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At least 757 records · Page 42

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NASA NTRS2013

The W-W02 Oxygen Fugacity Buffer at High Pressures and Temperatures: Implications for f02 Buffering and Metal-silicate Partitioning

Oxygen fugacity (fO2) controls multivalent phase equilibria and partitioning of redox-sensitive elements, and it is important to understand this thermodynamic parameter in experimental and natural systems. The coexistence of a metal and its oxide at equilibrium constitutes an oxygen buffer which can be used to control or calculate fO2 in high pressure experiments. Application of 1-bar buffers to high pressure conditions can lead to inaccuracies in fO2 calculations because of unconstrained pressure dependencies. Extending fO2 buffers to pressures and temperatures corresponding to the Earth's deep interior requires precise determinations of the difference in volume (Delta) V) between the buffer phases. Synchrotron x-ray diffraction data were obtained using diamond anvil cells (DAC) and a multi anvil press (MAP) to measure unit cell volumes of W and WO2 at pressures and temperatures up to 70 GPa and 2300 K. These data were fitted to Birch-Murnaghan 3rd-order thermal equations of state using a thermal pressure approach; parameters for W are KT = 306 GPa, KT' = 4.06, and αKT = 0.00417 GPa K-1. Two structural phase transitions were observed for WO2 at 4 and 32 GPa with structures in P21/c, Pnma and C2/c space groups. Equations of state were fitted for these phases over their respective pressure ranges yielding the parameters KT = 190, 213, 300 GPa, KT' = 4.24, 5.17, 4 (fixed), and αKT = 0.00506, 0.00419, 0.00467 GPa K-1 for the P21/c, Pnma and C2/c phases, respectively. The W-WO2 buffer (WWO) was extended to high pressure by inverting the W and WO2 equations of state to obtain phase volumes at discrete pressures (1-bar to 100 GPa, 1 GPa increments) along isotherms (300 to 3000K, 100 K increments). The slope of the absolute fO2 of the WWO buffer is positive with increasing temperature up to approximately 70 GPa and is negative above this pressure. The slope is positive along isotherms from 1000 to 3000K with increasing pressure up to at least 100 GPa. The WWO buffer is at a higher fO2 than the IW buffer at pressures lower than 40 GPa, and the magnitude of this difference decreases at higher pressures. This qualitatively indicates an increasingly lithophile character for W at higher pressures. The WWO buffer was quantitatively applied to W metal-silicate partitioning by using the WWO-IW buffer difference in combination with literature data on W metal-silicate partitioning to model the exchange coefficient (KD) for the Fe-W exchange reaction. This approach captures the pressure dependence of W metal-silicate partitioning using the WWO-IW buffer difference and models the activities of the components in the silicate and metallic phases using an expression of the Gibbs excess energy of mixing. Calculation of KD along a peridotite liquidus predicts a decrease in W siderophility at higher pressures that supports the qualitative behavior predicted by the WWO-IW buffer difference, and agrees with findings of others. Comparing the competing effects of temperature and pressure on W metal-silicate partitioning, our results indicate that pressure exerts a greater effect.

Shofner, G. A.↗

NASA NTRS2014

Impact Testing and Simulation of Composite Airframe Structures

Dynamic tests were performed at NASA Langley Research Center on composite airframe structural components of increasing complexity to evaluate their energy absorption behavior when subjected to impact loading. A second objective was to assess the capabilities of predicting the dynamic response of composite airframe structures, including damage initiation and progression, using a state-of-the-art nonlinear, explicit transient dynamic finite element code, LS-DYNA. The test specimens were extracted from a previously tested composite prototype fuselage section developed and manufactured by Sikorsky Aircraft Corporation under the US Army's Survivable Affordable Repairable Airframe Program (SARAP). Laminate characterization testing was conducted in tension and compression. In addition, dynamic impact tests were performed on several components, including I-beams, T-sections, and cruciform sections. Finally, tests were conducted on two full-scale components including a subfloor section and a framed fuselage section. These tests included a modal vibration and longitudinal impact test of the subfloor section and a quasi-static, modal vibration, and vertical drop test of the framed fuselage section. Most of the test articles were manufactured of graphite unidirectional tape composite with a thermoplastic resin system. However, the framed fuselage section was constructed primarily of a plain weave graphite fabric material with a thermoset resin system. Test data were collected from instrumentation such as accelerometers and strain gages and from full-field photogrammetry.

Jackson, Karen E.↗

NASA NTRSDate not supplied

Lightning Flash Behavior and Convective Characteristics in Hurricanes Florence (2018), Dorian (2019), and Laura (2020)

Lightning is a useful tool in forecasting and understanding the behavior of tropical cyclones (TCs). Flash extent density (FED) has been found to be indicative of strength and intensification in TCs, but optical energy is a newer parameter that has not been studied intensively. This presentation analyzes the relationship between convective characteristics, such as updraft speed and updraft size, and Geostationary Lightning Mapper (GLM) optical energy, flash area, and FED in Hurricanes Florence (2018) and Laura (2020). The maximum optical energy values were analyzed for each minute from the innermost 100 kilometers of the eye to determine if there was a relationship between optical energy, flash area, updraft behavior, and intensification. Microwave imagery and tail-doppler radar (TDR) were examined during rapid increases in flash energy to connect updraft size and strength to these spikes. Early results show an increase in size of a moderate updraft occurring just prior to an increase in lightning optical energy and TC intensity, while smaller updrafts coincide with a decrease in intensity or little to no change in intensity. Continuing work aims to investigate the role of moderate updraft size in lightning behavior and TC intensity.

Kiahna Mollette↗

NASA NTRS2026

Mathematical Model of a Regenerative Fuel Cell for System Optimization

This thesis developed a system-level optimization model of a regenerative fuel cell (RFC) system for long-duration, off-world energy storage applications. Prior RFC design studies have typically been limited to reduced parameter sets and simplified constraints due to computational limitations relative to the number of relevant degrees of freedom. As a result, important nonlinear interactions between subsystems have not been fully captured. This work began to address that gap by developing a higher-fidelity, nonlinear optimization framework that incorporates a broader set of design variables and coupled constraints, enabling a multidimensional model that captures the coupled behavior of RFC subsystems and demonstrates the feasibility of applying optimization to such systems. An expanded system-level optimization approach was established that captures interactions between electrochemical performance, structural requirements, and storage design. This enabled a more comprehensive evaluation of trade-offs than conventional formulations. The model integrates four coupled subsystems: a fuel cell, an electrolyzer, reactant gas, and high-pressure storage tanks, and was formulated to accommodate a wide range of mission parameters, including operational time and required output power. It incorporates constraints on available solar array power, reactant mass balance between production and consumption, and pressure-dependent storage requirements. To enable reliable convergence, the optimization problem was reformulated to reduce dimensionality and improve numerical stability, with subsystem models organized for efficient evaluation. Problem dimensionality was reduced by consolidating lower-level design variables into higher-level representative quantities, and subsystem behavior was evaluated within the optimization loop. A multi-start initialization strategy was employed to mitigate sensitivity to local minima and improve solution quality, while nonlinear relationships were solved using robust numerical methods. The results showed that convergence was achieved across a range of required output power values. Specific energy reached a maximum at a critical mission power level, where the electrolyzer power matched the available solar input and operated near its voltage and current density limits. Beyond this point, further increases in required power resulted in less mass-efficient operation, increasing total system mass and reducing overall performance. The developed model represents an advancement in RFC system-level optimization by enabling analysis of a broader and more tightly coupled design space than previous considerations. While convergence behavior and computational cost remain challenges, the methods introduced improve solvability and allow inclusion of additional design variables with minimal loss of physical fidelity. However, the numerical results should not be interpreted as definitive design recommendations, as the model includes simplifying assumptions and omits several higher-order effects. Future work should extend this framework by incorporating additional subsystems and loss mechanisms, such as thermal management, parasitic power consumption, and reactant losses, to improve fidelity and ensure more representative design conclusions.

Electrochemistry↗

NASA NTRSDate not supplied

Effect of Heat Treatments on the Tensile Properties of Additively Manufactured 15-5 Ph Stainless Steel

This study investigated the effect of post-manufacture heat treatments on the microstructure and mechanical properties of 15-5 PH stainless steel (SS) fabricated by laser powder-directed energy deposition (LP-DED). Various heat treatment procedures (CA-H900 and CA-H1150) were conducted to evaluate their effects on the tensile behavior of LP-DED 15-5 PH SS. Scanning electron microscopy was used to characterize the microstructural features and the fracture surfaces. Tensile tests were performed to evaluate the mechanical properties at cryogenic and room temperatures. Reduction in area of CA-H1150 treated specimens after tensile tests was significantly higher than CA-H900 ones, while the ultimate tensile and yield strengths of CA-H900 specimens were higher compared to the CA-H1150 ones. The mechanical behavior of the LP-DED 15-5 PH SS in various heat treatment conditions is discussed based on their microstructures and fracture surfaces.

Laser powder directed energy deposition (LP-DED)↗

DOE OSTI2023

Triple Excitations in Green’s Function Coupled Cluster Solver for Studies of Strongly Correlated Systems in the Framework of Self-Energy Embedding Theory

Embedding theories became important approaches used for accurate calculations of both molecules and solids. In these theories, a small chosen subset of orbitals is treated with an accurate method, called an impurity solver, capable of describing higher correlation effects. Ideally, such a chosen fragment should contain multiple orbitals responsible for the chemical and physical behavior of the compound. Handling a large number of chosen orbitals presents a very significant challenge for the current generation of solvers used in the physics and chemistry community. Here, we develop a Green’s function coupled cluster singles doubles and triples (GFCCSDT) solver that can be used for a quantitative description in both molecules and solids. This solver allows us to treat orbital spaces that are inaccessible to other accurate solvers. At the same time, GFCCSDT maintains high accuracy of the resulting self-energy. Moreover, in conjunction with the GFCCSD solver, it allows us to test the systematic convergence of computational studies. Developing the CC family of solvers paves the road to fully systematic Green’s function embedding calculations in solids. In this paper, we focus on the investigation of GFCCSDT self-energies for a strongly correlated problem of SrMnO 3 solid. Subsequently, we apply this solver to solid MnO showing that an approximate variant of GFCCSDT is capable of yielding a high accuracy orbital resolved spectral function.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Strange hadron collectivity in pPb and PbPb collisions

The collective behavior of K$_{S}^{0}$ and $Λ/ \overline{Λ}$ strange hadrons is studied by measuring the elliptic azimuthal anisotropy ($\mathcal{v}$ 2 ) using the scalar-product and multiparticle correlation methods. Proton-lead (pPb) collisions at a nucleon-nucleon center-of-mass energy $\sqrt{s_{NN}}$ = 8.16 TeV and lead-lead (PbPb) collisions at $\sqrt{s_{NN}}$ = 5.02 TeV collected by the CMS experiment at the LHC are investigated. Nonflow effects in the pPb collisions are studied by using a subevent cumulant analysis and by excluding events where a jet with transverse momentum greater than 20 GeV is present. The strange hadron $\mathcal{v}$ 2 values extracted in pPb collisions via the four- and six-particle correlation method are found to be nearly identical, suggesting the collective behavior. Comparisons of the pPb and PbPb results for both strange hadrons and charged particles illustrate how event-by-event flow fluctuations depend on the system size.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Assessment of Dynamic Fracture in Ultra-High Performance Concrete Using Synchrotron X-ray Source

Ultra-high-performance concretes (UHPCs) retain higher ultimate (compressive) strengths and greater durability relative to traditional concrete materials. As a result, they are enabling construction materials for blast resistant structures, where a higher capacity for energy absorption is required. In past investigations, the strength of UHPCs was shown to retain a dependency on strain rate. Still, the failure mechanisms which govern this rate dependency have yet to be completely elucidated. In the current study, the dynamic fracture behavior of Cor-tuf UHPC was assessed, in-situ, using a Synchrotron X-ray source in phase contrast imaging (PCI) mode. Prior to testing, the material’s morphology was characterized using X-ray computed tomography (CT) and scanning electron microscopy (SEM). A polychromatic pulsed X-ray source, high-speed camera and Kolsky bar apparatus were used in tandem, to observe the transient failure modes. A pin was placed at the end of the incident bar to control the location of damage initiation, and tests were performed at a constant velocity of ~6 m/s. These test conditions were observed to yield cracks with median and/or cone like geometries. Despite the variation in the crack paths, a significant difference in peak load was not observed. The failure mode was also observed to depend on the microstructure of the concrete samples.

Kolsky bar↗

DOE OSTI2025

In Situ Study of Resistive Switching in a Nitride‐Based Memristive Device

Abstract Resistive switching (RS) devices with ultra‐low‐voltage threshold and reliable switching repeatability exhibits great potential applications in energy‐efficient data storage and neuromorphic computing. Understanding switching mechanisms at nanoscale is critical to design RS devices with improved performance. In this work, a lamella memristive device using focused ion beam (FIB) method based on the metal/TiO x /TiN/Si structure device is fabricated. In situ transmission electron microscopy (TEM) and current–voltage ( I–V ) characteristic demonstrate that the lamella device shows a volatile RS behavior with a threshold switching at ≈ ± 0.4 V. In situ scanning transmission electron microscopy (STEM) experiments with electron energy loss spectroscopy (EELS) reveal that the charge carriers such as oxygen vacancies migrate under positive/negative DC bias and modulate Schottky barriers at the top and bottom metal/semiconductor interfaces. The RS mechanism of the lamella device is based on the Schottky barriers modulation and Joule heating assisted electric field triggered thermal runaway (FTTR) occurred at the metal/semiconductor interfaces. The fundamental insights gained from this study presents a perspective on interface‐type RS devices processing and opens up new technological opportunities of fabricating ultra‐low‐energy memristive devices.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Excitonic Mott insulator in a Bose-Fermi-Hubbard system of moiré WS 2 /WSe 2 heterobilayer

Understanding the Hubbard model is crucial for investigating various quantum many-body states and its fermionic and bosonic versions have been largely realized separately. Recently, transition metal dichalcogenides heterobilayers have emerged as a promising platform for simulating the rich physics of the Hubbard model. In this work, we explore the interplay between fermionic and bosonic populations, using a WS 2 /WSe 2 heterobilayer device that hosts this hybrid particle density. We independently tune the fermionic and bosonic populations by electronic doping and optical injection of electron-hole pairs, respectively. This enables us to form strongly interacting excitons that are manifested in a large energy gap in the photoluminescence spectrum. The incompressibility of excitons is further corroborated by observing a suppression of exciton diffusion with increasing pump intensity, as opposed to the expected behavior of a weakly interacting gas of bosons, suggesting the formation of a bosonic Mott insulator. We explain our observations using a two-band model including phase space filling. Our system provides a controllable approach to the exploration of quantum many-body effects in the generalized Bose-Fermi-Hubbard model.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Grain growth kinetics of the gamma phase metallic uranium

We report metallic uranium is a leading fuel form for sodium cooled fast reactors as an enabling technology of future nuclear energy systems. Mechanistic understanding of fuel behaviors and kinetics under thermodynamic equilibrium and highly non-equilibrium conditions are essential for evaluating fuel performance. It is important to understand and predict the grain and pore evolutions of metallic fuels under thermal and irradiation conditions. However, very limited data are available on the grain growth kinetics and mechanisms of pure gamma phase uranium. In this paper, the pure gamma uranium pellets with different grain structures were fabricated by combining high-energy ball milling and spark plasma sintering. Isothermal annealing tests were performed to investigate the grain growth behavior of the pure gamma phase uranium with different initial grain sizes. A parabolic relationship in grain growth with time was identified for the submicron-sized (374 nm) sample. In contrast, for the nano-sized (137 nm) sample, the grain growth shows a linear relationship with time. The activation energies of grain growth were determined as 199.5 KJ/mol and 80.6 KJ/mol for nano-sized and submicron-sized grain structures, respectively. For the nano-sized sample, the rate-control step of grain growth is dominated by the triple-junction migration, in which the grain boundary triple junction drags the grain growth, leading to a higher activation energy than the bulk diffusion. The dominating mechanism for the submicron-sized sample is grain boundary diffusion. The mechanistic understanding and critical data obtained on the kinetics of pure uranium phases will be useful to evaluate fuel behavior under thermodynamic equilibrium conditions and develop a high fidelity model to predict fuel performance.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Machine learning of Kondo physics using variational autoencoders and symbolic regression

In this work, we employ variational autoencoders to extract physical insight from a dataset of one-particle Anderson impurity model spectral functions. Autoencoders are trained to find a low-dimensional, latent space representation that faithfully characterizes each element of the training set, as measured by a reconstruction error. Variational autoencoders, a probabilistic generalization of standard autoencoders, further condition the learned latent space to promote highly interpretable features. In our study, we find that the learned latent variables strongly correlate with well known, but nontrivial, parameters that characterize emergent behaviors in the Anderson impurity model. In particular, one latent variable correlates with particle-hole asymmetry, while another is in near one-to-one correspondence with the Kondo temperature, a dynamically generated low-energy scale in the impurity model. Using symbolic regression, we model this variable as a function of the known bare physical input parameters and "rediscover" the nonperturbative formula for the Kondo temperature. The machine learning pipeline we develop suggests a general purpose approach, which opens opportunities to discover new domain knowledge in other physical systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

FLASH-therapy suitable single-pulse proton generation using TiH 2 under nanosecond laser irradiation

We investigated proton emission from titanium hydride (TiH 2 ) targets irradiated in vacuum by a 6-ns, 1064-nm Nd:YAG laser. Time-of-flight measurements with a Faraday cup and an electrostatic ion analyzer resolved distinct proton peaks at high pulse energies, with yields on the order of 10 9 protons per shot. Systematic scans over pulse energy and up to 1000 repeated shots showed that, while the peak amplitude gradually decreased, the integrated proton number remained nearly constant. This behavior is consistent with surface-induced broadening of the plasma expansion while bulk hydrogen is replenished by diffusion and repeated ablation of fresh TiH 2 layers. Using the measured proton numbers and pulse widths, a simple direct-plasma-injection-style scaling indicates peak currents of ∼100 mA and sub-microsecond pulse durations. The pulse structure and yield satisfy key ultra-high-dose-rate criteria and, together with sustained output over 1000 shots, support TiH 2 -based laser ion sources as practical candidates for FLASH-therapy (ultra-high-dose-rate)-oriented studies and injector development using direct plasma injection.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Isotherm, Kinetic, Process Modeling, and Techno-Economic Analysis of a Diamine-Appended Metal-Organic Framework for CO 2 Capture Using Fixed Bed Contactors

In this report, diamine-appended metal-organic frameworks exhibiting step-shaped CO 2 adsorption are exceptional candidates for energy-efficient carbon capture. However, there are few studies examining their performance in real-world capture scenarios, in part due to the challenge inherent in modeling their CO 2 uptake behavior. Here, we develop a dual-site Sips model to fit experimental CO 2 adsorption data for dmpn-Mg 2 (dobpdc) (dmpn = 2,2-dimethyl-1,3-diaminopropane; dobpdc 4- = 4,4'-dioxidobiphenyl-3,3'-dicarboxylate) and develop a linear driving force model for the adsorption kinetics based on available experimental data. These models are used to develop a dynamic, fixed bed, nonisothermal contactor model using shaped particles of the material, which is validated with experimental breakthrough data. We also examine the effects of the high heat of adsorption of the material on CO 2 uptake performance and find that heat removal is essential to maximize capture performance. We finally investigate "basic"(no bed cooling during adsorption) and "modified"(bed cooling during adsorption) temperature swing adsorption (TSA) processes using dmpn-Mg 2 (dobpdc), and their process economics are compared to a state-of-the-art monoethanolamine (MEA) capture system with and without heat recovery. In the absence of heat recovery, the adsorbent systems are more costly than established technology. However, with 85% heat recovery, both adsorbent-based TSA processes are projected to cost less than the MEA system. This work highlights that thermal management is vital for implementation of dmpn-Mg 2 (dobpdc) as a viable CO 2 capture technology. Investigation of other contactor technologies that can provide unique ways to manage system heat represent promising future areas of study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

AP-Net: An atomic-pairwise neural network for smooth and transferable interaction potentials

Intermolecular interactions are critical to many chemical phenomena, but their accurate computation using ab initio methods is often limited by computational cost. The recent emergence of machine learning (ML) potentials may be a promising alternative. Useful ML models should not only estimate accurate interaction energies but also predict smooth and asymptotically correct potential energy surfaces. However, existing ML models are not guaranteed to obey these constraints. Indeed, systemic deficiencies are apparent in the predictions of our previous hydrogen-bond model as well as the popular ANI-1X model, which we attribute to the use of an atomic energy partition. As a solution, we propose an alternative atomic-pairwise framework specifically for intermolecular ML potentials, and we introduce AP-Net—a neural network model for interaction energies. The AP-Net model is developed using this physically motivated atomic-pairwise paradigm and also exploits the interpretability of symmetry adapted perturbation theory (SAPT). We show that in contrast to other models, AP-Net produces smooth, physically meaningful intermolecular potentials exhibiting correct asymptotic behavior. Initially trained on only a limited number of mostly hydrogen-bonded dimers, AP-Net makes accurate predictions across the chemically diverse S66x8 dataset, demonstrating significant transferability. On a test set including experimental hydrogen-bonded dimers, AP-Net predicts total interaction energies with a mean absolute error of 0.37 kcal mol−1, reducing errors by a factor of 2–5 across SAPT components from previous neural network potentials. The pairwise interaction energies of the model are physically interpretable, and an investigation of predicted electrostatic energies suggests that the model “learns” the physics of hydrogen-bonded interactions.

Glick, Zachary L. (ORCID:0000000309002849)↗

DOE OSTI2020

Enabling “lithium-free” manufacturing of pure lithium metal solid-state batteries through in situ plating

Abstract The coupling of solid-state electrolytes with a Li-metal anode and state-of-the-art (SOA) cathode materials is a promising path to develop inherently safe batteries with high energy density (>1000 Wh L −1 ). However, integrating metallic Li with solid-electrolytes using scalable processes is not only challenging, but also adds extraneous volume since SOA cathodes are fully lithiated. Here we show the potential for “Li-free” battery manufacturing using the Li 7 La 3 Zr 2 O 12 (LLZO) electrolyte. We demonstrate that Li-metal anodes >20 μm can be electroplated onto a current collector in situ without LLZO degradation and we propose a model to relate electrochemical and nucleation behavior. A full cell consisting of in situ formed Li, LLZO, and NCA is demonstrated, which exhibits stable cycling over 50 cycles with high Coulombic efficiencies. These findings demonstrate the viability of “Li-free” configurations using LLZO which may guide the design and manufacturing of high energy density solid-state batteries.

25 ENERGY STORAGE↗

DOE OSTI2023

Observation of a massive phason in a charge-density-wave insulator

The lowest-lying fundamental excitation of an incommensurate charge density wave (CDW) material is widely believed to be a massless phason -- a collective modulation of the phase of the CDW order parameter. However, as first pointed out by Lee and Fukuyama, long-range Coulomb interactions should push the phason energy up to the plasma energy of the CDW condensate, resulting in a massive phason and a fully gapped spectrum. Whether such behavior occurs in a CDW system has been unresolved for more than four decades. Using time-domain THz emission spectroscopy, we investigate this issue in the material (TaSe 4 ) 2 I, a classical example of a quasi-one-dimensional CDW insulator. Upon transient photoexcitation at low temperatures, we find the material strikingly emits coherent, narrow-band THz radiation. The frequency, polarization and temperature-dependence of the emitted radiation imply the existence of a phason that acquires mass by coupling to long-range Coulomb interaction. Our observations constitute the first direct evidence of the massive "Lee-Fukuyama" phason and highlight the potential applicability of fundamental collective modes of correlated materials as compact and robust sources of THz radiation.

36 MATERIALS SCIENCE↗

DOE OSTI2024

How well do one-electron self-interaction-correction methods perform for systems with fractional electrons?

Recently developed locally scaled self-interaction correction (LSIC) is a one-electron SIC method that, when used with a ratio of kinetic energy densities (z σ ) as iso-orbital indicator, performs remarkably well for both thermochemical properties as well as for barrier heights overcoming the paradoxical behavior of the well-known Perdew–Zunger self-interaction correction (PZSIC) method. In this work, we examine how well the LSIC method performs for the delocalization error. Our results show that both LSIC and PZSIC methods correctly describe the dissociation of $H$$^{+}_{2}$ and $H$$^{+}_{2}$ but LSIC is overall more accurate than the PZSIC method. Likewise, in the case of the vertical ionization energy of an ensemble of isolated He atoms, the LSIC and PZSIC methods do not exhibit delocalization errors. For the fractional charges, both LSIC and PZSIC significantly reduce the deviation from linearity in the energy vs number of electrons curve, with PZSIC performing superior for C, Ne, and Ar atoms while for Kr they perform similarly. The LSIC performs well at the endpoints (integer occupations) while substantially reducing the deviation. The dissociation of LiF shows both LSIC and PZSIC dissociate into neutral Li and F but only LSIC exhibits charge transfer from Li + to F – at the expected distance from the experimental data and accurate ab initio data. Overall, both the PZSIC and LSIC methods reduce the delocalization errors substantially.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗