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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Complex Relationship between Side-Chain Polarity, Conductivity, and Thermal Stability in Molecularly Doped Conjugated Polymers

Molecularly doped conjugated polymers with polar side chains are an emerging class of conducting materials exhibiting enhanced and thermally stable conductivity. In this work, we study the electronic conductivity (σ) and the corresponding thermal stability of two polythiophene derivatives comprising oligoethylene glycol side chains: one having oxygen attached to the thiophene ring (poly(3-(methoxyethoxyethoxy)thiophene) (P3MEET)) and the other having a methylene spacer between the oxygen and the thiophene ring (poly(3-(methoxyethoxyethoxymethyl)thiophene) (P3MEEMT)). Thin films were vapor-doped with fluorinated derivatives of tetracyanoquinodimethane (FnTCNQ, n = 4, 2, 1) to determine the role of dopant strength (electron affinity) in maximum achievable σ. Specifically, when vapor doping with F 4 TCNQ, P3MEET achieved a substantially higher σ of 37.1 ± 10.1 S/cm compared to a σ of 0.82 ± 0.06 S/cm for P3MEEMT. Structural characterization using a combination of X-ray and optical spectroscopy reveals that the higher degree of conformational order of polymer chains in the amorphous domain upon doping with F 4 TCNQ in P3MEET is a major contributing factor for the higher σ of P3MEET. Additionally, vapor-doped P3MEET exhibited superior thermal stability compared to P3MEEMT, highlighting that the presence of polar side chains alone does not ensure higher thermal stability. Molecular dynamics simulations indicate that the dopant–side-chain nonbond energy is lower in the P3MEET:F 4 TCNQ mixture, suggesting more favorable dopant–side-chain interaction, which is a factor in improving the thermal stability of a polymer/dopant pair. Our results reveal that additional factors such as polymer ionization energy and side-chain–dopant interaction should be taken into account for the design of thermally stable, highly conductive polymers.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Metal Complex Molecular Solids Showing Band-like Transport Driven by In Situ Ligand Exchange

Transition-metal complexes exhibit excellent charge transport properties in solid films, rendering them promising for application in modern electronics. Although the charge transport mechanism of metal complex solids with multiple redox states is considered to be governed by self-exchange hole hopping, the effect of additives, such as Lewis bases, has not been identified. Herein, we describe the effect of 4- tert -butylpyridine (TBP) on the charge transport mechanism and film properties of [Cu(dmbpy) 2 ] 2 + / + (dmbpy = 6,6'-dimethyl-2,2'-bipyridine)-based molecular solids. The formation of [Cu(TBP) 4 ] 2 + , excess TBP, and free dmbpy from the ligand-exchange reaction between [Cu(dmbpy) 2 ] 2 + and TBP increases the film conductivity and changes the transport mechanism from hopping to band-like transport through a combination of chemical composition, film morphology, and crystallographic changes. In conclusion, these findings advance our understanding of the fundamental properties of molecular metal complex solids and enable optoelectronic applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Relationship of the Molecular Structure and Transport Properties of Imide-Based Lithium Salts of “Acetonitrile/Water-in-Salt” Electrolytes

“Water-in-salt” (WIS) electrolytes exhibit excellent safety and electrochemical performance. However, they possess high concentrations, relatively low diffusion coefficient, and high viscosity. “Acetonitrile/water in salt” (AWIS) electrolytes can overcome the disadvantages of WIS electrolytes. Under relatively low concentrations, AWIS electrolytes show good electrochemical performance comparable to WIS electrolytes and low conductivity. Herein, we investigate the relationship between the solvation structures and the transport properties using small-angle X-ray scattering and molecular dynamics simulation. We observed two solvation behaviors of AWIS: anions dissolved in acetonitrile forming small acetonitrile/anion clusters and additional water further dissolving the small acetonitrile/anion clusters. The introduction of acetonitrile weakens the water–solute interaction and enhances the cation–anion interaction, which results in an enhanced dynamical slowdown as the concentration increases. In conclusion, this work provides molecular-level understanding of the connection between two-stage solvation structures and transport properties for imide-based lithium salt solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Molecular Layer Etching of Metalcone Films Using Lithium Organic Salts and Trimethylaluminum

Advances in semiconductor device manufacturing are limited by our ability to precisely add and remove thin layers of material in multistep fabrication processes. Recent reports on atomic layer etching (ALE) have provided the means for the precise removal of inorganic thin films deposited by atomic layer deposition (ALD), opening new avenues for nanoscale device design. Here, we report on a new technique for the precise removal of metal organic thin films deposited by molecular layer deposition (MLD), which we term molecular layer etching. This etching process employs sequential exposures of lithium organic salt (LOS) and trimethylaluminum (TMA) precursors to produce self-limiting etching behavior. We employ quartz crystal microbalance experiments to demonstrate (i) etching of alucone films preloaded with LOS upon TMA exposures and (ii) layer-by-layer etching of alucone films using alternating exposures of LOS and TMA. We also identify the selectivity of these etching mechanisms. We probe the mechanism for the layer-by-layer etching of alucone using a quartz crystal microbalance and Fourier transform infrared spectroscopy and identify that the etching proceeds via heterolytic cleaving of Al-O bonds in alucone upon LOS exposure followed by methylation to produce volatile species upon TMA exposure. The etching process results in the removal of 0.4 nm/cycle of alucone at 160 °C and up to 3.6 nm/cycle of alucone at 266 °C in ex situ etching experiments on silicon wafers. This halogen-free etching process enables etching of MLD films and provides new fabrication pathways for the control of material geometries at the nanoscale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Molecular-Modified Photocathodes for Applications in Artificial Photosynthesis and Solar-to-Fuel Technologies

Nature offers inspiration for developing technologies that integrate the capture, conversion, and storage of solar energy. In this review article, we highlight principles of natural photosynthesis and artificial photosynthesis, drawing comparisons between solar energy transduction in biology and emerging solar-to-fuel technologies. Key features of the biological approach include use of earth-abundant elements and molecular interfaces for driving photoinduced charge separation reactions that power chemical transformations at global scales. Finally, for the artificial systems described in this review, emphasis is placed on advancements involving hybrid photocathodes that power fuel-forming reactions using molecular catalysts interfaced with visible-light-absorbing semiconductors.

14 SOLAR ENERGY↗
DOE OSTI2024

Effect of Aggregation and Molecular Size on the Ice Nucleation Efficiency of Proteins

Aerosol acts as ice-nucleating particles (INPs) by catalyzing the formation of ice crystals in clouds at temperatures above the homogeneous nucleation threshold (-38 °C). In this study, we show that the immersion mode ice nucleation efficiency of the environmentally relevant protein, ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO), occurs at temperatures between -6.8 and -31.6 °C. Further, we suggest that this range is controlled by the RuBisCO concentration and protein aggregation. The warmest median nucleation temperature (-7.9 ± 0.8 °C) was associated with the highest concentration of RuBisCO (2 × 10 –1 mg mL –1 ) and large aggregates with a hydrodynamic diameter of ~10 3 nm. We investigated four additional chemically and structurally diverse proteins, plus the tripeptide glutathione, and found that each of them was a less effective INP than RuBisCO. Ice nucleation efficiency of the proteins was independent of the size (molecular weight) for the five proteins investigated in this study. In contrast to previous work, increasing the concentration and degree of aggregation did not universally increase ice nucleation efficiency. RuBisCO was the exception to this generalization, although the underlying molecular mechanism determining why aggregated RuBisCO is such an effective INP remains elusive.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Molecular Iodine Interactions with Fe, Ni, Cr, and Stainless Steel Alloys

The adsorption behavior of molecular iodine is important for understanding the spread of radioiodine in a nuclear accident. Prior experiments indicate that, in addition to the interaction with Fe, molecular iodine [i.e., I 2(g) ] also interacts with the next most abundant components of austenitic stainless steel (i.e., Ni, and Cr) at room temperature. Here, we investigate iodine adsorption on Fe, Ni, and Cr while focusing on understanding the variables affecting adsorption as well as the iodine compounds that are formed during adsorption. Scanning electron microscopy and energy-dispersive X-ray spectroscopy were used to characterize the surfaces of exposed metal particles and aid in the understanding of the morphology and chemistry of iodine interactions with the substrates. Inductively coupled plasma optical emission spectroscopy was used to detect low levels of metal iodides and X-ray photoelectron spectroscopy was used to confirm the formation of the metal iodides. The role of environmental factors (e.g., humidity and oxygen content) for iodine adsorption on metal substrates is addressed. The individual metals demonstrated formation of metal iodides for Fe and Ni particles from interaction with I 2(g) . The formation of metal iodides may indicate the affinity of iodine for the respective metal. In this study, the iodine affinities ranked Fe > Ni > Cr as determined by the quantity of chemisorbed iodine. This trend is also supported by the distributions and proportions of metals in the corrosion product of the stainless steels. The exposures without oxygen and humidity indicate the potential of a multistep iodine adsorption process where iodine first attacks the oxide layer and then chemisorbs to the exposed metal.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Tailoring the Structure of Carbon Molecular Sieves Derived from an Aromatic Polyamide

Energy-efficient and selective separation technologies are required to reclaim aqueous waste streams for reuse. Carbon molecular sieves (CMS) are one material capable of separating organic solvent and gaseous mixtures due to the presence of permanent, rigid, and molecular sieving pores and could potentially be used in aqueous separations. Here, a novel CMS material is derived from an aromatic polyamide precursor with tailored fabrication techniques. Structural characteristics of this CMS have been probed with various analyses and are potentially ideal for selective separations as adsorbents. In this work, elemental analyses provide insight about the potential chemical structures of CMS materials that result from degradation mechanisms. Gravimetric sorption data is used to estimate sorption, diffusion, and permeability selectivity with water and N, N-dimethylformamide. While challenges to the development and implementation of such carbonaceous materials remain, highly selective materials are critical starting points for enabling ultra-challenging separation processes of the future.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Molecular Geometry and Electronic Structure of Copper Corroles

Copper corroles are known for their unique multiconfigurational electronic structures in the ground state, which arise from the transfer of electrons from the π orbitals of the corrole to the d-orbital of copper. While density functional theory (DFT) provides reasonably good molecular geometries, the determination of the ground spin state and the associated energetics is heavily influenced by functional choice, particularly the percentage of the Hartree–Fock exchange. Using extended multireference perturbation theory methods (XMS-CASPT2), the functional choice can be assessed. The molecular geometries and electronic structures of both the unsubstituted and the meso-triphenyl copper corroles were investigated. A minimal active space was employed for structural characterization, while larger active spaces are required to examine the electronic structure. The XMS-CASPT2 investigations conclusively identify the ground electronic state as a multiconfigurational singlet (S o ) with three dominant electronic configurations in its lowest energy and characteristic saddled structure. In contrast, the planar geometry corresponds to the triplet state (T o ), which is approximately 5 kcal/mol higher in energy compared to the S o state for both the bare and substituted copper corroles. Notably, the planarity of the T o geometry is reduced in the substituted corrole compared with that in the unsubstituted one. By analyzing the potential energy surface (PES) between the S o and T o geometries using XMS-CASPT2, the multiconfigurational electronic structure is shown to transition toward a single electron configuration as the saddling angle decreases (i.e., as one approaches the planar geometry). Despite the ability of the functionals to reproduce the minimum energy structures, only the TPSSh-D 3 PES is reasonably close to the XMS-CASPT2 surface. Significant deviations along the PES are observed with other functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits

Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron–electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. In conclusion, the transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Semi-Empirical Shadow Molecular Dynamics: A PyTorch Implementation

Here, extended Lagrangian Born–Oppenheimer molecular dynamics (XL-BOMD) in its most recent shadow potential energy version has been implemented in the semiempirical PyTorch-based software PySeQM. The implementation includes finite electronic temperatures, canonical density matrix perturbation theory, and an adaptive Krylov subspace approximation for the integration of the electronic equations of motion within the XL-BOMB approach (KSA-XL-BOMD). The PyTorch implementation leverages the use of GPU and machine learning hardware accelerators for the simulations. The new XL-BOMD formulation allows studying more challenging chemical systems with charge instabilities and low electronic energy gaps. The current public release of PySeQM continues our development of modular architecture for large-scale simulations employing semi-empirical quantum-mechanical treatment. Applied to molecular dynamics, simulation of 840 carbon atoms, one integration time step executes in 4 s on a single Nvidia RTX A6000 GPU.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Nonempirical Prediction of the Length-Dependent Ionization Potential in Molecular Chains

The ionization potential of molecular chains is well-known to be a tunable nanoscale property that exhibits clear quantum confinement effects. State-of-the-art methods can accurately predict the ionization potential in the small molecule limit and in the solid-state limit, but for intermediate, nanosized systems prediction of the evolution of the electronic structure between the two limits is more difficult. Recently, optimal tuning of range-separated hybrid functionals has emerged as a highly accurate method for predicting ionization potentials. This was first achieved for molecules using the ionization potential theorem (IPT) and more recently extended to solid-state systems, based on an ansatz that generalizes the IPT to the removal of charge from a localized Wannier function. Here, we study one-dimensional molecular chains of increasing size, from the monomer limit to the infinite polymer limit using this approach. By comparing our results with other localization-based methods and where available with experiment, we demonstrate that Wannier-localization-based optimal tuning is highly accurate in predicting ionization potentials for any chain length, including the nanoscale regime.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

MBX V1.2: Accelerating Data-Driven Many-Body Molecular Dynamics Simulations

The MBX software provides an advanced platform for molecular dynamics simulations, leveraging state-of-the-art MB-pol and MB-nrg data-driven many-body potential energy functions. Developed over the past decade, these potential energy functions integrate physics-based and machine-learned many-body terms trained on electronic structure data calculated at the "gold standard" coupled-cluster level of theory. Recent advancements in MBX have focused on optimizing its performance, resulting in the release of MBX v1.2. While the inherently many-body nature of MB-pol and MB-nrg ensures high accuracy, it poses computational challenges. MBX v1.2 addresses these challenges with significant performance improvements, including enhanced parallelism that fully harnesses the power of modern multicore CPUs. In conclusion, these advancements enable simulations on nanosecond time scales for condensed-phase systems, significantly expanding the scope of high-accuracy, predictive simulations of complex molecular systems powered by data-driven many-body potential energy functions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

FLAMES─Fast, Low-Storage, Accurate, and Memory-Efficient Adaptive Sampling─Approach to Resolve Spatially Dependent Dynamics of Molecular Liquids

Many critical phenomena in soft matter occur at large length scales, necessitating the resolution of their structure and dynamics at low wavenumbers. However, resolving wavenumber-dependent dynamics computationally via molecular dynamics simulations presents significant challenges, as these phenomena span several orders of magnitude in both time and length scales, resulting in high computational costs and memory demands. Here, this work highlights the computational and memory challenges associated with analyzing molecular trajectories in reciprocal space and demonstrates a method to address them. We introduce FLAMESFast, Low-storage, Accurate, and Memory-Efficient adaptive Sampling, which is a direct method for calculation of structure factors, allowing us to select only the required number of wavevectors for binning. We also use wavenumber-dependent time steps to extract dynamics. Our FLAMES approach effectively mitigates computational and memory/storage bottlenecks. We demonstrate the method using simulations of a model system, liquid octane, at various temperatures. Comparisons with experimental data and real space computation show that the FLAMES technique achieves high accuracy in resolving temperature- and spatially dependent dynamics while being significantly more computationally efficient and requiring less memory and storage than methods based on a uniform wavevector grid and fixed temporal spacing.

Chen, Guang [Argonne National Laboratory (ANL), Ar↗
DOE OSTI2026

Transfer Learning Meets Embedded Correlated Wavefunction Theory for Chemically Accurate Molecular Simulations: Application to Calcium Carbonate Ion Pairing

Achieving chemical accuracy for molecular simulations remains a central challenge in computational chemistry. Here, we present an embedded correlated wavefunction transfer learning (ECW-TL) framework for accurately simulating molecular dynamics in the condensed phase. ECW-TL incorporates high-level electron exchange and correlation effects in ECW theory while preserving the training and computational efficiency of machine-learned interatomic potentials. We demonstrate the framework on Ca 2+ –CO 3 2– ion pairing in aqueous solution, a key process underlying CO 2 mineralization in seawater. As proof of principle, we first show that fine-tuning a DFT-revPBE-D3(BJ) baseline model with embedded-DFT-SCAN data reproduces the DFT-SCAN free-energy surface within 1 kcal/mol across all solvation states. Extending the framework to embedded MP2 and localized natural-orbital CCSD(T) further refines the free-energy profile, revealing the crucial role of exact electron exchange and correlation in determining ion-pair stability and structure. The computed ion-pair association free energy is in quantitative agreement with experimental measurements, further validating the accuracy of the ECW-TL framework. ECW-TL thus provides a general, data-efficient route for transferring CW accuracy to efficient simulations of complex aqueous and interfacial chemical processes.

cluster chemistry↗
DOE OSTI2026

Charge Transport in Solvated Donor–Acceptor Functionalized Peptoids: Molecular Dynamics and Rate Theory

Scalable solar-energy conversion requires photoactive materials that combine the efficiency of natural photosynthetic systems with the stability and processability needed for practical applications. Achieving reliable charge transport in soft, self-assembled organic materials remains challenging, as structural fluctuations and environmental effects strongly influence charge-transfer (CT) rates. Here, we present a broadly applicable computational framework for evaluating CT rates in the condensed phase, combining Fermi’s golden rule rate theory with inputs from all-atom molecular dynamics (MD) simulations and first-principles electronic-structure calculations. The approach does not rely on system-specific parametrization and is applicable to a wide range of soft and disordered materials. We demonstrate the applicability and usefulness of the framework on redox-active peptoids functionalized with iron–porphyrin (Fe–P) complexes, a bioinspired platform with programmable donor–acceptor units and tunable three-dimensional organization. The calculated CT rates exhibit strong sensitivity to molecular conformation, with variations spanning several orders of magnitude. This dependence is shown to arise from the pronounced variation in diabatic electronic coupling with the relative orientations and separations of the Fe–P complexes across the conformational ensemble. The framework provides a consistent route for connecting atomistic structure to CT kinetics in the condensed phase and enables analysis of structure–rate relations in organic semiconducting systems.

Charge transfer↗
DOE OSTI2026

Molecular Modeling of Surfactant Interaction on Phospholipid Bilayers Mimicking Corneal Epithelium

Surfactants found in consumer products can compromise eye corneal membrane integrity upon accidental exposure. Traditional in vitro and in vivo approaches to evaluate membrane–surfactant interaction pose experimental limitations such as species variability, reproducibility, and most often do not provide the overall picture. These limitations motivate the use of in silico models to study phenomena like cellular disruption assays caused by surfactants at the molecular scale. In this work, coarse-grained molecular dynamics simulations have been employed to investigate how nonionic alcohol ethoxylate (AE) and anionic surfactant alcohol ethoxy sulfate (AES) interact with lipid bilayer liposomes that mimic corneal epithelial cell membranes. The spherical liposome is composed of 1,2-dihexadecanoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-di(9Z-octadecenoyl)-sn-glycero-3-phosphoethanolamine (DOPE), 1,2-di(9Z-octadecenoyl)-sn-glycero-3-phospho-l-serine (DOPS), and cholesterol, resembling the composition of the corneal epithelial cells’ membrane bilayer. The simulation consisted of varying degrees of representative surfactant compositions and two initial types of surfactant configurations within or outside the liposome. Our results reveal that both surfactants induce outer leaflet bulging, agreeing with membrane solubilization models. The more highly ethoxylated surfactant, AE, caused more consistent inner leaflet disruption than AES, resulting in significantly more water permeation and membrane thinning. In addition, both surfactants increase the lateral diffusion of lipids within the membrane layers, with higher ethoxylated AE showing a stronger effect than AES. This study demonstrates how surfactant structure and localization influence bilayer membrane integrity, offering mechanistic insights into the irritation potential, thus guiding the rational design of effective surfactant-based formulations.

Lipids↗
DOE OSTI2020

Data-Driven Many-Body Models for Molecular Fluids: CO 2 /H 2 O Mixtures as a Case Study

In this study, we extend the scope of the many-body TTM-nrg and MB-nrg potential energy functions (PEFs), originally introduced for halide ion–water and alkali-metal ion–water interactions, to the modeling of carbon dioxide (CO2) and water (H2O) mixtures as prototypical examples of molecular fluids. Both TTM-nrg and MB-nrg PEFs are derived entirely from electronic structure data obtained at the coupled cluster level of theory and are, by construction, compatible with MB-pol, a many-body PEF that has been shown to accurately reproduce the properties of water. Although both TTM-nrg and MB-nrg PEFs adopt the same functional forms for describing permanent electrostatics, polarization, and dispersion, they differ in the representation of short-range contributions, with the TTM-nrg PEFs relying on conventional Born–Mayer expressions and the MB-nrg PEFs employing multidimensional permutationally invariant polynomials. By providing a physically correct description of many-body effects at both short and long ranges, the MB-nrg PEFs are shown to quantitatively represent the global potential energy surfaces of the CO 2 –CO 2 and CO 2 –H 2 O dimers and the energetics of small clusters, as well as to correctly reproduce various properties in both gas and liquid phases. Furthermore, building upon previous studies of aqueous systems, our analysis provides further evidence for the accuracy and efficiency of the MB-nrg framework in representing molecular interactions in fluid mixtures at different temperature and pressure conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗