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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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Investigating property-porosity relationships for micro-architected lattice structures

Micro-architected structures are increasingly valued for their light weight and tunable mechanical properties; this class of material includes sheet structures like the Schöen gyroid and beam lattices like the octet. For design purposes, it is critical to understand how to tune the relative density (RD) to obtain desired mechanical properties. This study investigates the mechanical response of Ti-6Al-4V gyroid structures, spanning a broad range of RDs (0.03–0.90), unit cell sizes (1–4 cm), and sheet thicknesses (0.2–7.8 mm). Results demonstrate that the classical Gibson-Ashby power law scaling between RD and modulus and yield stress does not adequately capture the response over a wide range of RDs, nor does it extrapolate correctly to the fully dense solid. Analytical models, in concert with experimental results and high-fidelity finite element calculations, show that the deviation from Gibson-Ashby reflects a transition from structure-dominated to material-dominated behavior. Distinctions are drawn between scaling relationships and property-porosity models, and an analytical model is proposed to better capture the evolution of mechanical properties with RD. These observations are mirrored in other architected topologies, like the octet, and highlight the importance of understanding the relationship between mechanical properties and geometry for design purposes.

Materials science↗
DOE OSTI2025

A hybrid calorimetry-simulation model of mixing enthalpy for molten salt

Calorimetric determination of enthalpies of mixing (ΔH mix ) in multicomponent molten salts is often interpreted using empirical models that lack physically meaningful parameters. However, for improving pyrochemical separation of spent nuclear fuel, where lanthanides are major fission products and critical elements, a deeper thermodynamic understanding of the link between excess thermodynamic properties and solvation structure is critically needed. In this work, we implement a hybrid and physics-informed framework, MIVM+Calorimetry+AIMD, which integrates experimentally measured ΔH mix (via high temperature drop calorimetry) with solvation structures from ab initio molecular dynamics (AIMD). This approach is demonstrated using LaCl 3 mixed with eutectic LiCl-KCl (58 mol% – 42 mol%) at 873 K and 1133 K. MIVM-derived parameters enable extrapolation of excess Gibbs energy and La 3+ activity across compositions. In contrast, direct ΔH mix predictions from AIMD and polarizable ion model simulations deviate significantly. By incorporating experimentally benchmarked solvation structures into an interpretable thermodynamic model, the MIVM+Calorimetry+AIMD formalism achieves higher accuracy and generalizable method for studying molten salts, offering a robust path for understanding and optimizing molten salt chemistry relevant to nuclear fuel cycles and separation science.

Goncharov, Vitaliy G. [Washington State Univ., Pul↗
DOE OSTI2025

The design space of E(3)-equivariant atom-centred interatomic potentials

Abstract Molecular dynamics simulation is an important tool in computational materials science and chemistry, and in the past decade it has been revolutionized by machine learning. This rapid progress in machine learning interatomic potentials has produced a number of new architectures in just the past few years. Particularly notable among these are the atomic cluster expansion, which unified many of the earlier ideas around atom-density-based descriptors, and Neural Equivariant Interatomic Potentials (NequIP), a message-passing neural network with equivariant features that exhibited state-of-the-art accuracy at the time. Here we construct a mathematical framework that unifies these models: atomic cluster expansion is extended and recast as one layer of a multi-layer architecture, while the linearized version of NequIP is understood as a particular sparsification of a much larger polynomial model. Our framework also provides a practical tool for systematically probing different choices in this unified design space. An ablation study of NequIP, via a set of experiments looking at in- and out-of-domain accuracy and smooth extrapolation very far from the training data, sheds some light on which design choices are critical to achieving high accuracy. A much-simplified version of NequIP, which we call BOTnet (for body-ordered tensor network), has an interpretable architecture and maintains its accuracy on benchmark datasets.

Computer Science↗
DOE OSTI2025

Advancing molecular machine learning representations with stereoelectronics-infused molecular graphs

Molecular representation is a critical element in our understanding of the physical world and the foundation for modern molecular machine learning. Previous molecular machine learning models have used strings, fingerprints, global features and simple molecular graphs that are inherently information-sparse representations. However, as the complexity of prediction tasks increases, the molecular representation needs to encode higher fidelity information. This work introduces a new approach to infusing quantum-chemical-rich information into molecular graphs via stereoelectronic effects, enhancing expressivity and interpretability. Learning to predict the stereoelectronics-infused representation with a tailored double graph neural network workflow enables its application to any downstream molecular machine learning task without expensive quantum-chemical calculations. We show that the explicit addition of stereoelectronic information substantially improves the performance of message-passing two-dimensional machine learning models for molecular property prediction. We show that the learned representations trained on small molecules can accurately extrapolate to much larger molecular structures, yielding chemical insight into orbital interactions for previously intractable systems, such as entire proteins, opening new avenues of molecular design. Finally, we have developed a web application (simg.cheme.cmu.edu) where users can rapidly explore stereoelectronic information for their own molecular systems.

Boiko, Daniil A↗
DOE OSTI2026

A Permanently Porous Chalcogen-Bonded Organic Framework

The nature of connectivity between constituent atomic or molecular building blocks is fundamental in shaping the properties and functionality of materials. The extrapolation of emergent interatomic interactions to enable functional materials has driven transformative technological advancements. However, the bonding interactions used in material design have been largely static since the emergence of dynamic covalent chemistry ~30 years ago. Here we demonstrate that non-covalent chalcogen bonding (Ch-bonding) is a distinct mode of interatomic connectivity for constructing functional materials by design. This is established by leveraging self-complementary assembly of 1,2,5-telluradiazole moieties to construct a honeycomb-type permanently porous Ch-bonded organic framework, assembled and stabilized solely through non-covalent Te...N contacts. Empirical and computational studies of electronic structure, structural healing and lattice dynamics highlight the pi-type electronic communication, controlled assembly and modulated lattice dynamics in Trip3Tez-I arising directly from the unique nature of the Te...N Ch-bonding that holds substantial implications for next generation crystalline semiconductors. In addition to introducing a distinct class of permanently porous frameworks, this work establishes Ch-bonding as a programmable molecular tool for constructing functional materials with distinct properties.

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

Effect of rare earth size on network structure and glass forming ability in binary aluminum garnets

Rare earth aluminate glasses are potentially useful for optical, luminescence, and laser applications. As reluctant glass formers, these materials exhibit unconventional atomic structures. To better understand how their structures correlate with glass formation, we investigate two rare earth aluminum garnet melts, La 3 Al 5 O 12 (LAG) and Yb 3 Al 5 O 12 (YbAG), which represent the relative extremes of good and poor glass forming ability in rare earth aluminates. Structural models have been refined to high-energy X-ray diffraction data over 1340–2740 K. Both melts contain mixtures of AlO 4 , AlO 5 , and AlO 6 polyhedra, with larger fractions of [5] Al and [6] Al in YbAG. Extrapolation of the Al–O coordination distributions to the glass transition match closely with 27 Al nuclear magnetic resonance measurements of (La 1−z Y z ) 3 Al 5 O 12 glasses, z = 0 to 1. During cooling, the mean coordination numbers increase for La–O in LAG from 6.45(8) to 6.98(8) and for Yb–O in YbAG from 6.02(8) to 6.21(8). Linkedness among Al–O polyhedra at ∼2450 K is mostly corner-sharing, with 9% edge-sharing in LAG and 19% in YbAG. Among [4] Al units, both melts have 6% edge-sharing that convert to all corner-sharing upon cooling. Network connectivity is compared using a newly defined metric, K n , that is similar to the Q n distribution but that accounts for the edge-sharing and triply bonded oxygen present in these melts. The lower glass forming ability in YbAG as compared to LAG correlates with more edge-sharing, associated with the larger fractions of [5] Al and [6] Al, and lower connectivity among [4] Al units.

Wilke, Stephen K. [Materials Development, Inc., Ar↗
DOE OSTI2026

Investigating trends in actinide covalency and magnetism with 35/37 Cl SSNMR spectroscopy and first-principles calculations

Solid-state NMR (SSNMR) spectroscopy is a powerful technique for studying actinide chemistry but has been significantly limited due to the complex paramagnetism, and radiological hazards presented by these materials. Lanthanide and actinide salts often feature magnetic ordering and can be paramagnetic, ferromagnetic, or antiferromagnetic depending on temperature and electronic structure. Paramagnetic interactions can manifest in SSNMR both as secular spectral shifts and/or couplings as well as contributions from non-secular relaxation. Both effects can be directly measured with NMR and used to extrapolate rich chemical information such as coordination environments, bonding characteristics, local molecular dynamics, and correlation times. Typically, these studies are carried out on high-γ and highly abundant NMR-active isotopes (e.g., 1 H, 6/7 Li, 19 F, 23 Na, etc.) or on enriched rare isotopes (e.g., 2 H and 17 O), which can be expensive. Herein, we present a facile methodology to measure the 35/37 Cl electric-field gradient (EFG) and paramagnetic shift anisotropy (SA) tensor components using static wideline SSNMR measurements of LaCl 3 , NdCl 3 , UCl 3 , and UCl 4 . The static powder spectra were measured with both 35 Cl and 37 Cl SSNMR to increase the fidelity of the extracted tensor parameters. Variable temperature NMR of a select case confirms the Curie–Weiss paramagnetism. Relaxation measurements of both nuclei further corroborate observations owing to the paramagnetic relaxation enhancement and reveal simultaneous quadrupolar relaxation mechanisms. Density functional theory (DFT) calculations using Hubbard U corrections to the uranium valence orbitals show excellent agreement with experimental EFG tensor parameters and help describe the bonding characteristics in these lanthanide and actinide systems.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Spectroscopic investigation of cation effects in U(VI)-NO3- complexation in aqueous solutions

Understanding and manipulating uranyl speciation in aqueous solutions is critical for advancing chemical separation, sensing, and understanding environmental transport of uranyl. We report on the significant enhancement in the complexation of uranyl with nitrate in aqueous solutions containing quaternary ammonium cations leading to the formation of anionic complexes. We base this on the comparative study of the effect of monovalent cations (Na+, Li+, NH4+, and N(CH3)4+) on the complexation equilibria of uranyl-nitrate in solutions, probed by time-resolved laser induced fluorescence spectroscopy (TRLFS). Lifetime-corrected spectra, obtained by extrapolating the time-resolved spectra to t = 0, were used to study speciation to mitigate the effects of variations in the fluorescence lifetimes that depend on extraneous factors such as dynamic quenching. We demonstrate that the lifetime-corrected spectra can be used to determine uranyl speciation in aqueous solutions where the mono-nitrate complex forms, and in acetonitrile with N(CH3)4NO3 where di-nitrate and tris-nitrato species are formed. Aqueous solutions containing N(CH3)4+ are shown to promote the formation of higher complexes of uranyl compared to other inorganic nitrate salts based on the higher redshift in the spectra, poor fits to the two-component model, and the higher apparent formation constants. Comparing the trends in uranyl speciation in the presence of N(CH3)4+ in aqueous and acetonitrile solutions, it is proposed that the quaternary ammonium cations (quats) promote the formation of anionic complexes of uranyl by the ion-association mechanism. These results provide a basis for designing quat-assisted separation systems that target anionic actinide species in aqueous solutions.

Nayak, Srikanth (ORCID:0000000302135796)↗
DOE OSTI2024

Avoiding pitfalls in molecular simulation of vapor sorption: Example of propane and isobutane in metal–organic frameworks for adsorption cooling applications

This study introduces recommendations for conducting molecular simulations of vapor adsorption, with an emphasis on enhancing the accuracy, reproducibility, and comparability of results. The first aspect we address is consistency in the implementation of some details of typical molecular models, including tail corrections and cutoff distances, due to their significant influence on generated data. We highlight the importance of explicitly calculating the saturation pressures at relevant temperatures using methods such as Gibbs ensemble Monte Carlo simulations and illustrate some pitfalls in extrapolating saturation pressures using this method. For grand canonical Monte Carlo (GCMC) simulations, the input fugacity is usually calculated using an equation of state, which often requires the critical parameters of the fluid. We show the importance of using critical parameters derived from the simulation with the same model to ensure internal consistency between the simulated explicit adsorbate phase and the implicit bulk phase in GCMC. We show the advantages of presenting isotherms on a relative pressure scale to facilitate easier comparison among models and with experiment. Extending these guidelines to a practical case study, we evaluate the performance of various isoreticular metal–organic frameworks (MOFs) in adsorption cooling applications. This includes examining the advantages of using propane and isobutane as working fluids and identifying MOFs with a superior performance.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Internal measurements of electromagnetic geodesic acoustic mode (GAM) in EAST plasmas

Velocity, density, and magnetic fluctuations of the geodesic acoustic mode (GAM) have been measured using the Doppler backscattering system, Faraday-effect polarimeter-interferometer, and external pick-up coils in the Experimental Advanced Superconducting Tokamak. Simultaneous measurements of density and velocity fluctuations at the midplane and top of plasmas demonstrate that m = 1 density fluctuations are quantitatively balanced by the compression of perpendicular flow fluctuations. Furthermore, internal magnetic fluctuations associated with GAM have now been directly measured by laser-based Faraday-effect polarimetry for the first time. Line-averaged magnetic fluctuations (up to 16 Gauss, B̃¯R,GAMBT∼0.066%) are significantly larger than those extrapolated from edge coils (a few Gauss) and that magnetic fluctuations increase with β. The observed discrepancy between finite β theory and experimental data indicates the need for further theoretical investigations.

Physics↗
DOE OSTI2024

Diagnostic development and needs for laser driven MeV x-ray radiography

Laser-driven MeV x-ray radiography of dynamic, dense objects demands a small, high flux source of energetic x-rays to generate an image with sufficient quality. Understanding the multi-MeV x-ray spectrum underscores the ability to extrapolate from the current laser sources to new future lasers that might deploy this radiography modality. Here, in this study, we present a small study of the existing x-ray diagnostics and techniques. We also present work from National Ignition Facility-Advanced Radiographic Capability, where we deploy three diagnostics to measure the x-ray spectrum up to 30 MeV. Finally, we also discuss the needs and developments of two new diagnostics: a single crystal scintillator spectrometer and a fast decay activation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Improving equations of state calibrations in the toroidal DAC—The case study of molybdenum

We report an updated isothermal equation of state (EoS) of molybdenum (Mo) obtained by compression in beveled and toroidal diamond-anvil cells (DACs). For an improved compression environment, we developed a copper (Cu) pressure-transmitting medium (PTM) for the toroidal diamond-anvil cell samples, as it is a soft metal compared to Mo with a well calibrated EoS. A Ne PTM was used for the conventional beveled DAC samples. The unit-cell volumes of Mo were measured to 336(1) GPa in the Cu PTM and 231.2(6) GPa in the Ne PTM at room temperature. We additionally calculated elastic stiffness and compliance constants and evaluated the uniaxial stress of Mo and Cu with pressure. A new EoS for Mo is presented from data collected in all sample environments and compared to our theoretical predictions as well as previous compression studies of Mo. The (200) lattice plane of Mo produced the lowest volumes across the pressure range of this study for all compression environments, suggesting that it is less affected by nonhydrostatic stresses in the DAC compared to the other observed diffraction planes. The presented Mo EoS is compatible with extrapolations of EoS fits of Mo in helium (He) within ~1% at 330 GPa. Results from this work demonstrate that compressing a sample in a softer metal in the toroidal DAC can improve the compression environment and result in measured sample volumes comparable to those collected in noble-gas media at multi-megabar conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Anion photoelectron spectroscopy and chemical bonding of ThS 2 – and ThSO –

Anion photoelectron spectra of ThSO – and ThS 2 – were recorded using the third (355 nm) harmonic of an Nd-YAG laser; these provided the measured vertical detachment energies of each anion. The experiments are supported by extensive coupled cluster calculations on ThSO, ThSO – , ThS 2 , and ThS 2 – , as well as the oxygen congeners ThO 2 and ThO 2 – . The ab initio calculations, which included complete basis set extrapolations, spin–orbit effects using four-component coupled cluster, and higher-order correlation contributions through CCSDT(Q), yielded an adiabatic electron affinity for ThO 2 – that was within 0.02 eV of the previously determined experimental value. The singly occupied molecular orbital (SOMO) in all three anions corresponds primarily to the 7s orbital on Th. Successive substitution of S for each O in ThO 2 leads to larger electron affinities and smaller bond angles in the neutral molecules, but larger angles in the anions. As demonstrated by Franck–Condon simulations of the spectra using the CCSD(T) spectroscopic constants, substitution of O by S significantly complicates the resulting detachment spectra due to the lower vibrational frequencies in the sulfur species. Altogether the calculated vertical detachment energies are in very good agreement with the experiment. In addition to the adiabatic electron affinities of each species, atomization energies and heats of formation have also been determined via the FPD approach with expected uncertainties of 1–2 kcal/mol.

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

Progress toward hydro-equivalent ignition in OMEGA direct-drive DT-layered implosions

Considerable progress has been made in deuterium-tritium-layered implosion experiments on the OMEGA Laser System, bringing the prospects for thermonuclear ignition in direct-drive configurations with megajoule-class lasers closer to reality. Doing so has required navigating the balance between improved 1D performance and multidimensional stability. Using statistical modeling based on over 350 cryogenic implosions to identify various degradation mechanisms, and combined with multidimensional simulations and experimental techniques such as target offsets to combat residual flows, core conditions have repeatably been achieved that extrapolate to the burning-plasma state when scaled to 2.15 MJ of symmetric laser illumination. Using high implosion velocities (⁠> 450 km/s) and moderately high adiabats (⁠~5⁠), these experiments produced record-high scaled Lawson parameters in direct drive equal to 89 ± 2% of that required for ignition with expected yields of up to 1.5 ± 0.2 MJ. To improve these results still further, focused physics studies are performed to improve physics understanding and identify routes to even greater performance. Recent studies include investigations into the impact of mounting features, laser imprint, reduced fuel temperatures, and greater on-target intensities through subscale experiments. This manuscript gives a summary of the cryogenic direct-drive program on the OMEGA laser, including routes taken to achieve the current best performance, the status of recent focused physics investigations, and future designs—such as target solutions to laser imprint and reducing vapor density to increase convergence—that are expected lead to the demonstration of hydro-equivalent ignition on OMEGA.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Novel application of neutrinos to evaluate U.S. nuclear weapons performance

There is a growing realization that neutrinos can be used as a diagnostic tool to better understand the inner workings of a nuclear weapon. Robust estimates demonstrate that an Inverse Beta Decay (IBD) neutrino scintillation detector built at the Nevada Test Site with a 1000-ton active target mass at a standoff distance of 500 m would detect thousands of antineutrino events per nuclear test. This would provide less than 4% statistical error on the measured antineutrino rate and 5% error on antineutrino energy. Extrapolating this to an error on the test device explosive yield requires knowledge from evaluated nuclear databases, non-equilibrium fission rates, and assumptions on internal neutron fluxes. Initial calculations demonstrate that the total number of neutrinos emitted per fission in the first 10 3 s after a short pulse of 239 Pu fission is about a factor of two less than that from Pu fissioning under steady state conditions. Furthermore, there are significant energy spectral differences as a function of time after the pulse that must be considered. These and other model dependencies will be discussed in the paper. In the absence of nuclear weapons testing, many of the technical and theoretical challenges of a full nuclear test could be mitigated with a low cost smaller scale 20 ton fiducial mass IBD demonstration detector placed near a pulsed reactor. Potential reactors include the Texas A&M University TRIGA 1 GW–10 ms pulsed facility or the Sandia Annular Core Research Reactor. The short duty cycle and repeatability of pulses would provide critical real environment testing and measurements, which would be valuable for planning a possible real test shot in the future. Furthermore, the antineutrino rate as a function of time data would provide unique constraints on fission databases and model assumptions. Finally, there are impactful science drivers such as sensitive searches for ∼1 eV 2 sterile neutrinos and ∼MeV scale axions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Machine learning enhanced predictions of ICRF heating: Overcoming numerical limitations via data curation

In this work, we present the development of robust surrogate models for Ion Cyclotron Range of Frequencies (ICRF) and High-Harmonic Fast Wave (HHFW) heating predictions in fusion plasmas. Building upon our previous efforts to achieve real-time capable models, we identify the cause of the outliers found using TORIC in certain HHFW heating scenarios. The outliers are observed to be spurious ion Bernstein wave (IBW)-like modes caused by a wavelength control algorithm designed to address challenging scenarios with high perpendicular wavenumbers. The effect arises from the modulation in the perpendicular susceptibility, which can induce sign reversal and IBW-like propagation for scenarios featuring normalized ion Larmor radius λ i ≫ 1. We use TORIC with this algorithm disabled to generate a novel HHFW-NSTX database that is free of outliers. Surrogate models trained on this database, including Random Forest Regressor (RFR), Multi-Layer Perceptrons, and Gaussian Process Regressors (GPR), demonstrate the ability to accurately predict HHFW heating profiles, with regression scores of R 2 ∈[0.93−0.99]. Additionally we demonstrate that it is possible to generalize predictions beyond training data by the use of both RFR and GPR models, enabling the prediction of scenarios previously limited to the original model. GPR models also provide uncertainty quantification, offering insights into model confidence. This work introduces a comprehensive Verification, Validation, and Uncertainty Quantification methodology for surrogate modeling, applicable not only to ICRF heating but also to other RF heating challenges and fusion physics problems. Beyond accelerated inference, these models show effective extrapolation capabilities, providing an alternative for addressing numerical challenges.

Artificial neural networks↗
DOE OSTI2025

Implementation of compound refractive lenses for large field-of-view x-ray phase-contrast imaging during hypervelocity impact experiments

Synchrotron x-ray phase-contrast imaging (XPCI) offers time-resolved visualization of dynamic compression phenomena, but its intrinsically small field-of-view (FOV) limits the time that key features remain in frame. A novel approach to enlarge the FOV is achieved by positioning a two-dimensional parabolic compound refractive lens (CRL) upstream of the sample to deliberately defocus the white beam. Ray-tracing simulations and XPCI measurements show that this CRL configuration can expand the beam by ∼50% vertically and ∼15% horizontally based on the full width at half-maximum of the beam. Implementing the CRL, however, attenuates the photon flux and lowers signal-to-noise ratio (SNR). Task-based analysis using a calibration grid (30 μm dots) showed that both setups fail to consistently meet the Rose criterion (SNR ≥ 5) for features of this size in single-bunch imaging. Extrapolating the measured SNR Rose values suggests that the minimum consistently detectable feature lies closer to 30–40 μm for the standard XPCI setup and above 40 μm for CRL-XPCI. Despite this limitation, the CRL configuration nearly doubles the illuminated area, enabling simultaneous tracking of front and rear observations of boron carbide targets subjected to rod and sphere impacts at 1.0–2.6 km/s. Image tracking algorithms and photonic Doppler velocimetry were used to measure penetration and rear-surface velocity histories. Together, these measurements capture crack fronts, penetration, and material breakout, offering new benchmark data for validating high-strain-rate constitutive models of ceramic materials.

Ceramic materials↗
DOE OSTI2026

Bootstrap embedding for interacting electrons in phonon coherent-state mean field

Here, we develop a Fermi–Bose bootstrap embedding framework for the ground state of interacting electrons coupled to a phonon mean field. The method combines bootstrap embedding for correlated electrons with a self-consistent coherent-state mean-field treatment for phonons. This method models the interacting electron–phonon problem as a system of correlated electrons traveling in a self-consistently specified potential landscape, allowing for efficient treatment of large lattice systems. Convergence of the methods for fragment size and total system size is demonstrated for the one-dimensional Hubbard–Holstein model for up to 350 sites. Finite-size scaling is performed to extrapolate to the infinite system size. Benchmarking against the density matrix renormalization group for a small 8-site system at half- and quarter-filling shows an orders-of-magnitude runtime advantage. The comparison further reveals that the method performs best in regimes dominated by localization, such as the Mott insulating phase and the strong-coupling tiny polaron regime, where the local embedding ansatz is still valid. However, due to the mean-field treatment for phonons, we find limitations of our methods in the weakly coupled delocalized region and at the Peierls transition, where quantum phonon fluctuations and long-range kinetic correlations become substantial.

Islam, Shariful [North Carolina State University, ↗