of thermal transport across the interface of two different materials is critical to micro-/nanoscale electronic, photonic, and phononic devices. Although several examples of compositional intermixing at the interfaces having a positive effect on interfacial thermal conductance (ITC) have been reported, an optimum arrangement has not yet been determined because of the large number of potential atomic configurations and the significant computational cost of evaluation. On the other hand, computation-driven materials design efforts are rising in popularity and importance. Yet, the scalability and transferability of machine learning models remain as challenges in creating a complete pipeline for the simulation and analysis of large molecular systems. In this work we present a scalable Bayesian optimization framework, which leverages dynamic spawning of jobs through the Message Passing Interface (MPI) to run multiple parallel molecular dynamics simulations within a parent MPI job to optimize heat transfer at the silicon and aluminum (Si/Al) interface. We found a maximum of 50% increase in the ITC when introducing a two-layer intermixed region that consists of a higher percentage of Si. Because of the random nature of the intermixing, the magnitude of increase in the ITC varies. We observed that both homogeneity/heterogeneity of the intermixing and the intrinsic stochastic nature of molecular dynamics simulations account for the variance in ITC.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗