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DOE OSTI2024

Manufactured solutions for an electromagnetic slot model

The accurate modeling of electromagnetic penetration is an important topic in computational electromagnetics. Electromagnetic penetration occurs through intentional or inadvertent openings in an otherwise closed electromagnetic scatterer, which prevent the contents from being fully shielded from external fields. To efficiently model electromagnetic penetration, aperture or slot models can be used with surface integral equations to solve Maxwell's equations. A necessary step towards establishing the credibility of these models is to assess the correctness of the implementation of the underlying numerical methods through code verification. Surface integral equations and slot models yield multiple interacting sources of numerical error and other challenges, which render traditional code-verification approaches ineffective. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources for the method-of-moments implementation of the electric-field integral equation with a slot model. Finally, we demonstrate the effectiveness of these approaches for a variety of cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

A fully implicit, asymptotic-preserving, semi-Lagrangian algorithm for the time dependent anisotropic heat transport equation

In this paper, we extend the operator-split asymptotic-preserving, semi-Lagrangian algorithm for time dependent anisotropic heat transport equation proposed in Chacón et al. (2014) [18] to use a fully implicit time integration with backward differentiation formulas. The proposed implicit method can deal with arbitrary heat-transport anisotropy ratios $\mathcal{X}$∥ /$ \mathcal{X}$⟂ $\ggg$ 1 (with $\mathcal{X}$∥, $ \mathcal{X}$⟂ the parallel and perpendicular heat diffusivities, respectively) in complicated magnetic field topologies in an accurate and efficient manner. Further, the implicit algorithm is second-order accurate temporally and demonstrates an accurate treatment at boundary layers (e.g., island separatrices), which was not ensured by the operator-split implementation. The condition number of the resulting algebraic system is independent of the anisotropy ratio, and is inverted with preconditioned GMRES. We propose a simple preconditioner that renders the finite-dimensional linear operator compact, resulting in mesh-independent convergence rates for topologically simple magnetic fields, and convergence rates scaling as ~ (NΔt) 1/4 (with N the total mesh size and Δt the timestep) in topologically complex magnetic-field configurations. We demonstrate the accuracy and performance of the approach with test problems of varying complexity, including an analytically tractable boundary-layer problem in a straight magnetic field, and a topologically complex magnetic field featuring magnetic islands with extreme anisotropy ratios $\mathcal{X}$∥ /$ \mathcal{X}$⟂ = 10 10 ) .

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Osmotic control of the spacing of parallel shear cracks in shale growing subcritically in geologic past

The geological genesis of natural cracks in sedimentary rocks such as shale is a problem that needs to be understood to improve the technology of hydraulic fracturing as well as deep sequestration of harmful fluids. Why are the vertical natural cracks roughly parallel and equidistant, and why is the spacing roughly 10 cm rather than 1 cm or 100 cm? Fracture mechanics of critical cracks cannot answer this question. Neither can the material heterogeneity. The growth of critical parallel cracks is impossible because the relative crack face displacements would immediately localize into one crack, leading to an earthquake. The cracks must have formed, on the tectonic time scale, by a slow growth of subcritical shear cracks governed by the Charles-Evans law. The idea advanced here is that what controls the crack spacing is the balance between the reduction, due to shear dilatancy, of the concentration of ions such as Na + and Cl - in each fracture process zone (PFZ), which decelerates the cracks, and the restoration of ion concentration by diffusion of ions from the space between the cracks into the FPZ. This diffusion of water is driven mainly by the osmotic pressure gradient, which offsets the deceleration and depends strongly on the crack spacing. A simple analytical solution of the steady state is rendered possible by approximating the ion concentration profiles between adjacent cracks by parabolic arcs. Applying this theory to Woodford shale yields the approximate crack spacing of 10 cm, which is realistic. Furthermore, the stability of unlimited parallel mode II frictional crack growth is proven by examining the second variation of the free energy. Water concentration drop in the FPZ due to shear dilatancy and its restoration by water diffusion from the inter-crack space have similar effect, although probably much weaker.

42 ENGINEERING↗

DOE OSTI2026

Identifying microstructures susceptible to pulverization in commercially irradiated high burnup UO2 under LOCA conditions

High burnup fuel fragmentation (HBFF) has been a concern in the nuclear industry for many years. When UO2 reaches and exceeds pellet average burnups around 55 GWd/tU, microstructural changes in the fuel pellet begin to occur that render the pellet susceptible to fine fragmentation under loss-of-coolant accident (LOCA) conditions. During a LOCA event, the cladding balloons and bursts, potentially releasing part of these fine fuel fragments into the reactor pressure vessel. This process is known as fuel fragmentation, relocation, and dispersal (FFRD). Presently, the US nuclear industry is developing a safety basis for FFRD with the goal of increasing burnups and pressurized water reactor cycle lengths. Increased cycle lengths would push the burnup limits of the fuel rods past the known threshold for HBFF susceptibility. In this work, the microstructural impact on HBFF was investigated by comparing the microstructures of as-irradiated rod segments to their post-LOCA tested counterparts. This investigation found that varied operational histories result in different microstructural evolutions across the pellet radius, which impacts the fragmentation behavior and radial location of the fragmentation. It is noted that regions with a high bubble density and a high density of grain boundaries fragment under LOCA-relevant conditions. In addition to the fragmentation that has been previously reported at the periphery of the fuel, fragmentation was also noted in the dark zone toward the fuel center. Analysis of the power histories of the fuel samples suggests that the dark zone forms in the central regions of the pellet between temperatures of approximately 740 and 960 °C.

McKinney, Casey [ORNL] (ORCID:0000000335383614)↗

DOE OSTI2025

Mapping of fracture and ionic conductivity changes in ion implanted solid electrolytes: Insights from molecular dynamics

Ion implantation emerges as a promising technique to address the persistent challenge of lithium (Li) filament growth in solid-state electrolytes as it can induce compressive stresses inhibiting crack growth and deflect dendrites, de facto mitigating early electrolyte failure. In this study, we examine the potential paradox of ion implantation: while aiming to enhance electrolyte performance, the radiation damage associated with implantation might inadvertently compromise both the ionic conductivity and the intrinsic fracture toughness of the material, rendering the material unsuitable for battery applications. Specifically, we employed molecular dynamics simulations to examine the scope of the downsides of ion implantation, specifically: (i) reduced ionic conductivity (due to radiation-induced amorphization) and (ii) mechanical stability (due to radiation-induced embrittlement) in ion-implanted Li 7 La 3 Zr 2 O 12 (LLZO) solid-state electrolytes. We explore how radiation damage impacts LLZO’s crystalline structure, Li-ion diffusion, and fracture properties at various temperatures and radiation damage levels. The study aims to provide insights into the competing effects of ion implantation and suggest potential engineering strategies for developing more robust solid-state electrolytes with improved conductivity and dendrite resistance.

Conductivity↗

DOE OSTI2026

Enhanced electrochemical performance and extended cycling of resorcinol-formaldehyde derived N-doped carbon xerogel for alkali metal-ion (Li/Na/K) batteries

Resorcinol formaldehyde-derived carbon xerogel (RFC) is a versatile material with tuneable properties, synthesized through a simple sol-gel method. This study presents nitrogen-doped RF carbon xerogel (N-RFC) with 11.8 at% nitrogen doping, offering a microporous architecture ideal for alkali metal-ion (Li, Na, K) batteries. The porous N-doped framework enhances electrochemical performance by improving ion transport, increasing active storage sites, and significantly boosting metal-ion adsorption, particularly through pyrrolic nitrogen, as revealed by first-principles calculations supported by XPS analysis. N-RFC anodes showed excellent cycling stability, high-capacity retention, and fast charge/discharge capabilities, rendering them suitable for commercial applications. Notably, the N-RFC anode demonstrates high-rate long-term cycling stability, retaining its capacity of 83.5 % (188 mAh/g at 2 C-rate) and 50 % (133 mAh/g at 1250 mA/g) over 1000 cycles for Li and Na-ion batteries, respectively, favorable for commercial battery applications. Additionally, N-RFC demonstrates a reversible capacity of 120 mAh/g after 394 cycles with a retention of 82 % for K-ion batteries. The ability of the material to accommodate larger ions like Na + and K + further emphasizes its versatility and potential application in diverse alkali metal-ion battery systems.

25 ENERGY STORAGE↗

DOE OSTI2024

Support size regulated ruthenium-sulfoacid-nitrogen sites intensify cellulose hydrogenolysis to 1,2-propylene glycol

Rational design of metal-acid-base multifunctional catalysts for upgrading cellulose to 1,2-propylene glycol (1,2-PG) is of great significance for building a sustainable world. However, it is time-consuming and tedious to regulate metal-acid-base sites to balance major reactions to render a high 1,2-PG yield. We herein report support size simultaneously regulated ruthenium-sulfoacid-nitrogen (Ru–SO 3 H–N) sites for cellulose hydrogenolysis to high yield 1,2-PG. Originated from the depolymerization and reassembly of zinc-1,3,5-benzenetricarboxylic acid (ZnBTC) fiber with zeolitic imidazolate framework (ZIF-8) in water, 2-methylimidazole infiltrated nanorod (ZnBTC(mIM)) with a varied aspect ratio was fabricated by varying the feed ratio of ZIF-8/ZnBTC. Upon being pyrolyzed, sulfonated and impregnated with Ru ions, the supported sites were tailored in terms of Ru single-atom/nanocluster ratio, SO 3 H acidity and N basicity. Further, the elaborately fabricated catalyst delivers 32.3% yield of 1,2-PG, corresponding to a high productivity of 67.71 mol h -1 g Ru -1 and a large turnover number of 34193, two and three orders of magnitude higher than those by using other Ru-containing catalytic systems for cellulose hydrogenolysis. The excellent performance can be attributed to optimized electronic and molecular structure of Ru–SO 3 H–N sites that can improve rate-determining cellulose hydrolysis/fructose hydrogenolysis, pivotal glucose isomerization with others to proceed at a matched rate. This study opens a new avenue to facilely tailor the metal-acid-base sites by rational design of size controlled supporting matrix.

1,2-Propylene glycol↗

DOE OSTI2025

Constructing synthetic organosulfur additive for high voltage lithium-ion batteries

Despite its high anodic stability, common organosulfur solvents such as ethyl methyl sulfone and sulfolane typically exhibit poor solid-electrolyte interphase (SEI) formation capability. Here, to address this, the fluorinated organic sulfate 4-(trifluoromethyl)-1,3,2-dioxathiolane 2,2-dioxide (TFDTD) was developed as an effective additive for tailoring organosulfur-based electrolytes in lithium-ion batteries. This development was guided by the functionality selection principle and careful evaluation of feasibility in organic synthesis. TFDTD can be readily synthesized through the reaction between trifluoropropylene glycol and sulfuryl chloride. The ring structure of the organic sulfate enables the formation of a stable SEI on the anode, while the fluorination of the sulfate not only enhances its chemical stability and oxidation potential, but also its effectiveness to protect the anode by increasing its reduction potential, rendering it preferentially reduced on the anode surface before the decomposition of other electrolyte components. Introducing TFDTD facilitates the generation of a robust solidelectrolyte interphase on the graphite anode, significantly enhancing cell performance. Moreover, coupling the use of TFDTD with vinylene carbonate provides further protection on the cathode surface, enabling exceptionally stable, high-voltage, long-term cycling of Gr||NMC full cells.

Functionality selection principle↗

DOE OSTI2025

Development and application of two-step uncertainty propagation and sensitivity analysis methodology for fast reactor safety analysis

Uncertainty quantification (UQ) in nuclear reactors for transients is directly linked with safety assessment through the cross-sections uncertainties, provided as a covariance matrix, which are propagated through the reactor system to output of interest pertaining to reactor safety, such as peak temperatures in fuel/clad/coolant. Using a two-step approach, uncertainties are first quantified and propagated from basic input variables (such as reaction cross-sections) to intermediate quantities (such as reactivity feedback coefficients) through lattice level calculations. Uncertainties of intermediate quantities (from the first step) are then propagated through the system transient calculations, in the second step, to obtain uncertainties on reactor safety output parameters of interest. The scope of this work consists of Uncertainty Quantification & Propagation of nuclear data uncertainties that are highly correlated through unprotected transient overpower and unprotected loss of flow to assess their impact on core safety parameters. This two-step approach in the presence of covariance renders the sensitivity analysis very challenging. In fact, usually the sensitivity analysis is restricted to each step, which limits its application since the sensitivities between the system output quantities and the basic input variables are difficult to obtain. Here, in this work, we address this issue by proposing a simple, general methodology to combine the sensitivity indices obtained in each step by assuming the model behavior being linear. For the first step Generalized Perturbation theory based indices are used while in the second step the recently studied Johnson indices. The uncertainty quantification and sensitivity methodologies discussed here are demonstrated on a generic LFR design which is based on the 500 MWth demonstration Lead-cooled fast reactor (DLFR) using oxide fuel, developed by Westinghouse Electric Company (WEC).

42 - ENGINEERING↗

DOE OSTI2025

Stabilizing dynamic subsea power cables using Bi-stable nonlinear energy sinks

This study investigates vibration mitigation of dynamic subsea cables through passive bi-stable nonlinear energy sinks (B-NESs). These devices suppress vibration energy in a broadband way, and can be regarded as extensions of classical linear tuned mass dampers (TMDs) which are narrowband devices. Through the open-source MoorDyn library, we simulated the vibrations of a vertical subsea cable equipped with a set of B-NESs. Multi-objective optimization was performed to detect the B-NES parameters for optimal mitigation of the cable vibrations. Advanced signal processing verified the efficacy of the optimized B-NESs not only to rapidly absorb and locally dissipate vibration energy, but also to nonlinearly scatter vibration energy from low to high frequencies within the cable itself. This last feature is especially beneficial for vibration mitigation of the undersea cable, as at higher frequencies the cable vibrations exhibit drastically reduced amplitudes and are more effectively dissipated by inherent structural damping and hydrodynamic radiation damping. This contrasts with traditional TMDs which can mitigate vibration only at a single frequency. Furthermore, our robustness study confirms the B-NES's effectiveness under even varying environmental conditions. Overall, the B-NES's capacity for broadband vibration mitigation renders it a promising retrofit solution for improving the performance and operational safety of dynamic power cables in offshore wind farms and other marine applications.

17 WIND ENERGY↗

DOE OSTI2025

Expanding market opportunities: cogeneration strategies for integrated PWR and thermal energy storage systems

We assess the economic viability of nuclear cogeneration by investigating three different modes—fixed dispatch, fully flexible dispatch, and flexible dispatch with minimum heat supply requirements. The analysis focuses on an existing pressurized water reactor (PWR) integrated with thermal energy storage (TES). Heat production costs are estimated under these modes for two U.S. electricity markets: the Electric Reliability Council of Texas (ERCOT) and the Pennsylvania–New Jersey–Maryland Interconnection (PJM). A sensitivity analysis examines profitability at varying heat market prices. Results indicate that fixed heat dispatch inflates heat production costs, often rendering projects economically feasible only at higher heat price levels. Fully-flexible dispatch lowers heat production costs by an average of 43 % compared to fixed dispatch. However, the current 30 % thermal dispatch limit may be insufficient to serve high baseline industrial demands cost‐effectively; higher maximum dispatch rates could enhance project economics. Markets with higher and more volatile electricity prices (e.g., ERCOT) offer greater total energy sales potential (i.e., heat and electricity), but also increase opportunity costs when heat production scheduling restrictions are imposed. In contrast, lower-price, less volatile markets (e.g., PJM) experience smaller impacts from such constraints and provide greater flexibility in accommodating varying cogeneration modes. In conclusion, these findings provide a framework to guide nuclear plant operators in aligning cogeneration strategies with industrial process requirements and electricity market conditions.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Evaluating the role of green infrastructure features in post-disaster recovery – Case Study of Beaumont, Texas after tropical storm imelda

While green infrastructure (GI) can provide multiple environmental benefits, its role in post-disaster economic and social recovery remains relatively underexplored. This article investigates whether different characteristics of GI, such as size, shape, connectivity, and amenities, affect the resilience of local businesses following Tropical Storm Imelda in Beaumont, Texas. The study utilizes SafeGraph mobility data to analyze foot traffic patterns to local businesses before, during, and after the disaster. FRAGSTATS indices measure GI characteristics (e.g., area, shape index, fractal dimension, proximity) while park features such as sports facilities, playgrounds, water features, and accessibility are cataloged through manual observation. Ordinary Least Squares regression models assess the relationship between park characteristics and post-recovery business performance, controlling for demographic variables including income, race, and poverty levels. Results indicate that certain GI attributes significantly enhance business recovery. Points of interest within walking distance (0.5 miles) of parks demonstrated better post-recovery status compared to those beyond this range. Specifically, parks with larger areas (p < 0.01) and more complex shapes measured by fractal dimension index (p < 0.01) had the strongest positive impact on surrounding businesses' recovery. Interestingly, playgrounds showed a negative correlation with recovery (p < 0.05), likely due to flood damage rendering them unusable during the immediate recovery period. Social vulnerability factors, including higher poverty rates and minority populations, negatively affected recovery outcomes despite park proximity.

Economic resilience↗

DOE OSTI2024

Contrasting Effects of Catecholate and Hydroxamate Siderophores on Molybdenite Dissolution

Molybdenum (Mo) is essential for many enzymes but is often sequestered within minerals, rendering it not readily bioavailable. Metallophores, metabolites secreted by microorganisms and plants, promote mineral dissolution to increase metal bioavailability. However, interactions between metallophores and Mo-bearing minerals remain unclear. Here, in this study, catecholate protochelin and hydroxamate desferrioxamine B (DFOB) were utilized to examine their effects on dissolution of the common Mo-bearing mineral, molybdenite (MoS 2 ), under both oxic and anoxic conditions. Protochelin promoted molybdenite dissolution under oxic conditions with the formation of MoO 3 on the surface and Mo-siderophore complexes in solution. This was attributed to air-oxidation of both molybdenite and protochelin, as evidenced by lack of dissolution under anoxic conditions but enhanced dissolution by either pre-oxidized protochelin or pre-oxidized molybdenite. Liquid chromatography-mass spectroscopy (LC-MS), X-ray photoelectron spectroscopy (XPS), and Time-of-flight secondary ion mass spectrometry (ToF-SIMS) analyses revealed degradation of protochelin and adsorptions of its byproducts on molybdenite surface to promote dissolution. Conversely, DFOB inhibited molybdenite dissolution under both oxic and anoxic conditions, likely attributed to surface adsorption of DFOB and its weak complexation with Mo(VI) at the circumneutral pH. This work highlights the need to consider the balance between promoting and inhibitory effects of different metallophores on Mo-mineral dissolution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Desorption of Phosphate from Iron-Bearing Soil Minerals by a Plant Secondary Metabolite

In soils, phosphorus readily adsorbs to the surfaces of ubiquitous iron (oxyhydr)oxide minerals, rendering it less accessible to plants and microorganisms. Plants have a number of strategies to access iron, among them the secretion of redox-active metabolites from their roots. Although these strategies likely increase the bioavailability of surface-adsorbed phosphorus through reductive dissolution, their effect on phosphorus cycling has not yet been investigated. We tested the ability of fraxetin, a coumarin-type redox-active metabolite produced by the model plant Arabidopsis thaliana and other dicotyledon plant species, to reductively solubilize phosphate from the surface of ferrihydrite. Our findings show that, at low and neutral pH, fraxetin increased aqueous phosphate concentrations under both oxic and anoxic conditions; at high pH, it was only effective in anoxic experiments. Additionally, a combination of liquid chromatography–mass spectrometry and spectroscopic methods demonstrated substantial fraxetin adsorption to the mineral surface but showed that iron reduction did not alter the mineral structure or change the nature of the chemical environment of the phosphorus atom over short time scales. These results provide evidence that the secretion of redox-active metabolites from roots is likely to be an effective phosphorus acquisition tactic in iron-rich soils.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Analysis of the Structure of Heavy Ion Irradiated LaFeO 3 Using Grazing Angle X-ray Absorption Spectroscopy

Crystalline ceramics are candidate materials for the immobilization of radionuclides, particularly transuranics (such as U, Pu, and Am), arising from the nuclear fuel cycle. Due to the α-decay of transuranics and the associated recoil of the parent nucleus, crystalline materials may eventually be rendered amorphous through changes to the crystal lattice caused by these recoil events. Previous work has shown irradiation of titanate-based ceramics to change the local cation environment significantly, particularly in the case of Ti which was shown to change from 6- to 5-fold coordination. Here, this work expands the Ti-based study to investigate the behavior in Fe-based materials, using LaFeO 3 as an example material. Irradiation was simulated by heavy ion implantation of the bulk LaFeO 3 ceramic, with the resulting amorphous layer characterized with grazing angle X-ray absorption spectroscopy (GA-XAS). Insights into the Fe speciation changes exhibited by the amorphized surface layer were provided through quantitative analysis, including pre-edge analysis, and modeling of the extended X-ray absorption fine structure (EXAFS), of the GA-XAS data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Tetrel Bond-Mediated Photophysical Modulation and Fluoride Recognition in Carbazole-Organosilanes

Silicon-centered orbitals are typically regarded as electronically inert in donor–acceptor systems. Here, we show that silole-based carbazole–silane architectures can render these orbitals electronically relevant, enabling modulation of excited-state behavior and anion-responsive photophysics. Two carbazole–Dipp–silanes exhibit identical carbazole-localized LE singlet emission in solution yet diverge markedly in the solid state: one compound displays a broad long-wavelength emission band in the prompt spectrum and enhanced long-lived emission consistent with a triplet-derived excited state, likely arising from a combination of intramolecular structural locking and solid-state packing effects, whereas the more flexible analogue remains predominantly LE-emissive. Fluoride coordination further differentiates the two systems, producing ratiometric red-shifted emission in one case and fluorescence quenching in the other through a fully reversible coordination process. These results identify σ*(Si–Ar) orbitals as tunable contributors to excited-state landscapes in organosilane luminophores and suggest a broader design strategy for controlling excited-state behavior in tetrel-based photofunctional systems.

Haque, Md Hasanul↗

DOE OSTI2025

A Practical Framework for Simulating Time-Resolved Spectroscopy Based on a Real-Time Dyson Expansion

Time-resolved spectroscopy is a powerful tool for probing electron dynamics in molecules and solids, revealing transient phenomena on subfemtosecond time scales. The interpretation of experimental results is often enhanced by parallel numerical studies, which can provide insight and validation for experimental hypotheses. However, developing a theoretical framework for simulating time-resolved spectra remains a significant challenge. The most suitable approach involves the many-body nonequilibrium Green's function formalism, which accounts for crucial dynamical many-body correlations during time evolution. While these dynamical correlations are essential for observing emergent behavior in time-resolved spectra, they also render the formalism prohibitively expensive for large-scale simulations. Substantial effort has been devoted to reducing this computational cost─through approximations and numerical techniques─while preserving the key dynamical correlations. The ultimate goal is to enable first-principles simulations of time-dependent systems ranging from small molecules to large, periodic, multidimensional solids. Here, in this perspective, we outline key challenges in developing practical simulations for time-resolved spectroscopy, with a particular focus on Green's function methodologies. We highlight a recent advancement toward a scalable framework: the real-time Dyson expansion (RT-DE) [Phys. Rev. Lett. 2024, 133, 226902]. We introduce the theoretical foundation of RT-DE and discuss strategies for improving scalability, which have already enabled simulations of system sizes beyond the reach of previous fully dynamical approaches. We conclude with an outlook on future directions for extending RT-DE to first-principles studies of dynamically correlated, nonequilibrium systems.

Reeves, Cian C. [Univ. of California, Santa Barbar↗

DOE OSTI2026

SCF Framework, HF Stability, and RPA Correlation for Jordan–Wigner-Transformed Spin Hamiltonians on Arbitrary Coupling Topologies

Mapping spins to fermions via the Jordan–Wigner (JW) transformation can render mean-field (Hartree–Fock, HF) descriptions effective for strongly correlated spin systems. As established in recent work, the application of such approaches is not limited by the nonlocal structure of JW strings or by site ordering because string operators can be absorbed into Thouless rotations of a Slater determinant, and the variational optimization of a unitary Lie-algebraic similarity transformation removes any ordering dependence. Leveraging these ideas, we develop a self-consistent field (SCF) scheme that expresses the mean-field energy as a functional of the single-particle density matrix, providing an alternative to gradient-based optimization of Thouless parameters. We derive the analytical orbital Hessian to diagnose HF stability and compute the ground-state correlation energy through the random-phase approximation (RPA). Benchmark results for the XXZ and J 1 –J 2 model on one- and two-dimensional lattices demonstrate that RPA significantly improves mean-field accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗