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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A fast, dense Chebyshev solver for electronic structure on GPUs

Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes (≲4000), performance of traditional dense diagonalization algorithms on modern GPUs is underwhelming compared to the peak performance of these devices. This motivates the exploration of alternative algorithms better suited to these types of architectures. We newly derive, and present in detail, an existing Chebyshev expansion algorithm whose number of required matrix multiplications scales with the square root of the number of terms in the expansion. Focusing on dense matrices of modest size, our implementation on GPUs results in large speed ups when compared to diagonalization. Additionally, we improve upon this existing method by capitalizing on the inherent task parallelism and concurrency in the algorithm. Furthermore, this improvement is implemented on GPUs by using CUDA and HIP streams via the MAGMA library and leads to a significant speed up over the serial-only approach for smaller (≲1000) matrix sizes. Finally, we apply our technique to a model system with a high density of states around the Fermi level, which typically presents significant challenges.

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

Causal discovery from data assisted by large language models

Knowledge-driven discovery of novel materials necessitates the development of causal models for property emergence. While in the classical physical paradigm, the causal relationships are deduced based on physical principles or via experiment, the rapid accumulation of observational data necessitates learning causal relationships between dissimilar aspects of material structure and functionalities based on observations. For this, it is essential to integrate experimental data with prior domain knowledge. Here, we demonstrate this approach by combining high-resolution scanning transmission electron microscopy data with insights derived from large language models (LLMs). By applying ChatGPT to domain-specific literature, such as arXiv papers on ferroelectrics, and combining the obtained information with data-driven causal discovery, we construct adjacency matrices for directed acyclic graphs that map the causal relationships between structural, chemical, and polarization degrees of freedom in Sm-doped BiFeO 3 . This approach enables us to hypothesize how synthesis conditions influence material properties and guides experimental validation. Furthermore, the ultimate objective of this work is to develop a unified framework that integrates LLM-driven literature analysis with data-driven discovery, facilitating the precise engineering of ferroelectric materials by establishing clear connections between synthesis conditions and their resulting material properties.

Causal inference↗
DOE OSTI2020

Identification and Quantification of Beta-Emitters in Waste Packages by Segmented Gamma-Scanning - 20114

A commonly applied method for the non-destructive characterization of the radioactive inventory of waste packages (e.g. 200-l drums) is segmented gamma-scanning. The gamma-emitting inventory is identified via their characteristic lines in the measured spectra. The corresponding net peak areas allow for quantification applying appropriate models. The identification and quantification of beta-emitters present in the waste package require further evaluation. While some of them emit gamma-rays, too, which can be used for identification and quantification, pure beta-emitters contribute to the gamma-spectra only by their Bremsstrahlung-spectra. {sup 32}P, {sup 90}Sr and {sup 90}Y are typical representatives of these isotopes. A method is developed for identification and quantification of these pure beta-emitters in radioactive waste packages. Origin of the procedure is the evaluation of the measured gamma-spectrum. After the identification of all lines present in the spectrum (characteristic gamma-lines, single- and double-escape-lines, X-ray-lines, annihilation peak etc.) this information is used together with calibration data of the detection system and further a-priori information like matrix composition, cross-section data from databases etc. to simulate the spectra without the Bremsstrahlung-components by an appropriate method. This may be Monte Carlo simulations or, like in our case, a computer code taking into account mathematical descriptions of the physical effects like photo effect, (multiple) Compton scattering, backscattering etc. and the attenuation effects of the waste matrix. In any case, the resulting spectrum must simulate the real spectrum without its Bremsstrahlung-component as good as possible. Subtracting the simulated from the measured spectrum then results in the Bremsstrahlung-components caused by the beta-emitters. Prior to evaluation, a set of Bremsstrahlung-spectra is calculated and stored for different beta-emitters in different matrices using the Bethe-Heitler equation. This data set can be extended for new conditions, if necessary, and is allocated in a data base for future application. Applying a non-linear optimization using the generalized reduced gradient method for comparing the calculated with the derived Bremsstrahlung-spectra results in the identification of the beta-emitter and a factor, which is proportional to its activity. The proportionality is determined by previous calibration measurements. The application of the method is demonstrated by measurements on a 200-l mock-up drum and a real waste package. (authors)

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2022

$\mathrm{Z}$ero-jettiness resummation for top-quark pair production at the $\mathrm{LHC}$

We study the resummation of the 0-jettiness resolution variable $\mathcal{T}_o$ for the top-quark pair production process in hadronic collisions. Starting from an effective theory framework we derive a factorisation formula for this observable which allows its resummation at any logarithmic order in the $\mathcal{T}_o$→ o limit. We then calculate the $\mathcal{O}(a_s)$ corrections to the soft function matrices and, by employing renormalisation group equation methods, we obtain the ingredients for the resummation formula up to next-to-next-to-leading logarithmic (NNLL) accuracy. We study the impact of these corrections to the 0-jettiness distribution by comparing predictions at different accuracy orders: NLL, NLL', NNLL and Approximate NNLL' (NNLL$^{'}_{a}$). We match these results to the corresponding fixed order calculations both at leading order and next-to-leading order for the $t\bar{t}$+jet production process, obtaining the most accurate prediction of the 0-jettiness distribution for the top-quark pair production process at NNLL$^{'}_{a}$+NLO accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Fitting Matérn smoothness parameters using automatic differentiation

The Mat$\acute{e}$rn covariance function is ubiquitous in the application of Gaussian processes to spatial statistics and beyond. Perhaps the most important reason for this is that the smoothness parameter $\nu$ gives complete control over the mean-square differentiability of the process, which has significant implications for the behavior of estimated quantities such as interpolants and forecasts. Unfortunately, derivatives of the Mat$\acute{e}$rn covariance function with respect to $\nu$ require derivatives of the modified second-kind Bessel function $K$ $\nu$ with respect to $\nu$. While closed form expressions of these derivatives do exist, they are prohibitively difficult and expensive to compute. For this reason, many software packages require fixing $\nu$ as opposed to estimating it, and all existing software packages that attempt to offer the functionality of estimating $\nu$ use finite difference estimates for $\partial$ $\nu$ $K$ $\nu$ . In this work, we introduce a new implementation of $K$$\nu$ that has been designed to provide derivatives via automatic differentiation (AD), and whose resulting derivatives are significantly faster and more accurate than those computed using finite differences. Here, we provide comprehensive testing for both speed and accuracy and show that our AD solution can be used to build accurate Hessian matrices for second-order maximum likelihood estimation in settings where Hessians built with finite difference approximations completely fail.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Dynamics of photosynthetic light harvesting systems interacting with N-photon Fock states

Here, we develop a method to simulate the excitonic dynamics of realistic photosynthetic light harvesting systems, including non-Markovian coupling to phonon degrees of freedom, under excitation by N-photon Fock state pulses. This method combines the input–output and the hierarchical equations of motion formalisms into a double hierarchy of density matrix equations. We show analytically that under weak field excitation relevant to natural photosynthesis conditions, an N-photon Fock state input and a corresponding coherent state input give rise to equal density matrices in the excited manifold. However, an N-photon Fock state input induces no off-diagonal coherence between the ground and excited subspaces, in contrast with the coherences created by a coherent state input. We derive expressions for the probability to absorb a single Fock state photon with or without the influence of phonons. For short pulses (or, equivalently, wide bandwidth pulses), we show that the absorption probability has a universal behavior that depends only upon a system-dependent effective energy spread parameter Δ and an exciton–light coupling constant Γ. This holds for a broad range of chromophore systems and for a variety of pulse shapes. We also analyze the absorption probability in the opposite long pulse (narrow bandwidth) regime. We then derive an expression for the long time emission rate in the presence of phonons and use it to study the difference between collective vs independent emission. Finally, we present a numerical simulation for the LHCII monomer (14-mer) system under single photon excitation that illustrates the use of the double hierarchy equations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

JIMWLK on a quantum computer

We propose a method for solving the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution equation on quantum computers. Our approach exploits the reformulation of the JIMWLK equation as a Lindblad master equation governing the rapidity evolution of the hadronic density matrix, as established in prior work. To render the problem tractable for quantum simulation, we introduce several approximations: the two-dimensional transverse plane is reduced to a one-dimensional radial lattice by assuming azimuthal symmetry of the jump operators; the gauge group is restricted to SU(2); and the infinite Wilson lines of the JIMWLK equation are replaced by finite Wilson links along the light-cone direction. The resulting bosonic Hilbert space is truncated using the electric field basis familiar from Hamiltonian lattice gauge theory, with states restricted to angular momenta 𝑗 ≤ 𝑗 max . We derive the matrix elements of the JIMWLK Lindblad jump operators in this basis. As a benchmark, we demonstrate rapid convergence of the fundamental dipole expectation value with 𝑗 max for both pure and mixed Gaussian initial density matrices. For the simplest truncation, 𝑗 max =1/2, we implement the Lindblad evolution using a quantum simulation algorithm verified with the Qiskit statevector simulator by decomposing the non-unitary evolution operator into a linear combination of unitaries. This work establishes a concrete pathway toward quantum simulation of high-energy quantum chromodynamics evolution equations, with direct relevance to the physics program of the Electron-Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

On the convexity of phase-field fracture formulations: Analytical study and comparison of various degradation functions

Efficient and accurate fracture modeling is of great importance in applications where catastrophic outcomes under extreme scenarios are possible. The phase-field (PF) approach to fracture received significant attention over the past decade, due to its capability to capture complicated fracture patterns (e.g., crack merging and branching). Specifically, crack initiation and propagation are modeled via minimization of the total energy functional, which is regularized with the aid of a phase field. Despite the promising results and modeling capabilities of the PF method in many applications, the solution of fracture problems remains computationally challenging mainly due to the non-convexity of the total energy functional with respect to the combined unknown (phase field and displacement) fields. Understanding the effects of their coupling on convexity is crucial in order to address frequently encountered hurdles in fracture modeling (e.g., inefficient solvers and non-physical crack nucleation). In this paper, we develop convexity criteria for a wide class of PF fracture formulations. For this class of formulations, the second variation of the total energy functional is expressed in terms of Hessian matrices (evaluated at individual material points). Depending on the choice of geometric crack functions and degradation functions, we classify the formulations into three categories and analytically study each one separately. To study the sign of the second variation, we derive inequalities which are satisfied at material points when the Hessian matrix is locally positive semi-definite. These inequalities provide objective criteria for comparing degradation functions. Finally, the applicability of the proposed convexity criteria is demonstrated in the context of a one-dimensional problem, solved using a conventional monolithic solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Dynamic Graph Sequence Data from Simulated Neutron Reflectometry Measurements

This dataset comprises dynamic graph sequences derived from simulated in-situ neutron reflectometry measurements, capturing the gradual evolution of a layer structure over time. Each graph sequence represents a synthetic sample, with node features detailing the scattering vector and corresponding reflectivity measurements, while adjacency matrices have corresponding reference material parameters attached as metadata. The dataset spans multiple sets, each with a different number of sequences, offering a comprehensive basis for training models that handle dynamic input sequences with embedded physics. This dataset is particularly suited for tackling inverse problems with hidden physical states that evolve over time, challenges that are typically difficult to address using conventional iterative fitting methods.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Time evolution of ML-MCTDH wavefunctions. I. Gauge conditions, basis functions, and singularities

We derive a family of equations-of-motion (EOMs) for evolving multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) wavefunctions that, unlike the standard ML-MCTDH EOMs, never require the evaluation of the inverse of singular matrices. All members of this family of EOMs make use of alternative static gauge conditions than those used for standard ML-MCTDH. These alternative conditions result in an expansion of the wavefunction in terms of a set of potentially arbitrary orthonormal functions, rather than in terms of a set of non-orthonormal and potentially linearly dependent functions, as is the case for standard ML-MCTDH. We show that the EOMs used in the projector splitting integrator (PSI) and the invariant EOM approaches are two special cases of this family obtained from different choices for the dynamic gauge condition, with the invariant EOMs making use of a choice that introduces potentially unbounded operators into the EOMs. As a consequence, all arguments for the existence of parallelizable integration schemes for the invariant EOMs can also be applied to the PSI EOMs.

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

Tough and circular glass fiber composites via a tailored dynamic boronic ester interface

Glass fiber reinforced polymer (GFRP) composites are valued for their strength and cost-effectiveness. However, traditional GFRPs often face challenges for end-of-life recycling due to their non-depolymerizable thermoset matrices, and long-term performance due to inadequate interfacial adhesion, which can lead to fiber–matrix delamination. Here, in this work, we have designed dynamic fiber–matrix interfaces to allow tough and closed-loop recyclable GFRPs by utilizing a vitrimer, derived from upcycled polystyrene-b-poly(ethylene-co-butylene)-b-polystyrene (SEBS) with boronic ester (S-Bpin) and amine-based diol crosslinker. The boronic ester groups in S-Bpin form dynamic covalent bonds with the naturally present hydroxyl groups on the unsized GF surface, which eliminates the need for fiber sizing and enables facile closed-loop recyclability of both the fibers and the vitrimer matrix. The resulting strong fiber–matrix interface, depicted by the Raman mapping, leads to a 552% increase in-plane shear toughness (6.2 ± 0.3 MJ m -3 ) and 27% ultimate tensile strength (361 ± 89.2 MPa) compared to those of the conventional epoxy-based matrix (0.95 ± 0.05 MJ m -3 and 264 ± 59.7 MPa, respectively). The network rearrangement through dynamic boronic ester exchange enables fast thermoformability and repairability of micro-cracks at elevated temperatures. Additionally, both the matrix and composite demonstrate strong adhesion to various surfaces including steel and glasses exhibiting ≥6 MPa lap shear strength, which expands their suitability for diverse industrial applications. The readily created dynamic interface between boronic ester functionalized vitrimer and neat GFs presents a promising strategy for developing closed-loop recyclable, multifunctional structural materials, offering a sustainable alternative to non-recyclable thermoset GFRPs and contributes to a circular economy in composite materials.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Mixed matrix membranes for post-combustion carbon capture: From materials design to membrane engineering

Mixed matrix materials (MMMs) containing nanofillers dispersed in continuous polymer matrices have emerged as an exciting and versatile platform to develop membranes with superior CO 2 /N 2 separation performance for post-combustion carbon capture. Both polymers and nanofillers can be vertically designed and engineered to combine the advantages of excellent processability (derived from polymers) and strong size-sieving ability or/and significant permanent porosity (originated from nanofillers). However, the MMMs face major challenges, such as interfacial incompatibility, particle agglomeration, and poor thin-film formability. This report provides a comprehensive yet critical review of various polymers and nanofillers (such as metal-organic frameworks, covalent organic frameworks, and two-dimensional materials) with promising CO 2 /N 2 separation properties. We exhaustively describe strategies to improve interfacial compatibility, such as in situ syntheses of polymers and nanofillers and functionalization of both components to improve adhesion. Moreover, we highlight various approaches to engineer the MMMs into thin-film composite (TFC) membranes. The review reveals the structure/property relationship in these MMMs and outlines the challenges and opportunities to realize their potential for practical applications.

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

Evaluation of a practical approach for field scale moisture flow modeling in heterogeneous media at a semiarid site

Abstract A practical approach for modeling field‐scale moisture flow in a highly heterogeneous unsaturated medium is described in this study. The validity of this approach is demonstrated through comparison of the numerical simulations with field observations at a semiarid site located in southcentral Washington State. The methodology is based on upscaling the core scale hydraulic properties and combining power‐law and tensorial connectivity‐tortuosity (PA‐TCT) approaches to derive macroscopic anisotropy parameters for each hydrostratigraphic unit (HSU) identified in the field. Each heterogeneous HSU is approximated by an equivalent homogeneous medium (EHM) model for which PA‐TCT parameters are used in the flow simulations. The available field data on moisture content and matric potential are compared with steady‐state flow simulations based on the mean form of Richards' equation. While the homogenization or averaging of heterogeneities, embedded in the EHM modeling approximation, cannot capture all of the field‐scale variability, the simulated steady‐state moisture and matric potential profiles capture well the central tendency of the field data. This approach is deemed practical for assessing the fate and transport of contaminants in highly heterogeneous unsaturated media at the transport scale of hundreds of meters.

Khaleel, Raziuddin↗
DOE OSTI2022

Sodium diffusion in heterogeneous porous media: Connecting laboratory experiments and simulations

Sodium has been suggested as a tracer for brine in reservoir formations where a significant amount of sodium ion is found mainly in the aqueous phase. Fortunately, the most abundant sodium isotope, 23 Na, is Nuclear Magnetic Resonance (NMR) active, making it possible to study the structure and dynamical properties of both bulk and pore confined fluid systems. We investigated the diffusion of key dissolved sodium species in bulk solution and porous media as a function of composition, ionic strength, and permeability of the carbonate samples using NMR relaxometry and pulsed-field gradient (PFG) NMR techniques. We use Indiana limestone as an example of natural porous media and water as a freely diffusible tracer and carrier. We demonstrate apparent diffusion measurement of sodium based on changes in spin–spin relaxation time (T 2 ) signal in pore confinement. The diffusion rate of sodium decreases with increasing counter-ion size. This effect is greater at higher ionic strengths and lower chemical potentials in porous media. The reactive transport code, CrunchFlow, was used to complement the NMR experiments to simulate diffusion behavior in porous media. Combining these two methods provides a powerful approach to estimating effective diffusion coefficients in heterogeneous matrices. The modeling considers the influence of physical properties (porosity and tortuosity) and chemical properties (geochemical composition and chemical gradients). The results presented in this work highlight the advantage of measuring apparent diffusivity using NMR T 2 relaxometry in conjunction with numerical simulation to derive effective diffusivity and the corresponding matrix properties (i.e., tortuosity) of the system.

58 GEOSCIENCES↗
DOE OSTI2024

A Bayesian Learning Approach to Wireless Outdoor Heatmap Construction using Deep Gaussian Process

We present a novel Bayesian learning approach to outdoor radio heatmap construction utilizing deep Gaussian process (GP). The proposed approach employs a two-layer hierarchy which consists of two cascaded Gaussian processes that are capable of modeling more complex input-output relations than standard single-layer Gaussian processes. Since deriving the exact model likelihood is challenging, a lower bound is optimized instead so that gradient descent-based methods can be performed to find out the optimal model parameters. Typically, inducing points are used in GPs to facilitate low-rank approximation of covariance (kernel) matrices for computation speedup. However, the inaccuracy induced by inducing points can accumulate when stacking multiple layers of GP which may hinder the performance of deep GP. Moreover, since inducing points need to be learned, having them at all layers of deep GP also incurs computational burden. To overcome the above challenges, in contrast to the canonical deep GP model, we use a modified architecture where a full standard GP resides in the first layer and inducing points are only introduced for the second layer. This modified architecture strikes a balance between model accuracy and training complexity. In the proposed model, the noise parameter of the first GP layer is also eliminated to improve the training efficiency as the noise parameter at the output of the second layer suffices to model the uncertainty in the output. The proposed approach is evaluated on real-world datasets, in the form of location-Received Signal Strength (RSS) pairs, collected from the Platform for Open Wireless Data-driven Experimental Research (POWDER) located at the campus of the University of Utah. Experiment results show that the proposed approach can achieve smaller prediction errors on various training and testing data configurations than DNN-based and GP-based methods.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Enhanced purification coupled with biophysical analyses shows cross-β structure as a core building block for Streptococcus mutans functional amyloids

Streptococcus mutans is an etiologic agent of human dental caries that forms dental plaque biofilms containing functional amyloids. Three amyloidogenic proteins, P1, WapA, and Smu_63c were previously identified. C123 and AgA are naturally occurring amyloid-forming fragments of P1 and WapA, respectively. We determined that four amyloidophilic dyes, ThT, CDy11, BD-oligo, and MK-H4, differentiate C123, AgA, and Smu_63c amyloid from monomers, but non-specific binding to bacterial cells in the absence of amyloid precludes their utility for identifying amyloid in biofilms. Congo redinduced birefringence is a more specific indicator of amyloid formation and differentiates biofilms formed by wild-type S. mutans from a triple ΔP1/WapA/Smu_63c mutant with reduced bioiflm forming capabilities. Amyloid accumulation is a late event, appearing in older S. mutans biofilms after 60hours of growth. Amyloid derived from pure preparations of all three proteins is visualized by electron microscopy as mat-like structures. Typical amyloid fibers become evident following protease digestion to eliminate non-specific aggregates and monomers. Amyloid mats, similar in appearance to those reported in S. mutans biofilm extracellular matrices, are reconstituted by co-incubation of monomers and amyloid fibers. X-ray fiber diffraction of amyloid mats and fibers from all three proteins demonstrate patterns reflective of a cross-β amyloid structure.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Effects of He Ion Irradiation in Simple Borosilicate Glasses for HLW Immobilisation - 20324

High-level radioactive waste (HLW) consists of fission products and minor actinides. Borosilicate glass is the host material of choice in most countries to safely immobilize HLW, followed by eventual geological disposal. HLW glasses will experience both self-heating and self-irradiation effects due to the decay of fission products and minor actinides present therein. During the first 500 years of geological disposal, beta-gamma decay will be the main source of radiation due to short half-lives of fission products, as compared to very long-lived actinides which will be responsible for irradiation over much longer timescales. High-energy alpha particles and alpha recoil nuclei can potentially have significant impact (stored energy, volume change, accumulated dose, chemical durability) on the performance of the wasteform over longer timescales. Thus, to ensure safe and economic disposal over geological periods (10{sup 4} - 10{sup 6} years), the assessment of performance and properties in terms of radiation effects becomes indispensable. This work aims to simulate the effects of alpha decay in radioactive waste glasses. Two international glasses, namely UK 'MW' lithium-sodium borosilicate and Indian sodium-barium borosilicate, which are being used as HLW immobilization matrices by the UK and India respectively, were prepared by a melt-quench method and annealed below their glass transition temperatures. Both glasses were irradiated with 650 KeV He{sup 2+} ions with doses ranging from 10{sup 15} to 10{sup 17} ions/cm{sup 2}. Structural analysis was carried out using electron paramagnetic resonance (EPR) and Raman spectroscopies. First derivative continuous wave EPR spectra were recorded for all pristine and irradiated glass monoliths at room temperature using an X-band (frequency 9.6 GHz) EPR Bruker spectrometer. Results from EPR analyses showed the formation of irradiation induced paramagnetic centers at g ∼ 2.00 in all irradiated glasses. Raman spectra of pristine and irradiated samples were acquired, and showed notable changes in glass structure post-irradiation, with the emergence of a broad Raman band at 1560 cm{sup -1} upon irradiation with high fluences. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Quantum Many-Body Theory from a Solution of the N -Representability Problem

Here, in this study, we present a many-body theory based on a solution of the N-representability problem in which the ground-state two-particle reduced density matrix (2-RDM) is determined directly without the many-particle wave function. We derive an equation that re-expresses physical constraints on higher-order RDMs to generate direct constraints on the 2-RDM, which are required for its derivation from an N-particle density matrix, known as N-representability conditions. The approach produces a complete hierarchy of 2-RDM constraints that do not depend explicitly upon the higher RDMs or the wave function. By using the two-particle part of a unitary decomposition of higher order constraint matrices, we can solve the energy minimization by semidefinite programming in a form where the low-rank structure of these matrices can be potentially exploited. We illustrate by computing the ground-state electronic energy and properties of the H 8 ring.

74 ATOMIC AND MOLECULAR PHYSICS↗