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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Ultrafast nonlinear absorption of TMDC quantum dots

Here, we study theoretically absorption properties of MoS 2 quantum dots placed in an ultrashort and strong optical pulse with the duration of a few femtoseconds and the amplitude up to 1.5 V/Å. While the monolayer of MoS 2 has a bandgap of ≈ 1.8 eV, the quantum dots of MoS 2 have in-gap edge states, which open additional absorption channels. The absorbance of the system strongly depends on the amplitude of the pulse. At small amplitude, less than 0.5 V/Å, the absorbance varies by more than 20% with the frequency of the pulse. The system shows saturable absorption if the frequency of the pulse is larger than the bulk bandgap and reverse saturable absorption if the frequency of the pulse is in the bandgap. At large amplitudes, > 0.5 V/Å, of the pulse, the ultrafast absorbance of a quantum dot has a weak dependence on the pulse frequency. If the frequency of the pulse is less than the corresponding bulk bandgap, the absorbance has a nonmonotonic dependence on the pulse amplitude with the maximum at ≈ 0.5 V/Å. We also present the results for QDs of different TMDC materials, which show that at large field amplitude, > 0.5 V/Å, the absorbance is universal and has weak dependence on the type of TMDC.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Time inversion symmetry in the Dirac and Schrödinger-Pauli theories

The Schrödinger-Pauli theory is generally believed to give a faithful representation of the nonrelativistic and weakly relativistic limit of the Dirac theory. However, the Schrödinger-Pauli theory is fundamentally incomplete in its account of broken time inversion symmetry, e.g., in magnetically ordered systems. Here, in the Dirac theory of the electron, magnetic order breaks time inversion symmetry even in the nonrelativistic limit, whereas time inversion symmetry is effectively preserved in the Schrödinger-Pauli theory in the absence of spin-orbit coupling. In the Dirac theory, the Berry curvature $1/(2m^2 c^2)$ is thus an intrinsic property of nonrelativistic electrons similar to the well-known spin magnetic moment $e\hbar/(2m)$, while this result is missed by the nonrelativistic or weakly relativistic Schrödinger-Pauli equation. In ferromagnetically ordered systems, the intrinsic Berry curvature yields a contribution to the anomalous Hall conductivity independent of spin-orbit coupling.

Winkler, R. [Northern Illinois Univ., DeKalb, IL (↗
DOE OSTI2022

QCD analysis of Δ S = 0 hadronic parity violation

We present a QCD analysis of the effective weak Hamiltonian at hadronic energy scales for strangeness-nonchanging (ΔS = 0) hadronic processes. Performing a leading-order renormalization group analysis in QCD from the W to the O(2 GeV) energy scale, we derive the pertinent effective Hamiltonian for hadronic parity violation, including the effects of both neutral and charged weak currents. We compute the complete renormalization group evolution of all isosectors and the evolution through heavy-flavor thresholds for the first time. We show that the additional four-quark operators that enter below the W mass scale from QCD operator mixing effects form a closed set, and they result in a 12 x 12 anomalous dimension matrix. Computing the resulting effective Hamiltonian and comparing to earlier results, we affirm the importance of operator mixing effects and find, as an example, that the parity-violating pion-nucleon coupling constant, using the factorization Ansatz and an assessment of the pertinent quark charge of the nucleon in lattice QCD at the 2 GeV scale, is in better agreement with recent experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

How threshold effects in spectroscopic factors influence heavy-ion knockout reactions

A two-decade-old puzzle in heavy-ion one-nucleon knockout reactions is the strong correlation between the reduction factor R S = σ exp /σ t h and the Fermi surface asymmetry ΔS. Theoretical cross sections typically rely on spectroscopic factors (SFs) from shell model (SM) calculations, which neglect continuum coupling effects. Here, we employ the Gamow shell model (GSM), which explicitly incorporates continuum coupling, to compute SFs for p-shell nuclei and predict corresponding theoretical cross sections. Systematic calculations demonstrate that using GSM-derived SFs substantially reduces discrepancies between theoretical and experimental results. This improvement is particularly significant for deeply bound nucleon knockout in nuclei near the dripline, where traditional SM-based calculations fall short. As a result, using GSM SFs, the ratio R s exhibits no pronounced dependence on ΔS. Furthermore, both the ratio of GSM SFs to SM SFs and their corresponding reaction cross sections ratios exhibit a strong ΔS dependence. We have also compared GSM SFs and cross sections with those from the no-core shell model calculations, giving a similar pronounced sensitivity to ΔS. Detailed analysis attributes these correlations to threshold effects for SFs in weakly bound systems. Overall, incorporating continuum coupling via GSM enhances the reliability of SF predictions for exotic, weakly bound nuclei and provides key insights toward resolving the enduring puzzle in heavy-ion knockout reactions from a nuclear structure perspective.

Gamow shell model↗
DOE OSTI2022

Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism

Nuclear weak decays provide important probes to fundamental symmetries in nature. A precise description of these processes in atomic nuclei requires comprehensive knowledge on both the strong and weak interactions in the nuclear medium and on the dynamics of quantum many-body systems. In particular, an observation of the hypothetical double beta decay without emission of neutrinos (0νββ) would unambiguously demonstrate the Majorana nature of neutrinos and the existence of the lepton-number-violation process. It would also provide unique information on the ordering and absolute scale of neutrino masses. The next-generation tonne-scale experiments with sensitivity up to 10 28 years after a few years of running will probably provide a definite answer to these fundamental questions based on our current knowledge on the nuclear matrix element (NME), the precise determination of which is a challenge to nuclear theory. Beyond-mean-field approaches have been frequently adapted for the study of nuclear structure and decay throughout the nuclear chart for several decades. In this review, we summarize the status of beyond-mean-field calculations of the NMEs of 0νββ decay assuming the standard mechanism of an exchange of light Majorana neutrinos. In conclusion, the challenges and prospects in the extension and application of beyond-mean-field approaches for 0νββ decay are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Structure-thermal property relationships of aikinite PbCuBiS 3

Understanding the structural properties and chemical bonding in complex multinary chalcogenides is highly valuable, as it provides vital information for controlling their physical properties to suit various technological applications. Here, we report on the structural, thermal, and electronic properties of PbCuBiS 3 by incorporating an experimental and theoretical investigation of this material. Analysis of the experimental temperature-dependent heat capacity and thermal conductivity data show that weak bonding and strong lattice anharmonicity give rise to ultralow thermal conductivity. Chemical bonding information obtained from the density functional theory electronic calculations reveal significant antibonding interactions that underscore the dominant role of the Cu-S tetrahedra on occupied antibonding states, as well as a highly distorted Pb/Bi-S environment inducing weak bonding and strong lattice anharmonicity. This study broadens our understanding of the structure-property relationships for this material, and can be useful for developing this and similar chalcogenide materials for potential applications of interest.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Performance characterization of nanofiltration, reverse osmosis, and ion exchange technologies for acetic acid separation

A major obstacle to widespread implementation of bio-based fuels and chemicals is the lack of efficient and costeffective separation methods. To purify acetic acid produced by biochemical conversion of biomass via anaerobic digestion, this work employs two commonly used separation technologies: (1) ion-exchange (IX) resin and (2) pressure-driven membranes. This study tested five commercially available strong- and weak-base anion-exchange resins and five commercially available nanofiltration (NF) and reverse osmosis (RO) membranes. The pH of the feed solution significantly affected adsorption capacity. At pH 6.3, a strong-base IX resin (IRN-78) performed best (95.1% acetate removal). With strong-base IX resins, the Langmuir isotherm model fit well, whereas for weak-base IX resins, the Freundlich isotherm provided a better fit. A pseudo-second-order kinetic model fit well for both IRN-78 and IRA-67. Regarding membrane separation, RO (BW30XFR membrane) achieved the highest rejection (98.6% acetate rejection), whereas an NF membrane (NF*) achieved the best combination of permeate flux (105 L/(h∙m 2 )) and rejection (83.1% acetate rejection). For membrane performance, the experimental data were fit using the solution diffusion model. Increased pH in the feed solution lowered permeate flux but increased acetic acid rejection. Finally, then the acetic acid concentration in the feed solution increased, both permeate flux and acetic acid rejection decreased for membrane NF*.

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

Use of physics to improve solar forecast: Part III, impacts of different cloud types

Cloud-type impacts present a great challenge to solar forecasting due to diverse and complex cloud-radiation interactions. This third part of our paper sequence seeks to address this challenge by quantifying the forecast accuracies under eight cloud types: cumulus (Cu), stratified clouds (St), altocumulus (Ac), altostratus (As), cirrostratus/anvil (Cr), cirrus (Ci), congestus (Co), deep convective clouds (Dc) across four physics-informed persistence models reported in Part I. To generalize the cloud impacts, the eight cloud types are further grouped into three cloud categories based on their common features: weak convective clouds, stratiform clouds, and strong convective clouds. Here, the decade-long (2001 ~ 2014) collocated measurements of irradiances and cloud types at the U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) Program South Great Plain (SGP) Central Facility site are used for model evaluation. Results reveal a clear performance hierarchy for global horizontal irradiance (GHI) and direct normal irradiance (DNI): best for weak convective clouds and cirrus, intermediate for stratiform clouds, and worst for strong convective clouds. Performance for diffuse horizontal irradiance (DHI) is less influenced by cloud types. Cloud albedo dominates all three irradiances for Dc, while both cloud albedo and cloud fraction are influential for other cloud types. A 12 %~33 % improvement in accuracy at 6-hour lead time compared to the benchmark smart model confirms the effectiveness of incorporating physics into the models for various cloud types; further improvements are expected by directly integrating cloud type information into forecasting models by modifying the physical formulation of cloud-radiation interaction, and/or using more advanced machine learning models.

14 SOLAR ENERGY↗
DOE OSTI2023

Uniform momentum and temperature zones in unstably stratified turbulent flows

Wall-bounded turbulent flows exhibit a zonal arrangement, in which streamwise velocity organizes into uniform momentum zones (UMZs), separated by thin layers of elevated interfacial shear. While significant research efforts have focused on these structural features in neutrally stratified flows, the effects of unstable thermal stratification on UMZs and on analogous uniform temperature zones (UTZs) have not been considered previously. In this article, statistical properties of UMZs and UTZs are investigated using a suite of large eddy simulations of unstably stratified turbulent channel flow spanning weakly to highly convective conditions. When normalized by the friction velocity and stability-dependent mixing length, the mean velocity gradient based on UMZ interfacial velocity jumps and the vorticity thickness exhibits good collapse for all stabilities, establishing a link between UMZ properties and scaling predictions from Monin–Obukhov similarity theory. A similar relationship is found between UTZ properties and surface-layer scaling of the mean temperature gradient. In the mixed layer, mean UMZ depth is quasi-constant with wall-normal distance, while the deepest UTZs are found in the centre of the boundary layer. These instantaneous structures are found to be linked to the well-mixed velocity and temperature profiles in the convective mixed layer. Conditional averaging indicates that both UMZ and UTZ interfaces are associated with ejections of momentum and warm updrafts below the interface and sweeps of momentum and cool downdrafts above the interface. These results demonstrate a tangible connection between instantaneous structural features, mean properties and scaling laws in unstably stratified flows.

Mechanics↗
DOE OSTI2020

Self-sustaining sound in collisionless, high- β plasma

Using analytical theory and hybrid-kinetic numerical simulations, we demonstrate that, in a collisionless plasma, long-wavelength ion-acoustic waves (IAWs) with amplitudes $δn/n_0≳2/β$ (where $β\gg1$ is the ratio of thermal to magnetic pressure) generate sufficient pressure anisotropy to destabilize the plasma to firehose and mirror instabilities. These kinetic instabilities grow rapidly to reduce the pressure anisotropy by pitch-angle scattering and trapping particles, respectively, thereby impeding the maintenance of Landau resonances that enable such waves’ otherwise potent collisionless damping. The result is wave dynamics that evince a weakly collisional plasma: the ion distribution function is near-Maxwellian, the field-parallel flow of heat resembles its Braginskii form (except in regions where large-amplitude magnetic mirrors strongly suppress particle transport), and the relations between various thermodynamic quantities are more ‘fluid-like’ than kinetic. A nonlinear fluctuation–dissipation relation for self-sustaining IAWs is obtained by solving a plasma-kinetic Langevin problem, which demonstrates suppressed damping, enhanced fluctuation levels and weakly collisional thermodynamics when IAWs with $δn/n_0≳2/β$ are stochastically driven. We investigate how our results depend upon the scale separation between the wavelength of the IAW and the Larmor radius of the ions, and discuss briefly their implications for our understanding of turbulence and transport in the solar wind and the intracluster medium of galaxy clusters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Self-organization in collisionless, high- β turbulence

The magnetohydrodynamic (MHD) equations, as a collisional fluid model that remains in local thermodynamic equilibrium (LTE), have long been used to describe turbulence in myriad space and astrophysical plasmas. Yet, the vast majority of these plasmas, from the solar wind to the intracluster medium (ICM) of galaxy clusters, are only weakly collisional at best, meaning that significant deviations from LTE are not only possible but common. Recent studies have demonstrated that the kinetic physics inherent to this weakly collisional regime can fundamentally transform the evolution of such plasmas across a wide range of scales. Here, we explore the consequences of pressure anisotropy and Larmor-scale instabilities for collisionless, β $\gg$ 1, turbulence, focusing on the role of a self-organizational effect known as ‘magneto-immutability’. We describe this self-organization analytically through a high-β, reduced ordering of the Chew–Goldberger–Low-MHD (CGL-MHD) equations, finding that it is a robust inertial-range effect that dynamically suppresses magnetic-field-strength fluctuations, anisotropic-pressure stresses and dissipation due to heat fluxes. As a result, the turbulent cascade of Alfvénic fluctuations continues below the putative viscous scale to form a robust, nearly conservative, MHD-like inertial range. These findings are confirmed numerically via Landau-fluid CGL-MHD turbulence simulations that employ a collisional closure to mimic the effects of microinstabilities. We find that microinstabilities occupy a small (~5%) volume-filling fraction of the plasma, even when the pressure anisotropy is driven strongly towards its instability thresholds. We discuss these results in the context of recent predictions for ion-vs-electron heating in low-luminosity accretion flows and observations implying suppressed viscosity in ICM turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Strong gradient effects on neoclassical electron transport and the bootstrap current in large aspect ratio tokamaks

Standard approaches to neoclassical theory do not extend into regions of strong gradients in tokamaks such as the pedestal and internal transport barriers. Here, we calculate the modifications to neoclassical electron physics inside strong gradient regions of large aspect ratio tokamaks in the banana regime. We show that these modifications are due to the different ion flow and the strong poloidal variation of the potential. We also provide a physical interpretation of the mechanisms that drive poloidal asymmetries and hence a poloidal electric field. We apply our model to two specific example cases of pedestal profiles, calculating the neoclassical electron flux and the bootstrap current. We find that, depending on the ion flow, weak gradient neoclassical theory overestimates or underestimates the neoclassical electron transport and the bootstrap current in regions with strong gradients. We show that the determination of the mean parallel flow is more complex than in weak gradient neoclassical theory. For vanishing turbulence, we can determine the radial electric field for a given flow profile in the pedestal.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

4D-STEM of Beam-Sensitive Materials

We report that a scanning electron nanobeam diffraction, or 4D-STEM (four-dimensional scanning transmission electron microscopy), is a flexible and powerful approach to elucidate structure from "soft" materials that are challenging to image in the transmission electron microscope because their structure is easily damaged by the electron beam. In a 4D-STEM experiment, a converged electron beam is scanned across the sample, and a pixelated camera records a diffraction pattern at each scan position. This four-dimensional data set can be mined for various analyses, producing maps of local crystal orientation, structural distortions, crystallinity, or different structural classes. Holding the sample at cryogenic temperatures minimizes diffusion of radicals and the resulting damage and disorder caused by the electron beam. The total fluence of incident electrons can easily be controlled during 4D-STEM experiments by careful use of the beam blanker, steering of the localized electron dose, and by minimizing the fluence in the convergent beam thus minimizing beam damage. This technique can be applied to both organic and inorganic materials that are known to be beam-sensitive; they can be highly crystalline, semicrystalline, mixed phase, or amorphous. One common example is the case for many organic materials that have a π-π stacking of polymer chains or rings on the order of 3.4-4.2 Å separation. If these chains or rings are aligned in some regions, they will produce distinct diffraction spots (as would other crystalline spacings in this range), though they may be weak or diffuse for disordered or weakly scattering materials. We can reconstruct the orientation of the π-π stacking, the degree of π-π stacking in the sample, and the domain size of the aligned regions. This Account summarizes illumination conditions and experimental parameters for 4D-STEM experiments with the goal of producing images of structural features for materials that are beam-sensitive. We will discuss experimental parameters including sample cooling, probe size and shape, fluence, and cameras. 4D-STEM has been applied to a variety of materials, not only as an advanced technique for model systems, but as a technique for the beginning microscopist to answer materials science questions. It is noteworthy that the experimental data acquisition does not require an aberration-corrected TEM but can be produced on a variety of instruments with the right attention to experimental parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Molecular Examination of Ion-Pair Competition in Alkaline Aluminate Solutions Using In Situ Liquid SIMS

Understanding the structure and composition of aluminate complexes in extremely alkaline systems such as Bayer liquors has received enormous attentions due to its fundamental and industrial importance. However, obtaining direct molecular information of the underlying ion-ion interactions using traditional approaches such as NMR or Raman spectroscopy is challenging due to the weakness of these interactions and/or their complex overlapping spectral signatures. Here, we exploit in situ liquid secondary ion mass spectrometry (SIMS) as a new approach and show how it enables new insights. In contrast with traditional techniques, using SIMS we succeeded in acquiring information on dominant ion clusters in these alkaline systems. In Na + /K + mixed alkaline aluminate solutions we clearly observe preferential formation of Na + -anion clusters over K + -anion clusters. Further, evaluation of these clusters by density functional theory (DFT) calculations shows that these structures are stable and that their relative bond energies are consistent with their observed SIMS signal intensity differences. This demonstrates a key advantage of in situ liquid SIMS for overcoming ambiguities obscuring important information in these systems on constituent molecular clusters defined by relatively weak ion pair competition and ion-solvent interactions.

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

Polymorphism and Negative Linear Compressibility in Pyrazine-d4

Pyrazine (1,4-diazine) is a widely used linker in coordination polymers, molecular magnets, and metal–organic frameworks, yet its solid-state polymorphism is controlled by weak C–H···N interactions. Using variable-temperature and high-pressure neutron diffraction, a previously unrecognized low-temperature transition to phase IV is identified, showing that the form stabilized under pressure can also be accessed below ∼90 K at ambient pressure in the perdeuterated compound. The transition from phase III → IV involves a symmetry-breaking lattice distortion driven by the reorganization of C–H···N hydrogen bonds, accompanied by negative linear compressibility, which is primarily accommodated through the reduction in void-space within the structure. Structural analysis reveals that while the overall monoclinic framework of phase IV is preserved under both temperature and pressure routes, the evolution of hydrogen-bonded network is distinct depending on the pathway taken. These results establish pyrazine as a model molecular solid for studying pressure–temperature polymorphism and demonstrate how weak directional interactions can produce anomalous mechanical responses in organic crystals.

Ridley, Christopher J. [Oak Ridge National Laborat↗
DOE OSTI2023

Expanding the Transuranic Metal–Organic Framework Portfolio: The Optical Properties of Americium(III) MOF-76

Reported here is the synthesis, crystal structure, and solid-state characterization of a new americium containing metal–organic framework (MOF), [Am(C 9 H 3 O 6 )(H 2 O)], MOF-76(Am). This material is constructed from Am 3+ metal centers and 1,3,5-tricarboxylic acid (BTC) ligands, forming a porous three-dimensional framework that is isostructural with several known trivalent lanthanide (Ln) analogs (e.g., Ce, Nd, and Sm–Lu). The Am 3+ ions have seven coordinates and assume a distorted, capped trigonal prismatic geometry with C1 symmetry. The Am 3+ –O bonds were studied via infrared spectroscopy and compared to several MOF-76(Ln) analogs, where Ln = Nd 3+ , Eu 3+ , Tb 3+ , and Ho 3+ . The results show that the strength of the ligand carboxylate stretching and bending modes increase with Nd 3+ < Eu 3+ < Am 3+ < Tb 3+ < Ho 3+ , suggesting the metal–oxygen bonds are predominantly ionic. Optical absorbance spectroscopy measurements reveal strong f–f transitions; some exhibit pronounced crystal field splitting. The photoluminescence spectrum contains weak Am 3+ -based emission that is achieved through direct and indirect metal center excitation. The weak emissive behavior is somewhat surprising given that ligand-to-metal resonance energy transfer is efficient in the isoelectronic Eu 3+ (4f 6 ) and related Tb 3+ (4f 8 ) analogs. The optical properties were explored further within a series of heterometallic MOF-76(Tb 1–x Am x ) (x = 0.8, 0.2, and 0.1) samples, and the results reveal enhanced Am 3+ photoluminescence.

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

Unexpected Hydricity of a Bis-Carbene Iridium Complex Provides Insight into Electronic Structure Impacts on Hydride Donor Ability

The hydricity (ΔG° H– ), or hydride donor ability, of a transition metal complex is a thermodynamic parameter which can aid in the design and interpretation of various catalytic reactions that involve hydride transfer as a key step. In an attempt to generate a strong hydride donor, the bis-carbene ligand 3,3′-methylenebis(1-methyl-imidazol-2-ylidene) (“bis-mim”) was installed in an iridium hydride complex, [Cp*Ir(bis-mim)H] + . Experimental and computational studies show that [Cp*Ir(bis-mim)H] + is actually a relatively weak hydride donor, however. To understand why the complex is an unexpectedly weak hydride donor, experimental and computational studies probing the steric and electronic effects on hydricity were conducted. Steric factors had a minimal impact on thermodynamic hydricity but dampened kinetic hydricity. In conclusion, the poor thermodynamic hydride donor ability can be attributed to an electronic structure that results in relatively long Cp*−Ir bonds, an unusually high Ir–H BDFE and pK a values that have an outsized influence on thermochemical cycles for hydricity.

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

Local Spin Density Approximation Strongly Improved by a Better-Informed Local Scaling of Its Self-Interaction Correction

The Perdew−Zunger self-interaction correction (PZSIC) makes density functional approximations (DFAs) exact for all one-electron densities. However, it overcorrects in manyelectron regions, introducing errors for the uniform-density limit, where uncorrected DFAs are exact. The locally scaled PZSIC (LSIC), based on the iso-orbital indicator zσ [which distinguishes single-orbital and slowly varying density regions and is used with the local spin density approximation (LSDA)], restores the uniform-density limit and significantly improves results for many properties, including chemical reaction barrier heights, atomization energies, and ionization potentials. Yet, LSIC performs poorly for weakly bonded systems, leaving many unbound, due to limitations of its iso-orbital indicator. To correct this, in this work we propose a new local scaling, LSIC-α, based on the iso-orbital indicator ασ (which additionally identifies regions of overlapping density tails). A two-parameter scaling function of ασ is fitted to a subset of the nonbonded appropriate norms for the SCAN and r2SCAN meta- GGAs, and tested on many properties of main-group atoms, molecules, and molecular complexes. LSIC-α greatly improves the interaction energies of weakly bonded systems in the S22 data set while retaining LSIC’s accuracy for other properties. This work shows that the errors of LSDA (and presumably of higher-level DFAs) can be largely but not entirely repaired by a proper “do no harm” self-interaction correction.

Approximation↗