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Analysis of an irradiated uranium sample for source attribution without chemical separation using microplasma ionization and ultrahigh resolution mass spectrometry

The use of element isotope ratios has great potential in not only determining the reactor type used to produce plutonium (Pu) but also in determining the burnup and the time since irradiation. While a powerful nuclear forensic technique, determining element isotope ratios is complicated by severe isobaric interferences when performed on typical inductively coupled plasma mass spectrometers. Such analyses require extensive chemical separations prior to analysis to alleviate the inter-elemental isobars. Ultrahigh mass resolution spectrometry provides a potential alternative, greatly reducing the complexity of sample preparation and turnaround times for these critical measurements. To demonstrate the power of the approach, a sample of irradiated, depleted uranium was analyzed with the liquid sampling—atmospheric pressure glow discharge ion source coupled to an Orbitrap mass spectrometer. The Orbitrap is augmented with an external data acquisition system, Spectroswiss’s FTMS-Booster X2T, allowing collection of extended ion transients, providing higher mass resolution. In using this approach, the 150 Sm/ 149 Sm and 152 Sm/ 149 Sm isotope ratios were found to be within 20% of predicted values without any chemical separations and without mass bias corrections. In addition, the 240 Pu/ 239 Pu isotope ratio was determined, free from the 238 UH + interferences common to the ICP-MS platforms, while at the same time allowing for the determination of U isotopic signatures. While these demonstrative results are from a single sample, the advantages of the microplasma/ultrahigh mass resolution approach to intra-element isotope ratio determinations are clear.

Fuel burnup

In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back

Computational chemistry is an indispensable tool for understanding molecules and predicting chemical properties. However, traditional computational methods face significant challenges due to the difficulty of solving the Schrödinger equations and the increasing computational cost with the size of the molecular system. In response, there has been a surge of interest in leveraging artificial intelligence (AI) and machine learning (ML) techniques to in silico experiments. Integrating AI and ML into computational chemistry increases the scalability and speed of the exploration of chemical space. However, challenges remain, particularly regarding the reproducibility and transferability of ML models. This review highlights the evolution of ML in learning from, complementing, or replacing traditional computational chemistry for energy and property predictions. Starting from models trained entirely on numerical data, a journey set forth toward the ideal model incorporating or learning the physical laws of quantum mechanics. This paper also reviews existing computational methods and ML models and their intertwining, outlines a roadmap for future research, and identifies areas for improvement and innovation. Ultimately, the goal is to develop AI architectures capable of predicting accurate and transferable solutions to the Schrödinger equation, thereby revolutionizing in silico experiments within chemistry and materials science.

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Electrically Accelerated Mechanochemical Film Formation by a Phosphonium Phosphate Ionic Liquid: An In Situ Chemical Kinetics Investigation

Powertrains in electric vehicles are exposed to stray currents that accelerate wear and cause failure of mechanical components. These durability issues are further aggravated when using low-viscosity lubricants, which are desired for energy efficiency but create harsher contact conditions at sliding interfaces. This study investigates a phosphonium phosphate ionic liquid as a performance-enhancing additive in a low-viscosity base oil for lubricating electrified sliding interfaces. Ionic liquids can adsorb and react on contact interfaces via stress-assisted chemical reactions, generating nanometric tribofilms that provide protection against wear. However, the effect of electric fields on the mechanochemistry of ionic liquids is poorly understood, hindering their adoption in lubricants for electrified powertrains. This article reports an in situ optical interferometry study of ionic liquid derived tribofilm growth kinetics at stressed sliding/rolling interfaces under direct currents. The application of electric currents accelerated tribofilm formation up to a critical current density (∼1.4 A/mm 2 ), beyond which pitting-induced wear dominated. The tribofilms were composed of iron phosphates, iron oxides, and carbon species, with iron oxides becoming predominant under applied currents. These tribofilms prevented the scuffing failure of steel surfaces under electrified conditions. Based on the results, a kinetic model is proposed that integrates electric current effect into the classical stress-assisted thermal activation framework to allow prediction of tribofilm growth at electrified sliding contacts. This framework provides crucial guidance for designing next-generation lubricants for electrified transportation and power generation systems.

additives

Microstructural Evolution and Mechanical Properties of LP-DED NASA HR-1 – A Hydrogen Resistant AM Superalloy for Space Propulsion Applications

The National Aeronautics and Space Administration (NASA) has actively pursued metal additive manufacturing (AM) technologies for spaceflight applications since the late 2000s. AM offers transformative advantages in cost, schedule, part consolidation, and design flexibility. Among the various AM techniques, laser powder directed energy deposition (LP-DED) is particularly well suited for fabricating complex geometries with fine feature resolution. In propulsion systems that utilize high-pressure gaseous hydrogen—such as liquid hydrogen rocket engines—hydrogen environment embrittlement (HEE) presents a serious threat to material performance 1,2 . Mechanical property degradation under these conditions can compromise component reliability, especially under cyclic loading. To address this challenge, NASA developed NASA HR-1 (Hydrogen Resistant-1) as a solution for liquid rocket engine components operating in hydrogen-rich environments, using the LP-DED technique 3-9 . A key component in a liquid rocket engine is the exhaust nozzle, which is typically regeneratively cooled (regen) due to the high heat flux. NASA HR-1 was specifically developed for regen nozzle applications using hydrogen as a propellant, providing resistance to HEE, a critical issue for many materials. The AM version of NASA HR-1 was also formulated to achieve high ultimate tensile strength, along with high yield strength and ductility in this environment 5,6 . Low-cycle fatigue (LCF) is another important consideration in nozzle design, as components are expected to endure multiple starts and missions. Additionally, the LP-DED version of the alloy exhibits improved thermal conductivity compared to its wrought counterpart, which benefits nozzle cooling. Overall, NASA HR-1 offers an excellent balance of high strength, HEE resistance, LCF performance, thermal conductivity, and ductility to meet the demanding requirements of channel-cooled nozzles and other components used with hydrogen and other propellants. The LP-DED–processed NASA HR-1 requires several post-processing heat treatment steps to achieve the material properties desirable for its intended application 6 . These steps include stress relief, homogenization, solution annealing, and aging for precipitation hardening. The stress relief treatment mitigates residual stresses accumulated during the LP-DED process and minimizes the potential for distortion. Homogenization, a common step for AM materials, reduces elemental segregation and promotes recrystallization to develop a more equiaxed grain structure. The subsequent solution annealing treatment heats the part to a solid solution temperature to dissolve the undesirable η-phase that forms during cooling from homogenization, followed by rapid cooling to retain an η-phase–free microstructure. Finally, aging promotes precipitation of the strengthening γ′ phase in the alloy. The integration of compositional design and optimized thermal processing enables high-quality LP-DED NASA HR-1 components with excellent microstructural and mechanical stability. Improved chemical and microstructure homogeneity enhances ductility and fatigue resistance—both critical for safe and reliable operation in high-pressure hydrogen environments. NASA has successfully fabricated and hot-fire tested multiple subscale and full-scale channel wall nozzles using LP-DED NASA HR-1 5,6, 9-14 . These efforts included process refinements to support thin-wall construction and various channel geometries. Throughout development, several key observations emerged. After homogenization, the as-built columnar grain structure transforms into a fully equiaxed microstructure. However, subsequent treatments—such as solution annealing and aging—result in changes that are more difficult to track. The grain structure remains largely unchanged, and the γ′ precipitates, typically 5–10 nm in diameter, are beyond the resolution of scanning electron microscopy (SEM). While transmission electron microscopy (TEM) can resolve these fine precipitates, TEM sample preparation is time-consuming and difficult for LP-DED material. As an alternative, differential scanning calorimetry (DSC) offers a useful, qualitative approach to monitor precipitate evolution throughout different stages of heat treatment. The overall goal is to improve the understanding of how heat treatment affects the microstructure and mechanical performance of LP-DED NASA HR-1. This paper presents heat treatment design considerations, microstructural characterization, mechanical testing – including tensile and LCF testing in both air and hydrogen environments.

Superalloy

All-Polyester Multilayer Plastics (‘All-Polyester MLPs’): A Redesign for Inherently Recyclable Plastics

Multilayer plastics (MLPs) are widely used in modern packaging because they combine multiple functions such as oxygen and moisture barriers, mechanical strength, puncture resistance, and heat sealability into lightweight and cost-effective packaging solutions. These attributes are essential for food, beverage, pharmaceutical, and consumer goods packaging. However, conventional commercial MLPs typically consist of five to twelve layers made from chemically incompatible materials, including polyolefins, polyethylene terephthalate, nylon, ethylene-vinyl alcohol (EVOH), adhesives, and tie layers. This complexity makes MLPs extremely difficult to recycle. As a result, the vast majority of multilayer plastics (MLPs) are disposed of through landfilling or incineration. This disposal pathway perpetuates demand for virgin material production, thereby driving high industrial energy consumption, increasing greenhouse gas (GHG) emissions, and contributing to the long-term accumulation of plastic waste. The scope of work included: (1) Design and fabrication of all-polyester multilayer structures using commercially relevant processing methods; (2) Experimental validation of barrier, mechanical, and sealing performance; (3) Demonstration of both mechanical and chemical recycling pathways; and (4) Comprehensive techno-economic analysis (TEA) and life-cycle assessment (LCA) to quantify cost, energy, and environmental impacts.

36 MATERIALS SCIENCE

Cost-effective valorization of 2,3-butanediol to high-value chemicals and jet fuel

Here, this work outlines an optimized process for converting 2,3-butanediol (BDO) into sustainable aviation fuel (SAF) and C4 chemicals. BDO is reactively separated from fermentation broth by forming dioxolanes, which are converted to isobutyraldehyde, methyl ethyl ketone (MEK), and 1,3-butadiene. These intermediates are reduced and dehydrated over Cu/ZSM-5 to form alkenes, which can be oligomerized and hydrotreated to jet-range alkanes. Previous BDO-dioxolane-alkene processes are limited by the requirement for a continuous aldehyde source for dioxolane formation. Brønsted acidic zeolites catalyze dioxolane deacetalization to form isobutyraldehyde and MEK in a >2:1 molar ratio, providing an internal, recyclable aldehyde source. Dioxolane formation optimization was performed to achieve >95% dioxolane yields over Amberlyst-15 and minimize isobutyraldehyde recycle. The overall BDO-dioxolane-fuel process yields an alkane mixture that enables at least a 50% v/v blend with Jet-A. Techno-economic analyses and life cycle assessments for this BDO-dioxolane-fuel process yield scenarios with <$2.50 per gallon gas equivalent and >58% reduction in CO2 emissions.

2,3-butanediol

Ion Transport and Crystal Rotation in Plastic Crystal Electrolytes Under Applied Electric Fields

Organic ionic plastic crystal electrolytes, containing a plastic crystal and lithium salt, offer a potential balance between mechanical and electrochemical properties for solid state lithium-ion battery electrolytes. These electrolytes contain multiple mobile ionic species (three or four), resulting in complex transport mechanisms which have not yet been established. Plastic crystals are defined by long-range positional order and short-range rotational disorder. It is therefore necessary to quantify changes in the local crystal structure of the electrolyte as current flows through it. Herein, we examine the electrochemical properties of pyrrolidinium-based plastic crystal electrolytes containing lithium salt and zwitterion additives, including measurements of current fraction and limiting current. We obtain species-specific insight into electrolyte transport using pulsed-field gradient nuclear magnetic resonance spectroscopy and find that, while the zwitterion additive increases ionic conductivity, it decreases lithium diffusivity with respect to other ionic components. With operando spatiotemporally resolved wide-angle X-ray scattering we observe location-specific crystal rotations due to the passage of ionic current. In conclusion, we posit that reducing energy dissipation due to rotation is essential for using plastic crystal electrolytes in practical applications.

Yap, Kyra M. K. [University of California, Berkele

List of Commercial and Advanced Developmental Niobium-Based Alloys of the Space Age

This report compiles a list of commercial and developmental niobium-based alloys developed during the Space Age (late 1950s through mid-1970s) for extreme-temperature applications, including rocket engine thrust chambers, hypersonic re-entry thermal protection systems, and space fission reactor loops. Niobium (Nb) was widely pursued because it provided the lowest density (~8.6 g/cc) among the primary refractory metals, a high melting temperature (~2470°C), exceptional low-temperature ductility, good formability, and compatibility with liquid alkali metals. An evaluation of physical metallurgy mechanisms, focusing on solid-solution strengthening via heavy refractory solutes (W, Mo, Ta), dual-purpose reactive solutes (Hf, Zr, Ti), and dispersion strengthening using carbides, nitrides, and oxides is presented. Additionally, the report compares Western and Soviet Union metallurgical approaches, explaining how supply chain factors and manufacturing infrastructure influenced element selection, interstitial chemistry, and alloy identification/naming conventions. Cataloging these historical alloy chemical compositions serves as a foundational reference for modern alloy additive manufacturing, thermodynamic CALPHAD modeling, and machine-learning discovery pipelines for next-generation extreme-environment niobium-based alloys.

Physical Metallurgy

Technoeconomic and Emissions Analysis of the Hybrid Redox Process for the Production of Acetic Acid with CO 2 Utilization

The production of oxygenated hydrocarbons, such as acetic acid, using captured CO 2 is a promising pathway to reduce greenhouse gas emissions in the chemical industry. The use of a chemical looping‐based hybrid redox process (HRP) is proposed to convert CO 2 and natural gas into separate CO and syngas streams that can be used to produce various commodity oxygenates, while allowing the beneficial utilization of captured CO 2 . Here, a detailed technoeconomic analysis of HRP applied to the production of acetic acid is presented. Emissions and energy analyses show the ability of HRP to lower the CO 2 emissions for acetic acid synthesis by 74% compared to a conventional steam and autothermal reforming route. HRP also offers a potential 34% reduction in capital costs. Compared to a dry reforming based acetic acid production route, HRP has the potential for significantly lower costs. If integrated with a low carbon energy source, HRP has the potential to achieve a negative emission of greenhouse gas (‐0.50 kg CO 2 per kg acetic acid).

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Manufacturing Research in Support of Saturn V

Research achievements applicable to the production of Saturn V components a r e described in this report. Leakage at the mechanical connections in high-pressure lines has been minimized or eliminated through the use of precisely flared tubes. Flaring to close tolerance is done with a n orbital flaring adapter, and the forming operation is precisely controlled with an electronic control console. A technique of “aging” or heat-treatment hardening of aluminum materials has been used to form cylindrical-tank segments and double-contoured gore segments precisely, and to remove weld distortions). The control of weld porosity has been improved as a result of research which demonstrated the close correlation between electrical energy input per inch of weld and weld porosity and metallurgical quality. Based on this information, the gas metallic arc method has been used successfully for two-pass welding, and thinner gage aluminum has been welded (LOX tunnel to fuel bulkhead) with an MSFC designed gas metallic arc unit.

COMPOSITE MATERIAL

Well-Defined Iron Sites in Crystalline Carbon Nitride

Carbon nitride materials can be hosts for transition metal sites, but Mössbauer studies on iron complexes in carbon nitrides have always shown a mixture of environments and oxidation states. Here we describe the synthesis and characterization of a crystalline carbon nitride with stoichiometric iron sites that all have the same environment. The material (formula C 6 N 9 H 2 Fe 0.4 Li 1.2 Cl, abbreviated PTI/FeCl 2 ) is derived from reacting poly(triazine imide)·LiCl (PTI/LiCl) with a low-melting FeCl 2 /KCl flux, followed by anaerobic rinsing with methanol. X-ray diffraction, X-ray absorption and Mössbauer spectroscopies, and SQUID magnetometry indicate that there are tetrahedral high-spin iron(II) sites throughout the material, all having the same geometry. As a result, the material is active for electrocatalytic nitrate reduction to ammonia, with a production rate of ca. 0.1 mmol cm –2 h –1 and Faradaic efficiency of ca. 80% at −0.80 V vs RHE.

Anions

Energy conversion and transport in molecular-scale junctions

Molecular-scale junctions (MSJs) have been considered the ideal testbed for probing physical and chemical processes at the molecular scale. Due to nanometric confinement, charge and energy transport in MSJs are governed by quantum mechanically dictated energy profiles, which can be tuned chemically or physically with atomic precision, offering rich possibilities beyond conventional semiconductor devices. While charge transport in MSJs has been extensively studied over the past two decades, understanding energy conversion and transport in MSJs has only become experimentally attainable in recent years. As demonstrated recently, by tuning the quantum interplay between the electrodes, the molecular core, and the contact interfaces, energy processes can be manipulated to achieve desired functionalities, opening new avenues for molecular electronics, energy harvesting, and sensing applications. This Review provides a comprehensive overview and critical analysis of various forms of energy conversion and transport processes in MSJs and their associated applications. We elaborate on energy-related processes mediated by the interaction between the core molecular structure in MSJs and different external stimuli, such as light, heat, electric field, magnetic field, force, and other environmental cues. Key topics covered include photovoltaics, electroluminescence, thermoelectricity, heat conduction, catalysis, spin-mediated phenomena, and vibrational effects. Furthermore, the review concludes with a discussion of existing challenges and future opportunities, aiming to facilitate in-depth future investigation of promising experimental platforms, molecular design principles, control strategies, and new application scenarios.

Charge transport

Unlocking superplasticity in medium and high-entropy alloys

Superplasticity, the capacity of materials to sustain extraordinary tensile elongations at elevated temperatures, underpins a range of advanced metal-forming technologies. Conventionally, it is achieved in fine-grained alloys where deformation is dominated by grain-boundary sliding, accommodated by diffusion and dislocation activity. The advent of medium- and high-entropy alloys (M/HEAs), with their high chemical complexity and unconventional phase stability, offers new pathways to superplastic behavior beyond traditional alloy systems. Although investigated only recently, several M/HEAs already exhibit elongations that rival or exceed those of classical superplastic materials, particularly when ultrafine or metastable microstructures are engineered. Here, we review progress in understanding superplastic deformation in M/HEAs, emphasizing the interplay among composition, initial microstructure, thermomechanical processing, and microstructural evolution during high-temperature deformation. We discuss approaches to generating the fine-grained structures necessary for grain-boundary sliding, including severe plastic deformation and tailored heat treatments. We further highlight dynamic phenomena such as phase transformations, evolving grain-boundary chemistry, and deformation-induced grain refinement that can enhance plasticity in these systems. These mechanisms often shift the balance of deformation processes, enabling large elongations even outside classical criteria. Finally, we outline key challenges for application, including cost, scalability, recyclability, and microstructural stability.

klenam, Desmond [University of the Witwatersrand,

High-Order Methods in NASA’s Next Generation of Computational Fluid Dynamics Tools

The missions of the National Aeronautics and Space Administration (NASA) routinely produce unique requirements and challenges for development and application of Computational Fluid Dynamics (CFD) methods. NASA presently embodies four distinct Mission Directorates: Aeronautics Research, Exploration Systems, Science, and Space Operations. These missions generate requirements for systems that operate in a wide variety of environments. They range from the high-speed flight of aerodynamically optimized vehicles operating in the earth’s atmosphere to spacecraft designed for missions that don’t favor aerodynamic optimization, some operating in the atmosphere of planets and planetary moons such as Mars and Venus or Saturn’s moon Titan. Systems supporting these vehicles, such as rocket and jet propulsion, reaction control systems, fluid and thermal transfer systems, etc. can also generate their own unique set of flow phenomena that challenge today’s CFD methodology. Through the NASA Engineering and Safety Center (NESC), NASA annually conducts state-of-the-discipline assessments in fifteen distinct engineering disciplines. These assessments are performed by the NASA Technical Fellows that lead Technical Discipline Teams (TDT) of recognized experts in these fifteen areas. In the Aerosciences discipline, three topics have been identified as the top challenges for the discipline: aero-plume interaction prediction, unsteady separated flows, and aerothermodynamic prediction. These challenge areas are defined by the Agency’s high-risk projects and problems on which the NESC is requested to perform independent testing, analysis, and assessments. When viewed as a whole, these tests, analyses, and assessments provide a clear view of the recurring technical challenges facing Agency engineers and researchers and can be used to guide future research and technology development. The present state-of-the-art in the application of CFD at NASA is the use of Reynolds-Averaged Navier- Stokes (RANS) solvers, primarily executed in a steady-state mode of operation. In isolated cases, Unsteady RANS (URANS) solvers have been employed when steady RANS solutions produce poorly converging or oscillating results or in cases, such as aeroelastic analysis, which require unsteady aerodynamic simulation. For most traditional external and internal aerodynamic flows, structured overset grids or unstructured grids are employed to minimize geometric modeling and grid generation times. Grid adaptation, primarily as a series of coarse-grain intermediate processing steps is also seeing use on particularly complex flow problems and configurations. In the case of aerothermodynamic flows, engineers have been forced to continue to employ structured grid techniques as the present unstructured grid methodology has proven inadequate in the prediction of surface heating. In the area of aero-plume interaction modeling, two-gas, frozen chemistry simulation is generally the state-of-the- art, with some production solvers capable of predicting flows with only a single gas component. Prediction of flows falling into the afore-mentioned top Aerosciences technical challenges have severely stressed the present state-of-the-art in CFD prediction and for some problems, such as unsteady separated flows and aero-plume interaction cases, engineers have begun employing Large Eddy Simulation (LES) and Hybrid RANS/LES techniques. In some isolated aero-propulsion interaction cases, chemically reacting flow simulations have been applied. These methods are highly evolutionary and engineers have little experience in their application, so they cannot be heavily relied upon in today’s application environment. Therefore, this leads one to muse over which numerical technologies will be included in the CFD tools that will be employed 30 years in the future. This presentation will describe specific technical problems that have stressed NASA’s traditional CFD methods to their breaking point and will link these issues to the Agency’s top Aerosciences technical challenges. The discussion will then shift to the characteristics of future CFD solvers that will be required to attack these challenges and how these characteristics differ from the present state-of-the- art. High-order methods certainly appear to have a place in the development of future CFD tools and some of the physical characteristics of our most challenging problems suggest that high-order methods are the only way to effectively solve them. But there are some relatively severe implementation issues that face these methods, particularly in the area of general applicability and robust operation as an engineering tool. Desired characteristics of next-generation CFD solvers will be discussed and the author’s view of which emerging numerical technologies might be employed to address these attributes will also be presented

David M Schuster

High entropy oxides prediction and discovery by the Mixed Enthalpy-Entropy Descriptor

The vast, high-dimensional composition space of high-entropy oxides (HEOs) offers exceptional opportunities for functional materials discovery, yet it also poses a fundamental challenge: the rational and efficient prediction of stable, synthesizable compositions and the corresponding structure–property relationships. Despite growing interest, the field still lacks broadly applicable, physically grounded descriptors capable of navigating various large chemical spaces. Here, we introduce a Mixed Enthalpy–Entropy Descriptor (MEED) that enables rapid, first-principles–based prediction of HEOs synthesizability across diverse chemistries. Using MEED, we perform high-throughput screening of two distinct HEO families: rocksalt oxides and perovskite oxides. The predicted top candidates in each family were experimentally validated. MEED reveals unifying thermodynamic and structural principles governing stability across both chemical compositions and polymorphs, providing mechanistic insight into the formation of high-entropy phases. This work significantly broadens the accessible chemical design space for HEOs and establishes a data-efficient framework for accelerating the discovery of next-generation functional materials.

Yu, Liping [University of Central Florida]

Revealing Hidden Quinones Through Diagnostic MS² Fragmentation of Peptide–Quinone Adducts

Quinones are redox-active components of natural organic matter that mediate electron transfer and influence biogeochemical processes, but many quinones in pyrogenic organic matter (PyOM) remain unresolved because they ionize poorly by mass spectrometry. Here, we present a peptide-tagging approach to improve detection of cysteine-reactive electrophiles in PyOM, with quinones expected to be a dominant subset based on reaction chemistry and selectivity experiments. A cysteine-containing peptide was used to form Michael-addition adducts, enhancing electrospray ionization and enabling untargeted screening by high-performance liquid chromatography-high-resolution tandem mass spectrometry. The method was benchmarked with five quinone standards and applied to extracts from charred plant material as a discovery-level screen for cysteine-reactive targets. We identified 98 quinone-candidate adducts (mean neutral mass ~603 Da), of which more than 70% were not detectable in native MS1 data. Among formula-assigned features, hidden quinone candidates had median (O+N)/C of 0.391 and normalized oxidation state of carbon of -0.281, consistent with relatively low polarity and low oxidation state. These results reveal a previously inaccessible pool of hidden redox-active compounds in PyOM and provide a framework for prioritizing quinone-like electrophiles for confirmation and incorporation into models of fire-driven biogeochemical cycling.

LC-MS/MS

Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments

In this work, we introduce an efficient method, TTN-HEOM, for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme with the bexcitonic generalization of the numerically exact hierarchical equations of motion (HEOM). The method yields a series of quantum master equations for all core tensors in the TTN that efficiently and accurately capture the open quantum dynamics for non-Markovian environments to all orders in the system–bath interaction. These master equations are constructed based on the time-dependent Dirac–Frenkel variational principle, which isolates the optimal dynamics for the core tensors given the TTN ansatz. The dynamics converges to the HEOM when increasing the rank of the core tensors, a limit in which the TTN ansatz becomes exact. We introduce TENSO, tensor equations for non-Markovian structured open systems, as a general-purpose Python code to propagate the TTN-HEOM dynamics. We implement three general propagators for the coupled master equations: two fixed-rank methods that require a constant memory footprint during the dynamics and one adaptive-rank method with a variable memory footprint controlled by the target level of computational error. We exemplify the utility of these methods by simulating a two-level system coupled to a structured bath containing one Drude–Lorentz component and eight Brownian oscillators, which is beyond what can presently be computed using the standard HEOM. Our results show that the TTN-HEOM is capable of simulating both dephasing and relaxation dynamics of driven quantum systems interacting with structured baths, even those of chemical complexity, with an affordable computational cost.

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