SEARCH · Search NASA

Results for “approximation theory”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4

All sources NASA NTRS DOE OSTI

DOE OSTI2024

Resonant inelastic x-ray scattering in the topological semimetal FeSi

The energy spectrum of topological semimetals contains protected degeneracies in reciprocal space that correspond to Weyl, Dirac, or multifold fermionic states. To exploit the unconventional properties of these states, one has to access the electronic structure of the three-dimensional bulk. In this paper, we present a joint theory-experiment study of the electronic structure of a candidate topological semimetal with resonant inelastic x-ray scattering (RIXS). We resolve the bulk electronic states of FeSi using momentum-dependent RIXS at the Fe L 3 edge. We observe a broad excitation continuum devoid of sharp features, consistent with particle-hole scattering in an underlying electronic band structure. Using density functional theory (DFT), we calculate the electronic structure of FeSi and derive a band theory formulation of RIXS in the fast collision approximation to model the scattering process with zero adjustable parameters. While band theory predicts an excitation continuum with broad spectral features similar to the observed ones, discrepancies between theory and experiment suggest the presence of low-energy processes that DFT alone does not account for. Further, this study of RIXS in a topological semimetal shows that RIXS is a useful tool for revealing unanticipated behavior of bulk electronic states in this class of materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Predicting the Slowing of Stellar Differential Rotation by Instability-driven Turbulence

Abstract Differentially rotating stars and planets transport angular momentum (AM) internally due to turbulence at rates that have long been a challenge to predict reliably. We develop a self-consistent saturation theory, using a statistical closure approximation, for hydrodynamic turbulence driven by the axisymmetric Goldreich–Schubert–Fricke instability at the stellar equator with radial differential rotation. This instability arises when fast thermal diffusion eliminates the stabilizing effects of buoyancy forces in a system where a stabilizing entropy gradient dominates over the destabilizing AM gradient. Our turbulence closure invokes a dominant three-wave coupling between pairs of linearly unstable eigenmodes and a near-zero frequency, viscously damped eigenmode that features latitudinal jets. We derive turbulent transport rates of momentum and heat and provide them in analytic forms. Such formulae, free of tunable model parameters, are tested against direct numerical simulations; the comparison shows good agreement. They improve upon prior quasi-linear or “parasitic saturation” models containing a free parameter. Given model correspondences, we also extend this theory to heat and compositional transport for axisymmetric thermohaline-instability-driven turbulence in certain regimes.

Astronomy & Astrophysics↗

DOE OSTI2025

On infinite tensor networks, complementary recovery and type II factors

We initiate a study of local operator algebras at the boundary of infinite tensor networks, using the mathematical theory of inductive limits. In particular, we consider tensor networks in which each layer acts as a quantum code with complementary recovery, a property that features prominently in the bulk-to-boundary maps intrinsic to holographic quantum error-correcting codes. In this case, we decompose the limiting Hilbert space and the algebras of observables in a way that keeps track of the entanglement in the network. As a specific example, we describe this inductive limit for the holographic Harlow-Pastawski-Preskill-Yoshida code model and relate its algebraic and error-correction features. We find that the local algebras in this model are given by the hyperfinite type II$_\infty$ factor. Next, we discuss other networks that build upon this framework and comment on a connection between type II factors and stabilizer circuits. We conclude with a discussion of multiscale entanglement renormalization ansatz networks in which complementary recovery is broken. We argue that this breaking possibly permits a limiting type III von Neumann algebra, making them more suitable ansätze for approximating subregions of quantum field theories.

holographic dualities↗

DOE OSTI2025

Toward improved property prediction of 2D materials using many-body quantum Monte Carlo methods

The field of 2D materials has grown dramatically in the past two decades. 2D materials can be utilized for a variety of next-generation optoelectronic, spintronic, clean energy, and quantum computing applications. These 2D structures, which are often exfoliated from layered van der Waals materials, possess highly inhomogeneous electron densities and can possess short- and long-range electron correlations. The complexities of 2D materials make them challenging to study with standard mean-field electronic structure methods such as density functional theory (DFT), which relies on approximations for the unknown exchange-correlation functional. To overcome the limitations of DFT, highly accurate many-body electronic structure approaches such as diffusion Monte Carlo (DMC) can be utilized. In the past decade, DMC has been used to calculate accurate magnetic, electronic, excitonic, and topological properties in addition to accurately capturing interlayer interactions and cohesion and adsorption energetics of 2D materials. Here, this approach has been applied to 2D systems of wide interest, including graphene, phosphorene, MoS 2 , CrI 3 , VSe 2 , GaSe, GeSe, borophene, and several others. In this review article, we highlight some successful recent applications of DMC to 2D systems for improved property predictions beyond standard DFT.

2D materials↗

DOE OSTI2025

Non-perturbative quarkonium dissociation rates in strongly coupled quark-gluon plasma

Heavy quarks and quarkonia are versatile probes of the transport properties of the hot QCD medium produced in ultra-relativistic heavy-ion collisions (URHICs). A robust description of heavy-flavor transport coefficients requires a microscopic approach that treats the open and hidden heavy-flavor sectors on the same footing. Here, we employ the quantum many-body T -matrix formalism to evaluate the dissociation rates of heavy quarkonia in the quark-gluon plasma (QGP). The basic ingredient is the heavy-light T -matrix, which utilizes a nonperturbative driving kernel constrained by lattice-QCD data. Its resummation in a ladder series provides a much enhanced interaction strength compared to a previously used perturbative coupling to the quasiparticle partons in the QGP. The in-medium quarkonium properties, particularly their temperature-dependent binding energies, are obtained from selfconsistent calculations with the same interaction kernel, including interference effects (also referred to as the imaginary part of the heavy-quark potential) as well as off-shell parton spectral functions. We systematically investigate the interplay of these effects and elaborate on the connections to the dipole approximation used in effective field theory.

effective field theories of QCD↗

DOE OSTI2025

Scalable freeform optimization of wide-aperture 3D metalenses by zoned discrete axisymmetry

We introduce a novel framework for design and optimization of 3D freeform metalenses that attains nearly linear scaling of computational cost with diameter, by breaking the lens into a sequence of radial “zones” with 𝑛-fold discrete axisymmetry, where 𝑛 increases with radius. This allows vastly more design freedom than imposing continuous axisymmetry, while avoiding the compromises of the locally periodic approximation (LPA) or scalar diffraction theory. Using a GPU-accelerated finite-difference time-domain (FDTD) solver in cylindrical coordinates, we perform full-wave simulation and topology optimization within each supra-wavelength zone. We validate our approach by designing millimeter and centimeter-scale, poly-achromatic, 3D freeform metalenses which outperform the state of the art. By demonstrating the scalability and resulting optical performance enabled by our “zoned discrete axisymmetry” (ZDA) and supra-wavelength domain decomposition, we highlight the potential of our framework to advance large-scale meta-optics and next-generation photonic technologies.

Sun, Mengdi [Wesleyan University]↗

DOE OSTI2026

Machine-learning guided search for phonon-mediated superconductivity in boron and carbon compounds

We present a workflow that iteratively combines ab-initio calculations with a machine-learning (ML) guided search for superconducting compounds with both dynamical stability and instability from imaginary phonon modes, the latter of which have been largely overlooked in previous studies. Electron-phonon coupling (EPC) properties and critical temperature (T c ) of 417 boron, carbon, and borocarbide compounds have been calculated with density functional perturbation theory (DFPT) and isotropic Eliashberg approximation. Our study addresses T c convergence of Brillouin zone sampling with an ansatz test, stabilizing imaginary phonon modes for significant EPC contributions, and comparing the performance of two ML models, especially when including compounds of dynamical instability. We predict a few promising superconducting compounds with formation energy just above the ground state convex hull, such as Ca 5 B 3 N 6 (35 K), TaNbC 2 (28.4 K), Nb 3 B 3 C (16.4 K), Y 2 B 3 C 2 (4.0 K), Pd 3 CaB (7.0 K), MoRuB 2 (15.6 K), RuVB 2 (15.0 K), RuSc 3 C 4 (6.6 K) among others.

Nepal, Niraj K. [Ames Laboratory (AMES), Ames, IA ↗

DOE OSTI2024

Understanding and Controlling the Formation of Nonradiative Defects in Blue Organic Triplet Emitters

Phosphorescent organic light-emitting devices (PHOLEDs) suffer from destructive molecular processes due to triplet-polaron and triplet-triplet annihilation. These processes are energetically driven and hence are particularly active in decreasing the lifetime of blue PHOLEDs. It has recently been shown that increasing triplet radiative rates via the Purcell effect effectively extends the device operational lifetime by reducing the triplet radiative lifetime, thus decreasing their density and the probability of triplet-annihilation reactions. We provide an analytical framework using Marcus theory to explain the observed, approximately exponential relationship between exciton energy and device lifetime. From transient drift-diffusion dynamics, we show that the Purcell effect reduces the exciton density in the steady state and increases the photoluminescent yield, thereby reducing defect generation rates and extending the device lifetime. We control the radiative rate of excitons in microcavities, thereby connecting the exciton energy and decay rates with the observed device lifetime. The device lifetime is shown to follow a power-law dependence on the Purcell factor ( PF m ) with m = 1.5 to 2.5, dependent on the TTA-to-TPA ratio and photoluminescence quantum yield. From our analysis, a fivefold increase in PF has the potential to extend the blue PHOLED lifetime by up to 2 orders of magnitude, making the blue PHOLED lifetime comparable to that of state-of-the-art green PHOLEDs. Published by the American Physical Society 2024

Zhao, Haonan (ORCID:0000000190584422)↗

DOE OSTI2024

ELECTRONIC STRUCTURE METHODS AND PROTOCOLS WITH APPLICATION TO DYNAMICS, KINETICS AND THERMOCHEMISTRY

Hydrocarbon combustion involves the reaction dynamics of a tremendous number of species beginning with many-component fuel mixtures and proceeding via a complex system of intermediates to form primary and secondary products. Combustion conditions corresponding to new advanced engines and/or alternative fuels rely increasingly on autoignition and low-temperature-combustion chemistry. In these regimes various transient radical species such as HO2, ROO·, ·QOOH, HCO, NO2, HOCO, and Criegee intermediates play important roles in determining the detailed as well as more general dynamics. A clear understanding and accurate representation of these processes is needed for effective modeling. Given the difficulties associated with making reliable experimental measurements of these systems, computation can play an important role in developing these energy technologies. Accurate calculations have their own challenges since even within the simplest dynamical approximations such as transition state theory, the rates depend exponentially on critical barrier heights and these may be sensitive to the level of quantum chemistry. Moreover, it is well-known that in many cases it is necessary to go beyond statistical theories and consider the dynamics. Quantum tunneling, resonances, radiative transitions, and non-adiabatic effects governed by spin-orbit or derivative coupling can be determining factors in those dynamics. Building upon progress made during a period of prior support through the DOE Early Career Program, this project combines developments in the areas of potential energy surface (PES) fitting and multistate multireference quantum chemistry to allow spectroscopically and dynamically/kinetically accurate investigations of key molecular systems (such as those mentioned above), many of which are radicals with strong multireference character and have the possibility of multiple electronic states contributing to the observed dynamics. An ongoing area of investigation is to develop general strategies for robustly convergent electronic structure theory for global multichannel reactive surfaces including diabatization of energy and other relevant surfaces such as dipole transition. Combining advances in ab initio methods with automated interpolative PES fitting allows the construction of high-quality PESs (incorporating thousands of high-level data) to be done rapidly through parallel processing on high-performance computing (HPC) clusters. In addition, new methods and approaches to electronic structure theory will be developed and tested through applications. This project will explore limitations in traditional multireference calculations (e.g., MRCI) such as those imposed by internal contraction, lack of high-order correlation treatment and poor scaling. Methods such as DMRG-based extended active-space CASSCF and various Quantum Monte Carlo (QMC) methods will be applied (including VMC/DMC and FCIQMC). Insight into the relative significance of different orbital spaces and the robustness of application of these approaches on leadership class computing architectures will be gained. Synergy with other components of this research program such as automated PES fitting and multireference quantum chemistry will be used to address challenges encountered by the standard approaches to computational thermochemistry (those being single-reference quantum chemistry and perturbative treatments of the anharmonic vibrational energy, which break down for some cases of electronic structure or floppy strongly coupled vibrational modes).

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Regioselective On-Surface Synthesis of [3]Triangulene Graphene Nanoribbons

The integration of low-energy states into bottom-up engineered graphene nanoribbons (GNRs) is a robust strategy for realizing materials with tailored electronic band structure for nanoelectronics. Low-energy zero-modes (ZMs) can be introduced into nanographenes (NGs) by creating an imbalance between the two sublattices of graphene. This phenomenon is exemplified by the family of [n]triangulenes (n ϵ $\mathbb{N}$). Here, we demonstrate the synthesis of [3]triangulene-GNRs, a regioregular one-dimensional (1D) chain of [3]triangulenes linked by five-membered rings. Hybridization between ZMs on adjacent [3]triangulenes leads to the emergence of a narrow band gap, E g,exp ~ 0.7 eV, and topological end states that are experimentally verified using scanning tunneling spectroscopy. Tight-binding and first-principles density functional theory calculations within the local density approximation corroborate our experimental observations. Our synthetic design takes advantage of a selective on-surface head-to-tail coupling of monomer building blocks enabling the regioselective synthesis of [3]triangulene-GNRs. Detailed ab initio theory provides insights into the mechanism of on-surface radical polymerization, revealing the pivotal role of Au-C bond formation/breakage in driving selectivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Quantum many-body linear algebra, Hamiltonian moments, and a coupled-cluster inspired framework

Here, we propose a general strategy to develop quantum many-body approximations of primitives in linear algebra algorithms. As a practical example, we introduce a coupled-cluster inspired framework to produce approximate Hamiltonian moments and demonstrate its application in various linear algebra algorithms for ground state estimation. Through numerical examples, we illustrate the difference between the ground-state energies arising from quantum many-body linear algebra and those from the analogous many-body perturbation theory. Our results support the general idea of designing quantum many-body approximations outside of perturbation theory, providing a route to new algorithms and approximations.

Algorithms and data structure↗

DOE OSTI2025

Power counting of the pion-dilaton effective field theory

Confining QCD-like theories close to the conformal window have a “walking” coupling. This is believed to lead to a light singlet scalar meson in the low-energy spectrum, a dilaton, which is the pseudo-Nambu-Goldstone boson for the approximate scale symmetry. Extending chiral perturbation theory to include the dilaton requires a new small parameter to control the dilaton mass and its interactions. In our previous work we derived a systematic power counting for the dilaton couplings by matching the effective low-energy theory to the underlying theory using mild assumptions. In this paper we examine two alternative power countings which were proposed in the literature based on a phenomenological picture for the conformal transition. We find that one of these power countings fails, in fact, to generate a systematic expansion; the other coincides with the power counting we derived. We also point out that the so-called Δ -potential coincides with the tree-level potential of the former, invalid, power counting. Published by the American Physical Society 2025

Golterman, Maarten (ORCID:0000000319830672)↗

DOE OSTI2025

Extended Gutzwiller Approximation for Nonlocal Electron-Electron and Electron-Boson Correlations (I): The Theory

Understanding electron-electron and electron-photon correlations is central to uncovering the fundamental mechanisms governing material properties, particularly in systems where strong interactions give rise to emergent phenomena such as superconductivity, magnetism, and polaritonic effects. These correlations play a pivotal role in cavity quantum materials, where hybridized light-matter states enable quantum control over electronic properties. However, capturing both local and nonlocal correlations in these systems presents a significant theoretical challenge. In this work, we extend the Gutzwiller wavefunction method to include nonlocal electron-photon and electron-electron interactions, providing a unified framework to study the intricate interplay between these effects. Our approach accurately captures the long-range correlations induced by photon exchange, enabling the exploration of exotic quantum phases and the effects of cavity coupling on electronic structure. By benchmarking the method across coupling regimes, we reveal the critical role of nonlocal correlations in stabilizing phases, such as superconducting and insulating states, that are inaccessible through local interactions alone. This generalized Gutzwiller framework offers a versatile tool for understanding and designing materials that harness the transformative potential of strong light-matter coupling.

36 MATERIALS SCIENCE↗

DOE OSTI2025

The importance of accounting for the Tolman correction to surface tension for nucleation and growth modeling of Fe clusters

Gibbs free energies of clusters are required for predictive modeling of cluster growth during condensation of a cooling vapor. Here, we present a straightforward method of calculating free energies of cluster formation using the data from molecular dynamics (MD) simulations. We apply this method to iron clusters having from 2 to 100 atoms. The energies obtained are verified by comparing to an MD-simulated equilibrium cluster size distribution in a sub-saturated vapor. We show that these free energies differ significantly from those obtained with a commonly used spherical cluster approximation, which relies on a surface tension coefficient of a flat surface, as it is used in the classical nucleation theory (CNT). We show that the spherical cluster approximation in CNT can be improved by using a cluster-size-dependent Tolman correction for the surface tension. The Tolman length and effective surface tension values were derived for iron clusters, and they significantly differ from the commonly used experimentally measured values. This improved approximation does not account for geometric magic number effects responsible for spikes and troughs in densities of neighbor cluster sizes. Nonetheless, it allows to more accurately model cluster formation from a cooling vapor. It better reproduces the condensation timeline, overall shape of the cluster size distribution, average cluster size, and the distribution width. In contrast, using a constant surface tension coefficient (as done in CNT) resulted in incorrect condensation dynamics and cluster size distributions. The analytical expression for cluster nucleation rate from CNT was updated to account for the size-dependence of cluster surface tension.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Towards a Deeper Fundamental Understanding of (Al,Sc)N Ferroelectric Nitrides

Density functional theory (DFT) calculations, within the virtual crystal alloy approximation, are performed, along with the development of a Landau-type model employing a symmetry-allowed analytical expression of the internal energy and having parameters determined from first principles, to investigate properties and energetics of Al1-xScxN ferroelectric nitrides in their hexagonal forms. These DFT computations and this model predict the existence of two different types of minima, namely, the fourfold-coordinated wurtzite (WZ) polar structure and a five-fold coordinated paraelectric hexagonal phase (denoted as H5), for any Sc composition up to 40%. The H5 minimum progressively becomes the lowest-energy state within hexagonal symmetry as the Sc concentration increases from 0 to 0.4. Furthermore, the model points to several key findings. Examples include the crucial role of the coupling between polarization and strains to create the WZ minimum, in addition to polar and elastic energies, and that the origin of the H5 state overcoming the WZ phase as the global minimum within hexagonal symmetry when increasing the Sc composition mostly lies in the compositional dependency of only two parameters-one linked to the polarization and another one being purely elastic in nature. Other examples are that forcing Al1-xScxN systems to have no or a weak change in lattice parameters when heating them allows us to reproduce their finite-temperature polar properties well and that a value of the axial ratio close to that of the ideal WZ structure implies a large polarization at low temperatures but not necessarily at high temperatures because of the ordered-disordered character of the temperature-induced formation of the WZ state. Such findings should allow for a better fundamental understanding of (Al,Sc)N ferroelectric nitrides, which may be used to design efficient devices having, e.g., low operating voltages.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

The Effect of Core-Hole Shape on Attosecond Valence Electron Dynamics

Rapid X-ray ionization of a core electron is known to induce the attosecond motion of valence electrons; however, the effect of core-hole shape on the triggered dynamics remains relatively unknown. In this work, the sub-four fs response of prototypical functionalized/heterocyclic/polycyclic molecules was simulated using real-time time-dependent density functional theory (RT-TDDFT), a sudden approximation core-hole, and phenomenologically Auger–Meitner (AM) decay. These molecules included fluorobenzene, chlorobenzene, bromobenzene, phenol, thiophenol, pyridine, phosphorus, and azulene. It is observed that the valence electron dynamics are essentially independent of the core-hole created, provided that it is ionized from an inner-shell orbital and not an inner-valence orbital. This has broad implications for free-electron laser studies of X-ray pumped attosecond processes since the flexibility in edge allows for a wide range of experimental modalities, core-holes with longer AM lifetimes, and molecular targets.

aromatic compounds↗

DOE OSTI2024

Importance of Electron Correlation on the Geometry and Electronic Structure of [2Fe–2S] Systems: A Benchmark Study of the [Fe 2 S 2 (SCH 3 ) 4 ] 2–,3–,4– , [Fe 2 S 2 (SCys) 4 ] 2– , [Fe 2 S 2 (S- p -tol) 4 ] 2– , and [Fe 2 S 2 (S- o -xyl) 4 ] 2– Complexes

Iron–sulfur clusters are crucial for biological electron transport and catalysis. Obtaining accurate geometries, energetics, manifolds of their excited electronic states, and reduction energies is important to understand their role in these processes. Here, using a [2Fe–2S] model complex with Fe II and Fe III oxidation states, which leads to different charges, i.e., [Fe 2 S 2 (SMe) 4 ] 2–,3–,4– , we benchmarked a variety of computational methodologies ranging from density functional theory (DFT) to post-Hartree–Fock methods, including complete active space self-consistent field (CASSCF), multireference configuration interaction, the second-order N-electron valence state perturbation theory (NEVPT2), and the linearized integrand approximation of adiabatic connection (AC0) approaches. Additionally, we studied three experimentally well-characterized complexes, [Fe 2 S 2 (SCys) 4 ] 2– , [Fe 2 S 2 (S-o-tol) 4 ] 2– , and [Fe 2 S 2 (S-o-xyl) 4 ] 2– , via DFT methods. We conclude that the dynamic electron correlation is important for accurately predicting the geometry of these complexes. Broken symmetry (BS) DFT correctly predicts experimental geometries of low-spin multiplicity, while CASSCF does not. However, BS-DFT significantly overestimates the difference between the low- and high-spin electronic states for a given oxidation state. At the same time, CASSCF underestimates it but provides relative energies closer to the reference NEVPT2 results. Finally, AC0 provides energetics of NEVPT2 quality with the additional advantage of being able to use large CASSCF sizes. NEVPT2 gives the best estimates of the Fe III /Fe III → Fe II /Fe III (4.27 eV) and Fe II /F III → Fe II /F II (7.72 eV) reduction energies. The results provide insight into the electronic structure of these complexes and assist in the understanding of their physical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Quantum mechanics and observers for gravity in a closed universe

Recent arguments based on the quantum extremal surface formula or the gravitational path integral have given fairly compelling evidence that the Hilbert space of quantum gravity in a closed universe is one-dimensional and real. How can this be consistent with the complexity of our own experiences? In this paper we propose that the experiences of any observer Ob in a closed universe can be approximately described by a quantum mechanical theory with a Hilbert space whose dimension is roughly e S Ob , where S Ob is the number of degrees of freedom of Ob. Moreover we argue that the errors in this description are exponentially small in S Ob . We give evidence for this proposal by incorporating it into the gravitational path integral and the coding interpretation of holography in simple models and seeing that it works, and we explain how similar effects arise in black hole physics in appropriate circumstances.

AdS-CFT Correspondence↗