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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

A simple method for obtaining a three-dimensional proton distribution function from Voyager plasma data

The main sensor of the Vogager plasma experiment consists of a cluster of three, modulated-grid Faraday cups whose normals are arranged symmetrically about the symmetry axis of the cluster at an angle of 20 degrees to that axis. In interplanetary space, each cup explores the positive ion distribution by accepting particles from contiguous slices in velocity space. The slices are narrow in the direction of the normal to the modulating grid but are broad in planes parallel to that grid. The resulting three sets of measurements can be combined to yield the three-dimensional distribution function in the following way: the distribution function is assumed to be gyrotropic. For each value of speed in a frame of reference moving with the bulk velocity of the solar wind, the variation of the distribution function with angle from the field direction is represented by a series of Legendre polynomials. Effects such as double-streaming and heat flow can be well represented by using only the first three terms of the series which are fully specified by the measurements. Examples of the use of this method in the analysis of Voyager data are shown.

Olbert, S.↗
NASA NTRS1985

Three-dimensional radiative transfer using a Fourier-transform matrix-operator method

The three-dimensional equation of transfer for a scattering medium with planar geometry is solved by using a spatial Fourier transform and extending matrix-operator techniques developed previously for the one-dimensional equation. Doubling and adding algorithms were derived by means of an interaction principle for computing the Fourier-transformed radiation field. The resulting expressions fully describe the radiative transfer process in a scattering medium, inhomogeneous in the x-, y- and z-directions, illuminated from above by an arbitrarily general intensity field and bounded from below by a surface with completely general reflection properties.

Martonchik, J. V.↗
DOE OSTI2026

Surface Reordering During Layer‐by‐Layer Growth on SrTiO 3

With the development of layer‐by‐layer growth techniques such as molecular beam epitaxy (MBE), it is now possible to construct materials with atomic‐level precision, with the layer sequence primarily determined by the growth recipe. However, materials can still restructure in the high‐temperature growth environment with surface thermodynamics strongly influencing growth behavior. Here, we demonstrate that growth on ${\rm SrTiO}_{3}$ (001), the principal platform for oxide electronics, does not occur in a layer‐by‐layer fashion but follows a more complex process in which a ${\rm TiO}_{2}$ plane continually diffuses toward the growth surface. Employing in situ synchrotron X‐ray scattering combined with ab initio thermodynamic calculations, we discover the existence of a stable ${\rm TiO}_{2}$ double‐layer structure on the pristine substrate and the occurrence of dynamic layer rearrangement during homoepitaxial growth by oxide MBE. Our findings suggest that the current methods used to precisely control ${\rm SrTiO}_{3}$ surfaces are limited, as well as our ability to dictate the composition of ultrathin films, resulting in important ramifications regarding the surface reactivity of perovskite materials grown on ${\rm SrTiO}_{3}$.

Coherent Bragg Rod Analysis↗
DOE OSTI2020

Comparison of active interrogation methods for source location in a scattering and absorbing medium, consisting of PGNAA, and an AmBe quasi-forward biased directional source

Source location of Special Nuclear Material (SNM) encompassing 95% 235 U and 239 Pu is identified by utilizing a directional source from Patent No: US20190013109A1 using Prompt Gamma Neutron Activation Analysis (PGNAA) and neutron spectroscopy simulated with Monte-Carlo N-Particle transport 6.2 (MCNP). BC-408, HPGe, LaBr 3 detector arrays were used to identify the location of the SNM using total counts incident on each detector, and PGNAA photopeaks from HPGe and LaBr 3 detector arrays in a polyethylene shield. The conducted simulations varied the volume and location of the SNM in the MCNP input files to observe how the source location method behaved. PGNAA photopeaks used for source identification include 61 keV from fission, 2.223 MeV prompt gamma from hydrogen, 511 keV annihilation, and a single and double escape peaks from the prompt gamma interaction from hydrogen. The capabilities of each detector systems to acquire well resolved photopeaks with a 1% relative error or less, and total relative error for F4 and F8 tallies were less than 0.015% relative error. Source predictions of the SNM with uneven amounts of polyethylene shielding between the source and detectors was observed to overpredict and give invalid source location predictions. Source locations of the SNM with even amounts of polyethylene material between the source and each detector were found to be valid. With a 1 Ci 241 Am source activity, it was determined that 1630 s were needed to obtain the results for each detector system with the quasi-forward directional AmBe source. Coupling source and material identification together would increase acquisition time but would only require one system to determine.

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

Performance of Diffusion Monte Carlo Calculations for Predicting the Relative Energies of Quinoidal and Nonquinoidal Species

Coupled cluster singles and doubles with perturbative triples [CCSD(T)] and single determinant fixed-node diffusion Monte Carlo (SD-DMC) have emerged as two of the most useful methods for providing benchmark reaction and interaction energies of chemical systems without strong static correlation. The errors in DMC energies are dominated by an inexact description of the nodal surfaces for electron exchange. One of the main approaches to addressing the fixed-node error is to use multideterminant (MD) trial wave functions. We consider here the energy differences between pairs of related molecules with aromatic and quinoidal structures as well as between quinoidal isomers. Quinoidal systems tend to have some diradical character, leading one to anticipate that SD-DMC calculations may face challenges in accurately describing their energetics. The MD trial wave functions were generated from the complete active space calculations. A comparison is made with the predictions of well-converged CCSD(T) calculations.

basis sets↗
DOE OSTI2020

Angle-dependent strong-field ionization and fragmentation of carbon dioxide measured using rotational wave packets

In this work, we experimentally study the angle-dependent single ionization of carbon dioxide (CO 2 ) by linearly and circularly polarized pulses. The angle dependence of the ionization probability by linearly polarized pulses extracted from time-domain measurements on an impulsively excited rotational wave packet is compared with data obtained from a direct angle-scan measurement. The results from the measurement with linear and circular polarization are consistent with the adiabatic ionization approximation. Further, we extend the time-domain method to extract the dependence of the asymptotic momentum distribution of fragment ions on the orientation of the molecular axis, and apply it to investigate dissociative double ionization of CO 2 . We show that such measurements can directly test the validity of the axial recoil approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

NORTH DAKOTA CARBONSAFE PHASE III: SITE CHARACTERIZATION AND PERMITTING OF GEOLOGIC STORAGE OF CARBON DIOXIDE

The Energy & Environmental Research Center (EERC), in partnership with Minnkota Power Cooperative Inc. (Minnkota), SLB, and Computer Modelling Group Ltd. (CMG), supported wide-scale deployment of carbon capture and storage (CCS) as part of the U.S. Department of Energy (DOE) National Energy Technology Laboratory Carbon Storage Assurance Facility Enterprise (CarbonSAFE) Initiative Phase III. This phase included the acquisition, analysis, and development of information to fully characterize two storage complexes to demonstrate viable storage resources for commercial volumes of CO2 (defined by DOE as a minimum of 50 million tonnes [MMt] of CO2 within a 30-year period) (National Energy Technology Laboratory, 2024). Phase III also involved the preparation, submission, and approval of North Dakota underground injection control (UIC) Class VI storage facility permits (SFPs)—required precursors to applications for Class VI injection well permits. The presumed viability of commercial-scale CCS, situated adjacent to Minnkota’s Milton R. Young Station (MRYS), is validated by Minnkota’s continued pursuit of Project Tundra—an initiative to build the world’s largest lignite-based CCS project in central North Dakota (www.projecttundrand.com). Project Tundra comprises two scopes of work, Tundra Capture (installation of postcombustion CO2 capture at MRYS) and Tundra SGS (secure geologic storage). The efforts of North Dakota CarbonSAFE Phase III, Site Characterization and Permitting, supported Tundra SGS. Extensive site-specific characterization activities included a successful multimeasurement geophysical approach and drilling a stratigraphic test well (J-ROC 1, subsequently renamed Liberty-1) adjacent to MRYS. Core collection and analyses, downhole testing and fluid sampling, and geophysical logging were performed on J-ROC 1 and on a nearby stratigraphic test well (known as J-LOC 1), which was drilled, cored, and tested under a complementary project funded by the North Dakota Lignite Research Program. The injection tests performed on J-LOC 1 positively impacted the CarbonSAFE project, resulting in fewer proposed injection wells and significant construction, operations, and monitoring cost savings. The characterization data collected and analyses performed were integrated into geologic models, and successive numerical simulations were run to determine CO2 plume extent and subsurface pressure buildup associated with the planned CO2 injection rate of nearly 4 MMt per year. The latter doubles the CarbonSAFE Initiative goal with an estimated 100 MMt of CO2 stored in 20 years. Application of the U.S. Environmental Protection Agency’s (EPA’s) method for estimating the Class VI Rule area of review (AOR) to the overpressurized Broom Creek Formation inspired an alternative method of calculation, called risk-based AOR delineation. This peer-reviewed method was applied for the first time during the storage facility-permitting process. The two SFP applications submitted in 2021 successfully resulted in North Dakota Industrial Commission (NDIC) orders in 2022 authorizing the creation of the storage facility areas and amalgamation of pore space as well as establishing financial responsibility requirements. After approval of the SFPs, Minnkota filed in 2022 applications for permits to reenter the J-ROC 1 well and to drill two new wells—all with the intended purpose to become Class VI injection wells. To establish eligibility under the Internal Revenue Code for Section 45Q tax incentives, a monitoring, reporting, and verification (MRV) plan was prepared and submitted by Minnkota to EPA in 2022, resulting in the first such plan approved in North Dakota. Also in 2022, under the National Environmental Policy Act (NEPA), Minnkota prepared and submitted an environmental information volume (EIV) describing the proposed CCS project and associated potential environmental impacts. Based on the EIV, DOE determined that the proposed construction project required an environmental assessment, and Minnkota submitted the first draft in 2023 and a revised draft in 2024. Both submissions were followed by a public comment period. Subsequently, DOE issued a finding of no significant impact (FONSI) on September 13, 2024. A successful outreach program, strongly based in the production, presentation, and dissemination of informational material, fostered an environment to aid stakeholders in making informed decisions regarding the planned project. Opportunities for public input were provided at various steps along the way, including at county planning and zoning meetings, before and during the SFP administrative hearing, and during environmental assessment public comment periods. In addition, land/pore space owners and mineral owners had various points of contact, including granting access rights, securing pore space leasing, and mineral owner notifications. Based upon the successful storage facility permitting issued by NDIC, approval of the MRV plan by EPA, and receipt of a FONSI under the NEPA, Minnkota is continuing its pursuit of Project Tundra. In December 2023, the Office of Clean Energy Demonstrations under its Carbon Capture Demonstrations Projects Program announced funding for the capture system (Office of Clean Energy Demonstrations, 2023) and a proposal for CarbonSAFE Phase IV: Construction funding was submitted in March 2024 for the storage project. A go/no-go decision to proceed with construction and operations in the Broom Creek Formation is anticipated in 2024. References National Energy Technology Laboratory, CarbonSafe Initiative, https://netl.doe.gov/carbon-management/carbon-storage/carbonsafe (accessed August 2024). Office of Clean Energy Demonstrations, 2023, OCED selects three projects in CA, ND, and TX to reduce harmful carbon pollution, create new economic opportunities, and advance carbon reducing technologies, December, www.energy.gov/oced/articles/oced-selects-three-projects-ca-nd-and-tx-reduce-harmful-carbon-pollution-create-new (accessed August 2024).

Peck, Wesley↗
NASA NTRS1973

Algorithms for changing the step size

Approximately ten different ways for changing the step size used by multistep methods are enumerated, and their good and bad features are compared. More efficient algorithms are given for the difference formulations of a frequently used halving and doubling process, and a cure for the instability inherent in this halving process is proposed.

Krogh, F. T.↗
NASA NTRS1987

Life prediction technologies for aeronautical propulsion systems

Fatigue and fracture problems continue to occur in aeronautical gas turbine engines. Components whose useful life is limited by these failure modes include turbine hot-section blades, vanes and disks. Safety considerations dictate that catastrophic failures be avoided, while economic considerations dictate that noncatastrophic failures occur as infrequently as possible. The design decision is therefore in making the tradeoff between engine performance and durability. The NASA Lewis Research Center has contributed to the aeropropulsion industry in the areas of life prediction technology for 30 years, developing creep and fatigue life prediction methodologies for hot-section materials. Emphasis is placed on the development of methods capable of handling both thermal and mechanical fatigue under severe environments. Recent accomplishments include the development of more accurate creep-fatigue life prediction methods such as the total strain version of Lewis' Strainrange Partitioning (SRP) and the HOST-developed Cyclic Damage Accumulation (CDA) model. Other examples include the Double Damage Curve Approach (DDCA), which provides greatly improved accuracy for cumulative fatigue design rules.

Mcgaw, Michael A.↗
NASA NTRS1995

Applications of Quantum Theory of Atomic and Molecular Scattering to Problems in Hypersonic Flow

The general status of a grant to investigate the applications of quantum theory in atomic and molecular scattering problems in hypersonic flow is summarized. Abstracts of five articles and eleven full-length articles published or submitted for publication are included as attachments. The following topics are addressed in these articles: fragmentation of heavy ions (HZE particles); parameterization of absorption cross sections; light ion transport; emission of light fragments as an indicator of equilibrated populations; quantum mechanical, optical model methods for calculating cross sections for particle fragmentation by hydrogen; evaluation of NUCFRG2, the semi-empirical nuclear fragmentation database; investigation of the single- and double-ionization of He by proton and anti-proton collisions; Bose-Einstein condensation of nuclei; and a liquid drop model in HZE particle fragmentation by hydrogen.

Malik, F. Bary↗
NASA NTRS2003

A Self-Contained Mapping Closure Approximation for Scalar Mixing

Scalar turbulence exhibits interplays of coherent structures and random fluctuations over a broad range of spatial and temporal scales. This feature necessitates a probabilistic description of the scalar dynamics, which can be achieved comprehensively by using probability density functions (PDFs). Therefore, the challenge is to obtain the scalar PDFs (Lundgren 1967; Dopazo 1979). Generally, the evolution of a scalar is governed by three dynamical processes: advection, diffusion and reaction. In a PDF approach (Pope 1985), the advection and reaction can be treated exactly but the effect of molecular diffusion has to be modeled. It has been shown (Pope 1985) that the effect of molecular diffusion can be expressed as conditional dissipation rates or conditional diffusions. The currently used models for the conditional dissipation rates and conditional diffusions (Pope 1991) have resisted deduction from the fundamental equations and are unable to yield satisfactory results for the basic test cases of decaying scalars in isotropic turbulence, although they have achieved some success in a variety of individual cases. The recently developed mapping closure approach (Pope 1991; Chen, Chen & Kraichnan 1989; Kraichnan 1990; Klimenko & Pope 2003) provides a deductive method for conditional dissipation rates and conditional di usions, and the models obtained can successfully describe the shape relaxation of the scalar PDF from an initial double delta distribution to a Gaussian one. However, the mapping closure approach is not able to provide the rate at which the scalar evolves. The evolution rate has to be modeled. Therefore, the mapping closure approach is not closed. In this letter, we will address this problem.

He, Guo-Wei↗
NASA NTRS2000

Context-specific adaptation of pursuit initiation in humans

PURPOSE: To determine if multiple states for the initiation of pursuit, as assessed by acceleration in the "open-loop" period, can be learned and gated by context. METHODS: Four normal subjects were studied. A modified step-ramp paradigm for horizontal pursuit was used to induce adaptation. In an increasing paradigm, target velocity doubled 230 msec after onset; in a decreasing paradigm, it was halved. In the first experiment, vertical eye position (+/-5 degrees ) was used as the context cue, and the training paradigm (increasing or decreasing) changed with vertical eye position. In the second experiment, with vertical position constant, when the target was red, training was decreasing, and when green, increasing. The average eye acceleration in the first 100 msec of tracking was the index of open-loop pursuit performance. RESULTS: With vertical position as the cue, pursuit adaptation differed between up and down gaze. In some cases, the direction of adaptation was in exact accord with the training stimuli. In others, acceleration increased or decreased for both up and down gaze but always in correct relative proportion to the training stimuli. In contrast, multiple adaptive states were not induced with color as the cue. CONCLUSIONS: Multiple values for the relationship between the average eye acceleration during the initiation of pursuit and target velocity could be learned and gated by context. Vertical position was an effective contextual cue but not target color, implying that useful contextual cues must be similar to those occurring naturally, for example, orbital position with eye muscle weakness.

NASA Discipline Neuroscience↗
NASA NTRS2004

Effects of Kinetic Processes in Shaping Io's Global Plasma Environment: A 3D Hybrid Model

The global dynamics of the ionized and neutral components in the environment of Io plays an important role in the interaction of Jupiter's corotating magnetospheric plasma with Io. The stationary simulation of this problem was done in the MHD and the electrodynamics approaches. One of the main significant results from the simplified two-fluid model simulations was a production of the structure of the double-peak in the magnetic field signature of the I0 flyby that could not be explained by standard MHD models. In this paper, we develop a method of kinetic ion simulation. This method employs the fluid description for electrons and neutrals whereas for ions multilevel, drift-kinetic and particle, approaches are used. We also take into account charge-exchange and photoionization processes. Our model provides much more accurate description for ion dynamics and allows us to take into account the realistic anisotropic ion distribution that cannot be done in fluid simulations. The first results of such simulation of the dynamics of ions in the Io's environment are discussed in this paper.

Lipatov, Alexander S.↗
NASA NTRS2014

Experimental Measurement of Frozen and Partially Melted Water Droplet Impact Dynamics

High-speed video of single frozen water droplets impacting a surface was acquired. The droplets diameter ranged from 0.4 mm to 0.9 mm and impacted at velocities ranging from 140 m/sec to 309 m/sec. The techniques used to freeze the droplets and launch the particles against the surfaces is described in this paper. High-speed video was used to quantify the ice accretion area to the surface for varying impact angles (30 deg, 45 deg, 60 deg), impacting velocities, and break-up angles. An oxygen /acetylene cross-flow flame used to ensure partial melting of the traveling frozen droplets is also discussed. A linear relationship between impact angle and ice accretion is identified for fully frozen particles. The slope of the relationship is affected by impact speed. Perpendicular impacts, i.e. 30 deg, exhibited small differences in ice accretion for varying velocities, while an increase of 60% in velocity from 161 m/sec to 259 m/sec, provided an increase on ice accretion area of 96% at an impact angle of 60 deg. The increase accretion area highlights the importance of impact angle and velocity on the ice accretion process of ice crystals. It was experimentally observed that partial melting was not required for ice accretion at the tested velocities when high impact angles were used (45 and 60 deg). Partially melted droplets doubled the ice accretion areas on the impacting surface when 0.0023 Joules were applied to the particle. The partially melted state of the droplets and a method to quantify the percentage increase in ice accretion area is also described in the paper.

Impact Dynamics↗
NASA NTRSDate not supplied

Mars Sample Receiving Facility Research and Development to Enable Preservation, Safe Containment, and Scientific Research of Martian Samples on Earth

NASA and ESA are working together to plan a joint campaign to potentially bring back the first Martian samples to Earth in the early 2030s. On the surface of Mars, the Mars 2020Perseverance Rover is selecting and packaging samples that could be returned to Earth for careful examination by an international team of scientists. In preparation for this historic sample return, advance planning is underway to design and build a Mars Sample Receiving Facility (SRF) in the mid-2020s. In 2022, a Mars Sample Receiving Facility Assessment Study(MSAS) will be conducted to further define construction modality and capability options for a facility in the conterminous United States. Since Mars Sample Return (MSR) is currently categorized as a planetary protection restricted Earth return, this new facility would feature biosafety level 4 (BSL-4)-like high containment to protect Earth’s biosphere from any potential hazard. In addition, the facility also requires integration of cleanroom technologies to mitigate against terrestrial contamination and preserve sample integrity for science investigations. The integration of both clean handling and high containment requires significant technology research and development (R&D) by the mid-2020s to support the definition and planning of a SRF before commencing the site specific design phase. The SRF project will need to solidify the inorganic, organic, and biological contamination control (CC) requirements for the facility. This could entail a translation of Mars 2020 mission CC requirements for geologic material to engineering requirements for surfaces and airborne molecular contamination inside isolators and cleanrooms. In tandem, the project will need to determine precision cleaning and sterilization approaches for cleanrooms, isolators, equipment, and tools. Initial material selections for the facility construction materials, cleanrooms, isolators, and BSL-4 suits/garments are an important activity. The recent construction of the OSIRIS-REx and Hayabusa2 curation cleanroom laboratories greatly benefited from early materials testing, before the design phase, to reduced organic outgassing and particulate shedding inside the laboratory. While the early biohazard investigations in the SRF may deem the samples safe to release to laboratories throughout the world, sterilization methods need to be defined to safely release Martian samples. One key aspect of enabling simultaneous sample containment and cleanliness is the concept of a Double-Walled Isolator (DWI) that ESA has been pursuing. Further R&D is needed about DWIs, sample handling, and instrumentation interfaces before beginning the SRF site specific design phase. A working isolator/DWI engineering model should be developed and fabricated. Isolator sizes, connections, pass-through antechambers, and configurations and basic interfaces with instruments and tools as well as the use of robotic, mechanical, and/or human manipulation need to be considered. Inert high purity gas supply (one-pass or recirculation) and other isolator utilities must be determined. Special accommodations for large instruments (e.g., XCT,SEM, etc.) need to be developed. Techniques for opening the sample tubes packaged by M2020and extracting the headspace gas while keeping samples pristine will be challenging, requiring additional R&D, and engagement of the M2020 project. In addition, careful micromanipulation for subdivision and packaging of samples will also need to be included. These combined R&D activities are important before commencing the SRF design phase to ensure safe biohazard containment, sample preservation, and science integrity for the samples that would be studied in the SRF and in laboratories around the world.

mars sample return↗
DOE OSTI2026

Pushing the Limits of Pulse Shape Discrimination in a Large Liquid Xenon Detector

The LUX-ZEPLIN (LZ) experiment is a direct-detection dark matter experiment, optimized to search for weakly interacting massive particles (WIMPs) through WIMP-nucleon interactions. The main challenge in dark matter detection is differentiating between WIMP signals and background events. In LZ, the ratio of ionization to scintillation signals (charge-to-light) is the primary method for rejecting electronic recoil (ER) background. Pulse shape discrimination (PSD) offers a method for additional ER backgrounds rejection in liquid xenon detectors. In this paper, the discrimination power of PSD with the LZ experiment is discussed. To precisely characterize the scintillation pulse shape, an analysis framework is developed to reconstruct the detection time of individual photons. Using LZ calibration data, the photon-timing prompt fraction discriminator is optimized and achieves ER leakage as low as $15\%$. For specific background processes such as $^{124}$Xe double electron capture, the leakage is reduced further to about $5\%$. PSD is combined with charge-to-light to form two-factor discrimination (TFD). The optimized TFD performance is compared with the performance of the charge-to-light method, with the corresponding false positive rate reduced by up to a factor of two for large scintillation pulses. Finally, PSD and TFD are applied to data from LZ's WS2024 run and their performance is summarized.

Akerib, D. S. [SLAC; KIPAC, Menlo Park]↗
DOE OSTI2020

Hole–hole Tamm–Dancoff-approximated density functional theory: A highly efficient electronic structure method incorporating dynamic and static correlation

The study of photochemical reaction dynamics requires accurate as well as computationally efficient electronic structure methods for the ground and excited states. While time-dependent density functional theory (TDDFT) is not able to capture static correlation, complete active space self-consistent field methods neglect much of the dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we revisit hole–hole Tamm–Dancoff approximated (hh-TDA) density functional theory for this purpose. The hh-TDA method is the hole–hole counterpart to the more established particle–particle TDA (pp-TDA) method, both of which are derived from the particle–particle random phase approximation (pp-RPA). In hh-TDA, the N-electron electronic states are obtained through double annihilations starting from a doubly anionic (N+2 electron) reference state. In this way, hh-TDA treats ground and excited states on equal footing, thus allowing for conical intersections to be correctly described. Furthermore, the treatment of dynamic correlation is introduced through the use of commonly employed density functional approximations to the exchange-correlation potential. Additionally, we show that hh-TDA is a promising candidate to efficiently treat the photochemistry of organic and biochemical systems that involve several low-lying excited states—particularly those with both low-lying ππ* and nπ* states where inclusion of dynamic correlation is essential to describe the relative energetics. In contrast to the existing literature on pp-TDA and pp-RPA, we employ a functional-dependent choice for the response kernel in pp- and hh-TDA, which closely resembles the response kernels occurring in linear response and collinear spin-flip TDDFT.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗