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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Two splits, three ways: advances in double splitting quenches

In this work we introduce a method for calculating holographic duals of BCFTs with more than two boundaries. We apply it to calculating the dynamics of entanglement entropy in a 1+1d CFT that is instantaneously split into multiple segments and calculate the entanglement entropy as a function of time for the case of two splits, showing that our approach reproduces earlier results for the double split case. Our manuscript lays the groundwork for future calculations of the entanglement entropy for more than two splits and systems at nonzero temperature.

AdS-CFT correspondence↗
DOE OSTI2020

Nondestructive measurements of residual 235 U mass of Israeli Research Reactor-1 fuel using the Advanced Experimental Fuel Counter

In 2018, a measurement campaign took place with participants from Los Alamos National Laboratory (LANL), the Nuclear Research Centre-Negev (NRCN) and Soreq Nuclear Research Center (SNRC) at the Israeli Research Reactor-1 (IRR-1) in which 14 of the reactor’s used fuel assemblies (FAs) with varied amount of depletion were measured with the nondestructive assay instrument Advanced Experimental Fuel Counter (AEFC). Designed for safeguards purposes, the AEFC measures both neutrons emitted from the FA (passive neutrons) and fission neutrons induced by an external neutron source (in this experiment, 252 Cf). Signals recorded with the AEFC include total neutron count rates (Singles), time-correlated neutron count rates (Doubles), and total gamma-ray count rates. The 235 U content of the FAs was previously assessed by two independent methods: (1) measurement of the transparency of the FA to low-energy gamma rays from an activated rhenium source (rhenium gamma transmission, or the RGT method) and (2) calculation of the 30-year burnup history of the core using detailed three-dimensional Monte-Carlo core depletion calculations. The results from the FAs that had been measured via the RGT method were used to construct the calibration curves, which translate the AEFC count rates to 235 U mass. Then, the calibration was evaluated using AEFC measurements of six additional FAs that were not measured via the RGT method. From the results, it was determined the Doubles calibration curve was more reliable than that of the Singles and follows a simple second-order polynomial fit for the whole range of residual 235 U mass content, albeit with larger statistical uncertainty. Detailed uncertainties quantification was conducted for both the AEFC Singles and Doubles. This includes the analysis of statistical uncertainties, calibration uncertainty, and random uncertainties due to the sensitivity of the AEFC to several sources of uncertainty, namely the FA position, FA orientation, interrogation source position, and ambient pool temperature. Finally, an overall total uncertainty of 6 g of 235 U is estimated for the Singles and Doubles, which is mainly due to calibration uncertainty (for the Singles) and statistical uncertainty (for the Doubles), and which constitutes 3%–6% of the 235 U total mass in the FAs, depending on their level of depletion.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Long-Term Photovoltaic System Performance in Cold, Snowy Climates

As countries around the world transition towards renewable energy, there is increasing interest in using photovoltaic (PV) technologies to help decarbonize northern and alpine communities due to their scalability and affordability. However, a barrier to large-scale adoption of PV in cold climates is long-term performance uncertainty under snowfall, freeze-thaw cycles, low temperatures, and high winds. In this work, we provide a comprehensive review of published silicon degradation rates in cold Koppen-Geiger climate classifications of Dfb (humid continental), Dfc (subarctic), and ET (tundra). We first analyze the system degradation rates of three subarctic ground-mounted photovoltaic sites in North America using the RdTools year-on-year method: an Al-BSF double-axis tracking site in Fairbanks, Alaska (65degrees N); a PERC and silicon heterojunction bifacial vertical and south-tilted site in Fairbanks, Alaska; and a PERC south-facing fixed-tilt site in Fort Simpson, Northwest Territories (62degrees N). Degradation rates of these newly analyzed sites vary between -0.4%/year and -1.5%/year. Combining these data with previously reported cold climate degradation rates, we show that the distribution of cold climate degradation peaks at -0.1%/year to -0.2%/year but has a large tail with rates above -0.5%/year. The average reported cold climate degradation rate is -0.45%/year, whereas the median value is -0.33%/year. These results suggest that despite frequent freeze-thaw cycles and potential exposure to high wind and snow loads, PV systems in cold climates tend to degrade slower than PV systems in warmer climates. The limited sample size of reported degradation rates in cold climates (27) motivates the need for further data acquisition and monitoring efforts as new technologies are deployed.

14 SOLAR ENERGY↗
DOE OSTI2025

BHResist [SWR-25-57]

BHResist is a pure python library for computing thermal resistance within single-u, double-u, and coaxial grouted borehole heat exchangers. For single and double u-tube configurations, the methods use the 1st-order closed-form multipole approximations, which typically produces results with less than 1% error when compared to the 10th-order multipole method. Coaxial borehole methods apply a simple 1D resistance network method. This is intended to be a lightweight library that can be easily imported into any other Python tool, with no bulky dependencies.

Mitchell, Matt [National Renewable Energy Laborato↗
DOE OSTI2023

Transformer Leakage Inductance Design Methodology

The leakage inductance exhibited by a transformer depends on its winding geometry, which generally involves the selection of several key design parameters in addition to the winding structure and the interleaving configuration. With few resources explaining the effects of these design choices on the observed leakage inductance, numerous trial-and-error iterations become necessary to realize the desired leakage inductance. This paper explores more than a hundred winding geometries feasible in a 2-winding transformer comprising the same magnetic core, number of turns, and wire gauge, and finds the leakage inductance for each unique design using 2-D finite element method (FEM) simulations in association with the semi-analytical double- 2-D model. These leakage inductances are plotted and further analyzed to understand the effects of different design parameters on the effective leakage inductance. The results presented herein and the conclusions drawn from this research can serve as a valuable resource for future design practitioners from both industry and academia.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Frequency Injection Based HVDC Attack-Defense Control Via Squeeze-Excitation Double CNN

Due to the independent controllability and fast power regulation capability, the High Voltage Direct Current (HVDC) system could be a prospective technology to provide multiple ancillary services to the system besides conventional bulk power transmission. However, with the increase of False Data Injection Attacks (FDIAs) on PMU data, the HVDC system could have the wrong response once the collected data that the HVDC system relied on is attacked, thus threatening the system operating security. How to ensure the security of the PMU-based HVDC ancillary service control become an urgent issue. To mitigate the risk, this paper proposed an HVDC attack-defense control based on the FDIAs detection method. Firstly, the Squeeze-Excitation based Double Convolutional Neural Networks (SE-DCNN) is proposed to realize fast identification of the attacking frequency type based on the time and frequency domain signals. Furthermore, the duration time of FDIAs is detected by the local outlier factor. Then, utilizing the results from SE-DCNN, HVDC ancillary service control framework is reorganized and an HVDC attack defense control is proposed for suppressing the potential influence of various types of FDIAs on the HVDC system ancillary service. Different experiments results demonstrate that the proposed method has the ability to significantly mitigate the frequency deviation and oscillation under the FDIA.

42 ENGINEERING↗
DOE OSTI2020

Production of two-colour radiation with polarisations of components rotating in opposite directions

A method is proposed for the production of two-colour radiation with monochromatic components, the polarisation vectors of which rotate in opposite directions, and the rotation speed is controlled by the sound frequency. The method is based on acousto-optic (AO) interaction upon double passage of two-colour radiation through an AO cell made of a gyrotropic crystal; the method efficiency is demonstrated by the example of radiation from an Ar laser generating at wavelengths of 0.488 and 0.514 μm and an AO cell made of TeO{sub 2}, operating at a sound frequency of 60 MHz. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Constant-potential molecular dynamics simulations of molten salt double layers for FLiBe and FLiNaK

We report the results of constant-potential molecular dynamics simulations of the double layer interface between molten 2LiF–BeF 2 (FLiBe) and 23LiF–6NaF–21KF (FLiNaK) fluoride mixtures and idealized solid electrodes. Employing methods similar to those used in studies of chloride double layers, we compute the structure and differential capacitance of molten fluoride electric double layers as a function of applied voltage. The role of molten salt structure is probed through comparisons between FLiBe and FLiNaK, which serve as models for strong and weak associate-forming salts, respectively. In FLiBe, screening involves changes in Be–F–Be angles and alignment of the oligomers parallel to the electrode, while in FLiNaK, the electric field is screened mainly by rearrangement of individual ions, predominantly the polarizable potassium cation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Understanding the evolution of double perovskite band structure upon dimensional reduction

Recent investigations into the effects of dimensional reduction on halide double perovskites have revealed an intriguing change in band structure when the three-dimensional (3D) perovskite is reduced to a two-dimensional (2D) perovskite with inorganic sheets of monolayer thickness (n = 1). The indirect bandgap of 3D Cs 2 AgBiBr 6 becomes direct in the n = 1 perovskite whereas the direct bandgap of 3D Cs 2 AgTlBr 6 becomes indirect at the n = 1 limit. Here, we apply a linear combination of atomic orbitals approach to uncover the orbital basis for this bandgap symmetry transition with dimensional reduction. We adapt our previously established method for predicting band structures of 3D double perovskites for application to their 2D congeners, emphasizing new considerations required for the 2D lattice. In particular, we consider the inequivalence of the terminal and bridging halides and the consequences of applying translational symmetry only along two dimensions. The valence and conduction bands of the layered perovskites can be derived from symmetry adapted linear combinations of halide p orbitals propagated across the 2D lattice. The dispersion of each band is then determined by the bonding and antibonding interactions of the metal and halide orbitals, thus affording predictions of the essential features of the band structure. We demonstrate this analysis for 2D Ag–Bi and Ag–Tl perovskites with sheets of mono- and bilayer thickness, establishing a detailed understanding of their band structures, which enables us to identify the key factors that drive the bandgap symmetry transitions observed at the n = 1 limit. Importantly, these insights also allow us to make the general prediction that direct → indirect or indirect → direct bandgap transitions in the monolayer limit are most likely in double perovskite compositions that involve participation of metal d orbitals at the band edges or that have no metal-orbital contributions to the valence band, laying the groundwork for the targeted realization of this phenomenon.

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

Vertically Aligned Carbon Nanotubes Grown on Copper Foil as Electrodes for Electrochemical Double Layer Capacitors

This study reports a binder-free, catalyst-free method for fabricating vertically aligned carbon nanotubes (VACNTs) directly on copper (Cu) foil using plasma-enhanced chemical vapor deposition (PECVD) for electrochemical double-layer capacitor (EDLC) applications. This approach eliminates the need for catalyst layers, polymeric binders, or substrate pre-treatments, simplifying electrode design and enhancing electrical integration. The resulting VACNTs form a dense, uniform, and porous array with strong adhesion to the Cu substrate, minimizing contact resistance and improving conductivity. Electrochemical analysis shows gravimetric specific capacitance (C grav ) and areal specific capacitance (C areal ) of 8 F g −1 and 3.5 mF cm −2 at a scan rate of 5 mV/s, with low equivalent series resistance (3.70 Ω) and charge transfer resistance (0.48 Ω), enabling efficient electron transport and rapid ion diffusion. The electrode demonstrates excellent rate capability and retains 92% of its initial specific capacitance after 3000 charge–discharge cycles, indicating strong cycling stability. These results demonstrate the potential of directly grown VACNT-based electrodes for high-performance EDLCs, particularly in applications requiring rapid charge–discharge cycles and sustained energy delivery.

25 ENERGY STORAGE↗
DOE OSTI2020

SCALE capabilities for high temperature gas-cooled reactor analysis

The SCALE code system’s ability to address stochastic distributions of fuel particles within a graphite matrix has been revisited in both multigroup (MG) features and continuous-energy (CE) Monte Carlo methods. Furthermore, this paper describes current and emergent SCALE capabilities within the CSAS sequence to address double-heterogeneous systems and presents verification and validation studies of these methods and data. Good agreement was obtained for a high temperature gas-cooled reactor (HTGR) fuel pebble model between CSAS MG eigenvalue calculations and corresponding CE reference solutions. Code-to-code comparisons for this HTGR pebble model showed good agreement of CSAS-KENO and CSAS-Shift CE calculations and the Serpent and MCNP codes in terms of eigenvalues and reaction rate ratios. Validation studies based on two HTGR experiments resulted in good agreement between MG and CE results, as well as between experiment and calculation, although the level of agreement was significantly influenced by the applied ENDF/B nuclear data library.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Breaking the Million-Electron and 1 EFLOP/s Barriers: Biomolecular-Scale Ab Initio Molecular Dynamics Using MP2 Potentials

The accurate simulation of complex biochemical phenomena has historically been hampered by the computational requirements of high-fidelity molecular-modeling techniques. Quantum mechanical methods, such as ab initio wave-function (WF) theory, deliver the desired accuracy, but have impractical scaling for modeling biosystems with thousands of atoms. Combining molecular fragmentation with MP2 perturbation theory, this study presents an innovative approach that enables biomolecular-scale ab initio molecular dynamics (AIMD) simulations at WF theory level. Leveraging the resolution-of-the-identity approximation for Hartree-Fock and MP2 gradients, our approach eliminates computationally intensive four-center integrals and their gradients, while achieving near-peak performance on modern GPU architectures. The introduction of asynchronous time steps minimizes time step latency, overlapping computational phases and effectively mitigating load imbalances. Utilizing up to 9,400 nodes of Frontier and achieving 59% (1006.7 PFLOP/s) of its double-precision floating-point peak, our method enables us to break the million-electron and 1EFLOP/s barriers for AIMD simulations with quantum accuracy.

Kurzak, Jakub↗
DOE OSTI2025

Form-factor dependence of neutrino-nucleus cross sections using microscopic methods

To achieve its design goals, the next generation of neutrino-oscillation accelerator experiments requires percent-level predictions of neutrino-nucleus cross sections supplemented by robust estimates of the theoretical uncertainties involved. The latter arise from both approximations in solving the nuclear many-body problem and in the determination of the single- and few-nucleon quantities taken as input by many-body methods. To gauge the sensitivity of realistic nuclear many body methods to these few-nucleon quantities, we compute flux-averaged double-differential cross sections using the Green’s function Monte Carlo and spectral function methods as well as different parameterizations of the nucleon axial form factors based on either deuterium bubble-chamber data or lattice quantum chromodynamics calculations. The cross-section results are compared with available experimental data from the MiniBooNE and T2K collaborations. We also discuss the uncertainties associated with N → Δ transition form factors that enter the two-body current operator. We quantify the relations between neutrino-nucleus cross section and nucleon form factor uncertainties. These relations enable us to determine the form factor precision targets required to achieve a given cross-section precision.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

EERC Final Topical Report – Findings on Subtask 3.2 – Produced Water Management Through Geologic Homogenization, Conditions, and Reuse

The Energy & Environmental Research Center (EERC) was awarded a contract by the North Dakota Industrial Commission (NDIC) Oil and Gas Research Program (NDIC No. G-051-101) to conduct a study on the recycling of water used in oil and gas operations, also known as produced water, from oil- and gas-producing regions of North Dakota as directed by Section 19 of North Dakota House Bill 1014. This final report provides a compilation of results of the study, which include regulatory, scientific, technological, and feasibility methods and considerations associated with North Dakota produced water management. The report provides a synopsis of this project’s previously submitted produced water assessment report entitled “Produced Water Management and Recycling Options in North Dakota” (Energy & Environmental Research Center, 2020), with updated values provided as appropriate. The report provides the results from the investigation of a novel produced water management strategy, referred to as geologic homogenization, conditioning, and reuse (GHCR), which aims to use a subsurface geologic formation as a natural medium for managing produced water recycling and reuse. Water management is a significant technical and economic challenge for sustainable oil and gas production, and water volumes are intrinsically linked to oil production volumes. North Dakota oil production rose to over 1.5 million barrels (MMbbl)/day in 2019, and despite a downturn in oil price in early 2020, North Dakota oil production has recovered to 1.1 MMbbl/day as of August 2021. Bakken petroleum system development between 2008 and 2020 has resulted in a nearly fourfold increase in produced water volumes to 642 MMbbl/yr in 2020 after peaking at 740 MMbbl/yr in 2019 and a fivefold increase in saltwater disposal (SWD) volumes to 565 MMbbl/yr in 2020 after a peak of 682 MMbbl/yr in 2019. Produced water and SWD volumes are forecasted to double by 2030. SWD is the primary method of produced water management used in North Dakota, with approximately 95% of the SWD volume occurring through subsurface injection into sandstones of the Dakota Group (Dakota). Localized pressurization of the Dakota resulting from SWD and projected increases in produced water volumes could impact the economics of North Dakota oil production. As a result, there is an emerging need to pursue alternative produced water management approaches, including recycling and reuse. While produced water recycling is not yet widespread, commercial operators are making strides in overcoming the technical challenges of using high salinity produced water in completion operations (Marathon Oil, 2020). As water management continues to be a key focal point in companies’ environmental, social, and governance (ESG) initiatives, focus on water management, including recycling, will likely continue to increase. Laboratory column testing, field sample collection, geologic modeling and numerical simulation, and techno-economic analysis all indicate that GHCR could feasibly be implemented as a potential water management option. Laboratory column testing and field sample collection indicate that the Inyan Kara sandstone and native formation fluid are capable of homogenizing with the Bakken produced water to a point where the fluid composition appears to stabilize. Extracting that stabilized fluid could be considered homogeneous and capable of providing individual batches of hydraulic fracturing fluid. Numerical simulation results indicate that extraction of fluids from the Inyan Kara in a GHCR implementation scenario is capable of reducing formation pressure, which would help ease localized pressurization of the Inyan Kara and extend the available capacity for nearby existing SWD wells. Economic analysis indicates that there are scenarios where GHCR implementation can be a competitive or even lower-cost option than a conventional water management approach. Site-specific conditions will dictate the economic potential of GHCR, but potentially attractive sites for GHCR implementation will be those that are located above a pressurized zone of the Inyan Kara, need six or more Bakken infill wells, and face high costs for conventional SWD and/or freshwater. Based on the regulatory review, drilling into the Inyan Kara for SWD and to harness as a source water for industrial use have precedent in North Dakota, and a workable regulatory solution for GHCR seems likely. However, restrictions in the state regarding surface storage and transport of produced fluids may limit some activities, which will affect how GHCR could ultimately be implemented. In summary, this study reveals pursuing GHCR can be a viable approach to water management in North Dakota. The GHCR concept addresses some of the challenges that hinder the more traditional approaches to recycling in the industry. Furthermore, an assessment of the current landscape of water management within the state reveals the ongoing trend of increasing volumes of produced water and SWD. Projections reveal that the volumes of produced water that need to be managed are expected to double over the next decade (Energy & Environmental Research Center, 2020). With the continued development of the Bakken and continuing driving factors related to ESG initiatives, implementing a practice such as GHCR is a feasible approach to adding recycling of produced water to industry within the state. This subtask was cofunded through the EERC–U.S. Department of Energy Joint Program on Research and Development for Fossil Energy-Related Resources Cooperative Agreement No. DE-FE0024233. Nonfederal funding was provided by the North Dakota Industrial Commission Oil and Gas Research Program. References Energy & Environmental Research Center, 2020, Produced water management and recycling options in North Dakota: Final Report for North Dakota Legislative Management Energy Development and Transmission Committee and North Dakota Industrial Commission. Marathon Oil, 2020, Sustainability report: https://cdn.sanity.io/files/ghcnw9z2/website/ 91744eb6ef8fbe59505a911c6b8d2e8dd9a537fa.pdf?dl (accessed November 2021).

02 PETROLEUM↗
DOE OSTI2025

Equilibrium Core Model for Micro Pebble Bed Reactors Using OpenMC

Estimating the equilibrium state for pebble bed reactors (PBRs) presents complex challenges as it requires simultaneous consideration of changes in the pebbles’ movement as well as their fuel compositions. Whereas traditional approaches use multigroup diffusion codes for neutronics calculations of PBRs’ equilibrium state, the double-heterogeneity of PBRs complicates neutron cross-section generation. Continuous-energy Monte Carlo (MC) methods are better suited for detailed PBR analysis because of their natural handling of double-heterogeneity, but they demand substantially more computational resources. Here, this study introduces a novel method for efficiently estimating the equilibrium state in small and micro PBRs with reduced computational cost. The method is anticipated to accelerate the processes of core design and performing parametric studies for utilizing advanced fuel and structural materials. The HTR-10 reactor design was used for validating the method’s predictions and evaluating its computational efficiency. When compared to reference calculation values from the literature, criticality (k-effective) was predicted to be approximately within the margin of error of the MC transport calculation, average core power density (in megawatts per cubic meter) was predicted within 2.5% relative error, and maximum thermal flux (10 13 n/cm 2 .s −1 ) was predicted within 1.8% relative error. The calculated inventory of fission products and fuel composition in the equilibrium core were within 15% and 16.6%, respectively, when compared to reported values from the literature. The difference is attributed to variance in the considered values of the core temperature, which was found to significantly affect the depletion analyses.

Equilibrium core↗
DOE OSTI2023

Comparison of methods to estimate aerosol effective radiative forcings in climate models

Abstract. Uncertainty in the effective radiative forcing (ERF) of climate primarily arises from the unknown contribution of aerosols, which impact radiative fluxes directly and through modifying cloud properties. Climate model simulations with fixed sea surface temperatures but perturbed atmospheric aerosol loadings allow for an estimate of how strongly the planet's radiative energy budget has been perturbed by the increase in aerosols since pre-industrial times. The approximate partial radiative perturbation (APRP) technique further decomposes the contributions to the direct forcing due to aerosol scattering and absorption and to the indirect forcing due to aerosol-induced changes in cloud scattering, amount, and absorption, as well as the effects of aerosols on surface albedo. Here we evaluate previously published APRP-derived estimates of aerosol effective radiative forcings from these simulations conducted in the sixth phase of the Coupled Model Intercomparison Project (CMIP6) and find that they are biased as a result of two large coding errors that – in most cases – fortuitously compensate. The most notable exception is the direct radiative forcing from absorbing aerosols, which is more than 40 % larger averaged across CMIP6 models in the present study. Correcting these biases eliminates the residuals and leads to better agreement with benchmark estimates derived from double calls to the radiation code. The APRP method – when properly implemented – remains a highly accurate and efficient technique for diagnosing aerosol ERF in cases where double radiation calls are not available, and in all cases it provides quantification of the individual contributors to the ERF that are highly useful but not otherwise available.

58 GEOSCIENCES↗
DOE OSTI2026

Reduced-Cost Four-Component Relativistic Double Ionization Potential Equation-of-Motion Coupled-Cluster Approaches with 4-Hole–2-Particle Excitations and Three-Body Clusters

The double ionization potential (DIP) equation-ofmotion (EOM) coupled-cluster (CC) method with 4-hole−2- particle (4h-2p) excitations on top of the CC with singles, doubles, and triples calculation, abbreviated as DIP-EOMCCSDT(4h-2p), along with its perturbative DIP-EOMCCSD(T)(a)(4h-2p) approximation, are extended to a relativistic four-component (4c) framework. In addition, we introduce and test a new computationally practical DIP-EOMCC approach, which we call DIPEOMCCSD( T)(ã)(4h-2p), that approximates the treatment of 4h- 2p correlations within the DIP-EOMCCSD(T)(a)(4h-2p) method and reduces the $\mathcal{N}$ 8 scaling characterizing DIP-EOMCCSDT(4h- 2p) and DIP-EOMCCSD(T)(a)(4h-2p) to $\mathcal{N}$ 7 with the system size $\mathcal{N}$. Further improvements in computational efficiency are obtained using the frozen natural spinor (FNS) approximation to reduce the numbers of unoccupied spinors entering the correlated steps of the DIP-EOMCC calculations according to a well-defined occupation-number-based threshold. The resulting 4c-FNS-DIPEOMCC approaches are used to compute DIPs for the series of inert gas atoms from argon to radon as well as the vertical DIPs in Cl 2 , Br 2 , HBr, and HI, which have been experimentally examined in the past. We demonstrate that, when using complete basis set extrapolations and FNS truncation threshold of 10 −4.5 , the 4c-FNS-DIP-EOMCCSD(T)(ã)(4h-2p) calculations are capable of predicting DIPs in agreement with experimental data, improving upon their nonrelativistic and spin-free scalar-relativistic counterparts, particularly when examining DIPs characterized by stronger spin−orbit coupling effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗