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At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Density limits as disruption forecasters for spherical tokamaks

Fusion power output from spherical tokamaks would benefit from increased confined plasma density, but there exists a limit on the density before confinement is lost and the plasma current is disrupted. This density limit has long been characterized by a simple, global Greenwald limit proportional to the plasma current and inversely proportional to the cross sectional area of the plasma. It is shown that in the database of discharges from the National Spherical Tokamak Experiment (NSTX) and Mega Ampere Spherical Tokamak (MAST) spherical tokamaks, the likelihood of disruption does increase above the Greenwald limit, and especially in the plasma current rampdown phase. The physics of the density limit has been recently theoretically explored through local criteria. Several of these are tested using the disruption event characterization and forecasting (DECAF TM ) code for their potential effectiveness as disruption warning signals. For a limited set of NSTX discharges, a local island power balance criteria was found to be less reliable, presently, than the Greenwald limit. For this work, an empirical critical edge line density and a boundary turbulent transport limit were both tested for MAST-U, which has an electron density profile measurement with high spatial resolution in the outer part of the plasma. Both were found to have similar dependencies on key plasma parameters. In a limited set of MAST-U discharges that appear to disrupt due to rising density at values under the Greenwald limit, crossing of the boundary turbulent transport limit occurred close to the time of disruption. Finally, these limits were evaluated for their potential use in real-time, and it was found that with the necessary real-time inputs and with refinement through further testing, these limits could be implemented in a real-time disruption forecasting system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Effect of resistivity on poloidal asymmetries in electron density in the edge and scrape off layer in 3D full-F gyro-fluid simulations with FELTOR

In this contribution, we analyze the poloidal asymmetries in electron density in the edge and scrape-off layer (SOL) in a COMPASS-sized, diverted tokamak with the 3D full-F, isothermal, electromagnetic, and gyro-fluid model FELTOR. The study is performed for different simulations that span over 2 orders of magnitude in resistivity. The poloidal asymmetries of density are evaluated in the edge and the SOL relative to the outer midplane (OMP), where the highest densities are usually found. In the closed magnetic surfaces, the relative poloidal asymmetry with respect to the OMP is not larger than 20% independently of the plasma resistivity. For the open field lines in the SOL, the relative density asymmetry can range from 55% for the highest resistivity to around 40% for the lowest. The lowest densities inside the separatrix are found between the inner midplane and the top of the magnetic configuration, away from the X-point. In the SOL it is usually close to the X-point in the high field side. The observations in the closed field lines are consistent with ballooning transport but in the SOL oppose experimental evidence for high-density plasmas. In conclusion, this indicates the necessity for more complex physics to reproduce the experimental observations in the SOL for higher density plasmas, such as neutral-plasma dynamics and realistic divertor conditions.

3D full-f gyrofluid↗
DOE OSTI2021

Enhanced particle transport events approaching the density limit of the J-TEXT tokamak

Enhanced particle transport events are discovered and analyzed as the density limit of the J-TEXT tokamak is approached. Edge shear layer collapse is observed and the ratio of Reynolds power to turbulence production decreases. Simultaneously, the divergence of turbulence internal energy flux (i.e. turbulence spreading) increases, indicating that shear layer collapse triggers an outward spreading event. Studies of correlations show that the enhanced particle transport events are quasi-coherent, and manifested primarily in density fluctuations which exhibit positive skewness. Furthermore, electron adiabaticity emerges as the critical parameter which signals transport event onset. For α < 0.35 as density approaches the Greenwald density, both turbulence spreading and density fluctuations rise rapidly. Taken together, these results elucidate the connections between edge shear layer, density fluctuations, particle transport events, turbulence spreading and plasma edge cooling as the density limit is approached.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Observation and analysis of lower-hybrid-current-drive density limit in EAST

Lower hybrid current drive (LHCD) experiments with line-averaged density up to ~5.1 × 10 19 m –3 were performed in EAST L-mode plasmas. When the line-averaged density rises above a critical value, the hard x-ray (HXR) emission falls to the noise level, indicating that the LHCD density limit is encountered. The experimental results show that the LHCD density limit can be increased with higher wave source frequency (ƒ 0 ) and higher magnetic field (B t ). Although a higher LHCD density limit is obtained by a higher magnetic field for both 2.45 GHz and 4.6 GHz waves, the results show a stronger dependence on the magnetic field for the 4.6 GHz case. Analysis suggests that, for normal operation with a relatively low magnetic field (1.6 T $\leqslant$ B t $\leqslant$ 2.5 T) on EAST, the dominant mechanisms responsible for the LHCD density limit are different between the 2.45 GHz and 4.6 GHz waves. The wave accessibility plays a more significant role during 4.6 GHz LHCD experiments, while parasitic losses due to parametric decay instability (PDIs) dominate the accessibility issue in the 2.45 GHz case. Collisional loss in the scrape-off layer (SOL) may explain the 4.6 GHz result when combined with the accessibility limit at high density and low temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

The role of isotope mass on neutral fueling and density pedestal structure in the DIII-D tokamak

Abstract Experimental measurements on DIII-D of hydrogen neutral penetration lengths ( λ n 0 ) on the high field side (HFS) are longer by a factor of 2 than for deuterium consistent with the thermal velocity ratio for neutrals at the same temperature ( v t h H / v t h D = 2 ) . This ratio is constant for both low and high pedestal electron density. At low pedestal density ( n e ∼ 4 × 10 19 m − 3 ) , the neutral penetration length is greater than the density pedestal width for both isotopes, and the additional 40% increase of neutral penetration in hydrogen widens the pedestal by the same amount. As the density pedestal height increases ( n e ∼ 6 × 10 19 m − 3 ) , the neutral penetration lengths drop below the density pedestal widths for both isotopes, and the increased penetration of hydrogen has no increased effect on the pedestal width compared to deuterium. Extrapolating to future reactor-relevant high electron density pedestals, the isotope-mass change in neutral fueling on the HFS from the deepest neutral penetration of hydrogen, to the shortest neutral penetration of tritium will be negligible (0.2–0.4 cm) in comparison to estimates of the density pedestal width (6–8.5 cm).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Density limit in peeling-limited pedestals at and above the Greenwald value in DIII-D high poloidal beta plasmas

High pressure, peeling limited pedestals with pedestal normalized beta β N,ped >2 and pedestal top density n ped at or above the Greenwald density nG have been achieved in DIII-D high poloidal beta plasmas, with high global normalized beta β N >3 and energy confinement H 98 ~1.2-1.7. Higher β N allows higher pedestal density above the Greenwald value and higher pedestal pressure, even with a low injected torque. MHD modeling confirms that the experimental profiles lie near the peeling-mode unstable boundary with high normalized pressure gradient βMHD and high edge current density. Experimental analysis and stability calculations indicate that the high poloidal beta with strong Shafranov shift, high βMHD and weak/negative magnetic shear improves the pedestal stability by decoupling the peeling and ballooning modes and stabilizing the ballooning modes, thus facilitating access to the second stable region of peeling-ballooning mode. The access to the second stable peeling-ballooning stability region opens Super-H-like channels without extremely strong shaping or strong torque injection. The high-pressure peeling pedestal allows the pedestal density to go beyond the Greenwald limit with strong ExB shear maintained: pedestal pressure increases with pedestal density even when n ped >n G , until reaching the ideal MHD instability boundary, where giant ELMs occur. The giant ELMs are dominated by a strong n=1 component and cause a large reduction of the edge pressure, but a negligible change of the core pressure, consistent with kink/peeling-mode induced instability. The pedestal recovers from the collapse and typically sustains a high baseline density, around the Greenwald limit, during the whole discharge duration. Experiments also found that internal transport barriers and n ped ~0.9nG, peeling limited pedestals could be simultaneously achieved in high β N plasmas, while an internal feedback between ITB strength and pedestal performance is found.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Generalization of the Kohn-Sham system that can represent arbitrary one-electron density matrices

Density functional theory is currently the most widely applied method in electronic structure theory. The Kohn-Sham method, based on a fictitious system of noninteracting particles, is the workhorse of the theory. The particular form of the Kohn-Sham wave function admits only idempotent one-electron density matrices whereas wave functions of correlated electrons in post-Hartree-Fock methods invariably have fractional occupation numbers. Here we show that by generalizing the orbital concept and introducing a suitable dot product as well as a probability density, a noninteracting system can be chosen that can represent the one-electron density matrix of any system, even one with fractional occupation numbers. This fictitious system ensures that the exact electron density is accessible within density functional theory. It can also serve as the basis for reduced density matrix functional theory. Moreover, to aid the analysis of the results the orbitals may be assigned energies from a mean-field Hamiltonian. This produces energy levels that are akin to Hartree-Fock orbital energies such that conventional analyses based on Koopmans' theorem are available. Lastly, this system is convenient in formalisms that depend on creation and annihilation operators as they are trivially applied to single-determinant wave functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Ab initio electronic density in solids by many-body plane-wave auxiliary-field quantum Monte Carlo calculations

We present accurate many-body results of the electronic densities in several solid materials, including Si, NaCl, and Cu. These results are obtained using the ab initio auxiliary-field quantum Monte Carlo (AFQMC) method working in a plane-wave basis with norm-conserving, multiple-projector pseudopotentials. AFQMC has been shown to be an excellent many-body total energy method. Computation of observables and correlation functions other than the ground-state energy requires back-propagation, whose adaption and implementation in the plane-wave basis AFQMC framework are discussed in the present paper. This development allows us to compute correlation functions, electronic densities, and interatomic forces, paving the way for geometry optimizations and calculations of thermodynamic properties in solids. Finite supercell size effects are considerably more subtle in the many-body framework than in independent-electron calculations. We analyze the convergence of the electronic density, and obtain best estimates for the thermodynamic limit. The densities from several typical density functionals are benchmarked against our near-exact results. The electronic densities we obtained can also be used to help construct improved density functionals.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Imposing correct jellium response is key to predict the density response by orbital-free DFT

Orbital-free density functional theory constitutes a computationally highly effective tool for modeling electronic structures of systems ranging from room-temperature materials to warm dense matter. Its accuracy critically depends on the employed kinetic energy (KE) density functional, which has to be supplied as an external input. In this work we consider several nonlocal and Laplacian-level KE functionals and use an external harmonic perturbation to compute the static density response at T = 0 K in the linear and beyond-linear response regimes. We test for the satisfaction of exact conditions in the limit of uniform densities and for how approximate KE functionals reproduce the density response of realistic materials (e.g., Al and Si) against the Kohn-Sham DFT reference, which employs the exact KE. The results illustrate that several functionals violate exact conditions in the uniform electron gas (UEG) limit. We find a strong correlation between the accuracy of the KE functionals in the UEG limit and in the strongly inhomogeneous case. This empirically demonstrates the importance of imposing the limit of UEG response for uniform densities and validates the use of the Lindhard function in the formulation of kernels for nonlocal functionals. This conclusion is substantiated by additional calculations for bulk aluminum (Al) with a face-centered cubic (fcc) lattice and silicon (Si) with an fcc lattice, body-centered cubic (bcc) lattice, and semiconducting crystal diamond state. The analysis of fcc Al, and fcc as well as bcc Si data follows closely the conclusions drawn for the UEG, allowing us to extend our conclusions to realistic systems that are subject to density inhomogeneities induced by ions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Skyrme pseudopotentials at next-to-next-to-leading order: Construction of local densities and first symmetry-breaking calculations

There is an ongoing quest to improve on the spectroscopic quality of nuclear energy density functionals (EDFs) of the Skyrme type through extensions of its traditional form. One direction for such activities is the inclusion of terms of higher order in gradients in the EDF. We report on exploratory symmetry-breaking calculations performed for an extension of the Skyrme EDF that includes central terms with four gradients at next-to-next-to-leading order (N2LO) and for which the high-quality parametrization SN2LO1 has been constructed recently. Up to now, the investigation of such functionals with higher-order terms was limited to infinite matter and spherically symmetric configurations of singly and doubly magic nuclei. We address here nuclei and phenomena that require us to consider axial and nonaxial deformation, both for reflection-symmetric and also reflection-asymmetric shapes, as well as the breaking of time-reversal invariance. Achieving these calculations demanded a number of formal developments. These all resulted from the formulation of the N2LO EDF requiring the introduction of new local densities with additional gradients that are not present in the EDF at NLO. Their choice is not unique, but can differ in the way the gradients are coupled. While designing a numerical implementation of N2LO EDFs in Cartesian three-dimensional coordinate-space representation, we have developed a novel definition and a new unifying notation for normal and pair densities that contain gradients at arbitrary order. Besides having mnemonic advantages, the new notation allows for the easy identification of redundancies and reducibilities in a given set of local densities, and the new definition makes it straightforward to construct densities that automatically adopt the symmetries of the many-body state they are constructed from. The resulting scheme resolves several issues with some of the choices that have been made for local densities in the past, in particular when breaking time-reversal symmetry. Guided by general practical considerations, we propose an alternative form of the N2LO contribution to the Skyrme EDF that is built from a different set of densities. It has exactly the same physics content, but is much more efficient to handle in formal discussions and, compared to the original formulation, leads to a substantial reduction of computational cost and memory requirements in deformed codes. As representative examples for the performance of SN2LO1, we have chosen the ground states of even-even Kr and Nd isotopes, the fission barrier of 240 Pu as well as the superdeformed rotational band of 194 Hg. Overall, for the nuclei and phenomena studied here, the SN2LO1 parametrization does not yet present a systematic improvement over standard NLO parametrizations. This finding calls for improved fit protocols that better discriminate between NLO and N2LO terms and better exploit the unique features of the additional degrees of freedom offered by the latter.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

eFESTA: Ensemble Feature Exploration with Surface Density Estimates

We propose surface density estimate (SDE) to model the spatial distribution of surface features-isosurfaces, ridge surfaces, and streamsurfaces-in 3D ensemble simulation data. The inputs of SDE computation are surface features represented as polygon meshes, and no field datasets are required (e.g., scalar fields or vector fields). The SDE is defined as the kernel density estimate of the infinite set of points on the input surfaces and is approximated by accumulating the surface densities of triangular patches. We also propose an algorithm to guide the selection of a proper kernel bandwidth for SDE computation. An ensemble Feature Exploration method based on Surface densiTy EstimAtes (eFESTA) is then proposed to extract and visualize the major trends of ensemble surface features. For an ensemble of surface features, each surface is first transformed into a density field based on its contribution to the SDE, and the resulting density fields are organized into a hierarchical representation based on the pairwise distances between them. The hierarchical representation is then used to guide visual exploration of the density fields as well as the underlying surface features. We demonstrate the application of our method using isosurface in ensemble scalar fields, Lagrangian coherent structures in uncertain unsteady flows, and streamsurfaces in ensemble fluid flows.

Computational modeling↗
DOE OSTI2019

Effects of group size and group density on trade–offs in resource selection by a group–territorial central–place foraging woodpecker

Trade-offs in resource selection by central-place foragers are driven by the need to balance the benefits of selecting resources against the costs of travel from the central place. For group-territorial central-place foraging birds, trade-offs in resource selection are likely to be complicated by a competitive advantage for larger groups at high group density that may limit accessibility of high-quality distant resources to small groups. We used the group-territorial, central-place foraging Red-cockaded Woodpecker Leuconotopicus borealis (RCW) as a case study to test predictions that increases in group density lead to differences in foraging distances and resource selection for groups of different sizes. We used GPS tracking and LiDAR-derived habitat data to model effects of group size on foraging distances and selection for high-quality pines (≥ 35.6 cm diameter at breast height (dbh)) and lower quality pines (25.4–35.6 cm dbh) by RCW groups across low ( n = 14), moderate ( n = 10) and high group density ( n = 10) conditions. At low and moderate group density, all RCW groups selected distant high-quality pines in addition to those near the central place because competition for resources was low. In contrast, at high group density, larger groups travelled further to select high-quality pines, whereas smaller groups selected high-quality pines only when they were close to the central place and, conversely, were more likely to select lower quality pines at greater distances from the central place. Selection for high-quality pines only when close to the cavity tree cluster at high group density is important to long-term fitness of small RCW groups because it allows them to maximize benefits from both territorial defence and selecting high-quality resources while minimizing costs of competition. Furthermore these relationships suggest that intraspecific competition at high group density entails substantive costs to smaller groups of territorial central-place foragers by limiting accessibility of distant high-quality foraging resources.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Multifactorial genetic control and magnesium levels govern the production of a Streptomyces antibiotic with unusual cell density dependence

Streptomyces bacteria are renowned both for their antibiotic production capabilities and for their cryptic metabolic potential. Their metabolic repertoire is subject to stringent genetic control, with many of the associated biosynthetic gene clusters being repressed by the conserved nucleoid-associated protein Lsr2. In an effort to stimulate new antibiotic production in wild Streptomyces isolates, we leveraged the activity of an Lsr2 knockdown construct and successfully enhanced antibiotic production in the wild Streptomyces isolate WAC07094. We determined that this new activity stemmed from increased levels of the angucycline-like family member saquayamycin. Saquayamycin has both antibiotic and anti-cancer activities, and intriguingly, beyond Lsr2-mediated repression, we found saquayamycin production was also suppressed at high density on solid or in liquid growth media; its levels were greatest in low-density cultures. This density-dependent control was exerted at the level of the cluster-situated regulatory gene sqnR and was mediated in part through the activity of the PhoRP two-component regulatory system, where deleting phoRP led to both constitutive antibiotic production and sqnR expression. This suggests that PhoP functions to repress the expression of sqnR at high cell density. We further discovered that magnesium supplementation could alleviate this density dependence, although its action was independent of PhoP. Finally, we revealed that the nitrogen-responsive regulators GlnR and AfsQ1 could relieve the repression exerted by Lsr2 and PhoP. Intriguingly, we found that this low density-dependent production of saquayamycin was not unique to WAC07094; saquayamycin production by another wild isolate also exhibited low-density activation, suggesting that this spatial control may serve an important ecological function in their native environments.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

Connecting the dots: Tracking galaxy evolution using constant cumulative number density at 3 ≤ z ≤ 7

Using the cosmological smoothed particle hydrodynamical code GADGET-3, we make a realistic assessment of the technique of using constant cumulative number density as a tracer of galaxy evolution at high redshift. We find that over a redshift range of 3 ≤ z ≤ 7 one can on average track the growth of the stellar mass of a population of galaxies selected from the same cumulative number density bin to within ∼0.20 dex. Over the stellar mass range that we probe (10{sup 10.4}⩽M{sub s}/M{sub ⊙}⩽10{sup 10.8} at z = 3 and 10{sup 8.5}⩽M{sub s}/M{sub ⊙}⩽10{sup 9.6} at z = 7), one can reduce this bias by selecting galaxies based on an evolving cumulative number density. We find that this cumulative number density evolution exhibits a trend toward higher values which can be quantified by simple linear formulations of −0.10Δz for descendants and 0.12Δz for progenitors. Utilizing such an evolving cumulative number density increases the accuracy of descendant/progenitor tracking by a factor of ∼2. This result is in excellent agreement, within 0.10 dex, with abundance matching results over the same redshift range. However, we find that our more physically realistic cosmological hydrodynamic simulations produce a much larger scatter in descendant/progenitor stellar masses than previous studies, particularly when tracking progenitors. This large scatter makes the application of either the constant cumulative number density or evolving cumulative number density technique limited to average stellar masses of populations only, as the diverse mass assembly histories caused by stochastic physical processes such as gas accretion or mergers lead to an even larger scatter in other physical properties such as metallicity and star formation rate.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

NITROGEN CAN LIMIT OVERSTORY TREE GROWTH FOLLOWING EXTREME STAND DENSITY INCREASE IN A PONDEROSA PINE FOREST

Extreme stand density increases have occurred in ponderosa pine forests throughout the western U.S. since the early 20th Century, with adverse implications for growth, physiological functioning, and mortality risk. Identifying primary stressors on large, old overstory trees in dense forests can inform management decisions to promote resilience and survival. We tested the impact of stand density increase on overstory treering growth, and the relative influence of water and nitrogen, in an old-growth ponderosa pine forest subject to variable density increase. We measured annual tree-ring growth and carbon discrimination in trees before stand density increased, in a climatically-similar period post-density increase, and in recent transition to drought. We expected density-driven water stress to drive reduced tree-ring growth in overstory trees in dense stands. We found reduced growth and higher mortality in dense stands, but nitrogen rather than water constrained growth, as determined by carbon isotope discrimination in tree rings, leaf nitrogen concentration, and soil nitrogen supply. In dense stands, less available nitrogen limited photosynthetic rate, leading to reduced assimilation of intracellular 13C and higher discrimination with low tree-ring growth and a reduced relationship with climate. This unexpected result illustrates that a variety of limiting factors can influence forest dynamics, as density-driven nitrogen limitation interacts with water stress to influence tree growth and physiological functioning.

dendroecology, tree-ring width, limiting factors, ↗
DOE OSTI2019

Method for Measuring Dry Density of Compacted Bentonite Mixture Soil Using 3D Laser Scanner data - 19119

The bentonite mixture soil is planned to be used for the low-permeability layer of low-level radioactive waste (LLW) disposal facilities. The construction of the bentonite mixture soil is similar to that of normal soil construction, and the rolling pressure and/or vibration compaction are used. The quality control of construction is the same as normal soil work, and the construction management has to confirm that the compaction degree (that is ratio of the dry density to the modified proctor curve) is above specified value. As a method of measuring the dry density after construction, the conventional methods are the core cutter method and the sand replacement method. The measurement principle of these methods is simple and the reliability of the measurement value is high, but during measurements digging holes disturb the construction place, and the measurement duration is a disadvantage in these methods. Therefore, we developed a non-destructive method that can make measurements in a short time. The developed method uses the correlation between the density change and the layer thickness change before and after compaction, and estimates the density after compaction from the height change obtained from the survey results. However, since the material is compressed while the cross-sectional area spreads, this cross-sectional area change is also taken into consideration. By using the point cloud data of the 3D laser scanner surveying, it is possible to obtain almost continuous data in a short period of time. Corrected dry density values calculated by the above procedure ρ'{sub 3D} are generally consistent with dry density after compaction ρ{sub core} by the core cutter method. This method differs depending on the boundary conditions of the bottom and the side of the construction place. Then, the reliability of the method was evaluated by applying it to two boundary conditions and comparing it with the core cutter method. The proposed estimation method showed good agreement with the core cutter method. Therefore, it was confirmed that it is possible to estimate dry density with high reliability. Although this method needs to be used in set with core cutter method, the measurement frequency of the core cutter method can be reduced, and the measurement of a vast area can be done in a short time without disturbance. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2016

Phosphorus and carrier density of heavily n-type doped germanium

The threshold current density of n-type, tensile-strained Ge lasers strongly depends on the electron density. Although optical net gain analyses indicate that the optimum electron density should be on the order of 1 × 10{sup 20} cm{sup −3} to get the lowest threshold, it is not a simple task to increase the electron density beyond the mid range of 10{sup 19} cm{sup −3}. The present paper analyzes the phenomenon where electron density is not proportional to phosphorus donor density, i.e., “saturation” phenomenon, by applying the so-called amphoteric defect model. The analyses indicate that the saturation phenomenon can be well explained by the charge compensation between the phosphorus donors (P{sup +}) and doubly negative charged Ge vacancies (V{sup 2−}).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Perdew-Zunger self-interaction correction: How wrong for uniform densities and large- Z atoms?

Semilocal density functionals for the exchange-correlation energy of a many-electron system cannot be exact for all one-electron densities. In 1981, Perdew and Zunger (PZ) subtracted the fully nonlocal self-interaction error orbital-by-orbital, making the corrected functional exact for all collections of separated one-electron densities and making no correction to the exact functional. Although the PZ self-interaction correction (SIC) eliminates many errors of semilocal functionals, it is often worse for equilibrium properties of sp-bonded molecules and solids. Nonempirical semilocal functionals are usually designed to be exact for electron gases of uniform density and, thus, also make 0% error for neutral atoms in the limit of large atomic number Z, but PZ SIC is not so designed. For localized SIC orbitals, we show analytically that the local spin density approximation (LSDA)-SIC correlation energy per electron of the uniform gas in the high-density limit makes an error of -50% in the spin-unpolarized case and -100% in the fully spin-polarized case. Then we extrapolate from the Ne, Ar, Kr, and Xe atoms to estimate the relative errors of the PZ SIC exchange-correlation energies (with localized SIC orbitals) in the limit of large atomic number: about +5.5% for the LSDA-SIC and about -3.5% for nonempirical generalized gradient [Perdew-Burke-Ernzerhof (PBE)-SIC] and meta-generalized gradient strongly constrained and appropriately normed (SCAN)-SIC approximations. Finally, the SIC errors are considerably larger than those that have been estimated for LSDA-SIC by approximating the localized SIC orbitals for the uniform gas and may explain the errors of PZ SIC for equilibrium properties, opening the door to a generalized SIC that is more widely accurate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗