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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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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Alkaline Ethanol Oxidation Reaction on Carbon Supported Ternary PdNiBi Nanocatalyst using Modified Instant Reduction Synthesis Method

Direct ethanol fuel cells (DEFC) still lack active and efficient electrocatalysts for the alkaline ethanol oxidation reaction (EOR). In this work, a new instant reduction synthesis method was developed to prepare carbon supported ternary PdNiBi nanocatalysts with improved EOR activity. Synthesized catalysts were characterized with a variety of structural and compositional analysis techniques in order to correlate their morphology and surface chemistry with electrochemical performance. The modified instant reduction synthesis results in well-dispersed, spherical Pd85Ni10Bi5 nanoparticles on Vulcan XC72R support (Pd85Ni10Bi5/C(II-III)), with sizes ranging from 3.7 +/- 0.8 to 4.7 +/- 0.7 nm. On the other hand, the common instant reduction synthesis method leads to significantly agglomerated nanoparticles (Pd85Ni10Bi5/C-(I)). EOR activity and stability of these three different carbon supported PdNiBi anode catalysts with a nominal atomic ratio of 85:10:5 were probed via cyclic voltammetry and chronoamperometry using the rotating disk electrode method. Pd85Ni10Bi5/C-(II) showed the highest electrocatalytic activity (150 mA.cm(-2); 2678 mA.mg(-1)) with low onset potential (0.207 V) for EOR in alkaline medium, as compared to a commercial Pd/C and to the other synthesized ternary nanocatalysts Pd85Ni10Bi5/C-(I) and Pd85Ni10Bi5/C-(III). This new synthesis approach provides a new avenue to developing efficient, carbon supported ternary nanocatalysts for future energy conversion devices. The modified instant reduction method for synthesis of ternary Pd85Ni10Bi5/C-(II) nanocatalyst using Vulcan XC72R as carbon support initiates an agglomeration reduction, provides low average particle size, and enables enhanced activity for the alkaline ethanol oxidation reaction (EOR) compared to the common instant reduction method and to a commercial Pd/C catalyst.

Alkaline direct ethanol fuel cell↗
DOE OSTI2022

Subcell limiting strategies for discontinuous Galerkin spectral element methods

Here, we present a general family of subcell limiting strategies to construct robust high-order accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is to construct compatible low order finite volume (FV) type discretizations that allow for convex blending with the high-order variant with the goal of guaranteeing additional properties, such as bounds on physical quantities and/or guaranteed entropy dissipation. For an implementation of this main strategy, four main ingredients are identified that may be combined in a flexible manner: (i) a nodal high-order DG method on Legendre–Gauss–Lobatto nodes, (ii) a compatible robust subcell FV scheme, (iii) a convex combination strategy for the two schemes, which can be element-wise or subcell-wise, and (iv) a strategy to compute the convex blending factors, which can be either based on heuristic troubled-cell indicators, or using ideas from flux-corrected transport methods. By carefully designing the metric terms of the subcell FV method, the resulting methods can be used on unstructured curvilinear meshes, are locally conservative, can handle strong shocks efficiently while directly guaranteeing physical bounds on quantities such as density, pressure or entropy. We further show that it is possible to choose the four ingredients to recover existing methods such as a provably entropy dissipative subcell shock-capturing approach or a sparse invariant domain preserving approach. We test the versatility of the presented strategies and mix and match the four ingredients to solve challenging simulation setups, such as the KPP problem (a hyperbolic conservation law with non-convex flux function), turbulent and hypersonic Euler simulations, and MHD problems featuring shocks and turbulence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Residual estimation for grid modification in wall-modeled large eddy simulation using unstructured high-order methods

Here, the accuracy and computational cost of a large eddy simulation are highly dependent on the computational grid. Building optimal grids manually from a priori knowledge is not feasible in most practical use cases; instead, solution-adaptive strategies can provide a robust and cost-efficient method to generate a grid with the desired accuracy. We adapt the residual estimation algorithm developed by Toosi and Larsson for Discontinuous Galerkin Spectral Elements Methods (DGSEM) to guide the grid-adaptation process. The core of the method is the computation of the estimated modeling residual using the polynomial basis functions used in DGSEM, and the averaging of the estimated residual over each element. The final method is assessed in multiple channel flow test cases and for the transonic flow over an airfoil, in both cases making use of mortar interfaces between elements with hanging nodes. The method is found to be robust and reliable, and to provide solutions on grids with significantly fewer elements at comparable accuracy compared to when using human-generated grids.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

An efficient reconstruction algorithm for diffusion on triangular grids using the nodal discontinuous Galerkin method

High-energy-density (HED) hydrodynamics studies such as those relevant to inertial confinement fusion and astrophysics require highly disparate densities, temperatures, viscosities, and other diffusion parameters over relatively short spatial scales. This presents a challenge for high-order accurate methods to effectively resolve the hydrodynamics at these scales, particularly in the presence of highly disparate diffusion. A significant volume of engineering and physics applications use an unstructured discontinuous Galerkin (DG) method developed based on the finite element mesh generation and algorithmic framework. This work discusses the application of an affine reconstructed nodal DG method for unstructured grids of triangles. Solving the diffusion terms in the DG method is non-trivial due to the solution representations being piecewise continuous. Hence, the diffusive flux is not defined on the interface of elements. The proposed numerical approach reconstructs a smooth solution in a parallelogram that is enclosed by the quadrilateral formed by two adjacent triangle elements. The interface between these two triangles is the diagonal of the enclosed parallelogram. Similar to triangles, the mapping of parallelograms from a physical domain to a reference domain is an affine mapping, which is necessary for an accurate and efficient implementation of the numerical algorithm. Thus, all computations can still be performed on the reference domain, which promotes efficiency in computation and storage. This reconstruction does not make assumptions on choice of polynomial basis. Reconstructed DG algorithms have previously been developed for modal implementations of the convection–diffusion equations. However, to the best of the authors’ knowledge, this is the first practical guideline that has been proposed for applying the reconstructed algorithm on a nodal discontinuous Galerkin method with a focus on accuracy and efficiency. As a result, the algorithm is demonstrated on a number of benchmark cases as well as a challenging substantive problem in HED hydrodynamics with highly disparate diffusion parameters.

Computational efficiency↗
DOE OSTI2026

A projection method for particle resampling

Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase-space due to their better scalability than continuum approaches with respect to dimension. Complex processes collectively referred to as particle noise hamper long time simulations with particle methods. One approach to address this problem is particle mesh adaptivity, or remapping, known as particle resampling and remeshing. Here, this work introduces a resampling method that projects particles to and from a (finite element) function space. The method is simple, using standard sparse linear algebra and finite element techniques, and it preserves all moments up to the order of a polynomial represented exactly by the continuum function space. It is distinguished from most other mesh-based methods in that new particle positions and number are decoupled from the mesh, allowing particle and continuum meshes to be adapted relatively independently. While this work is developed with structured particle and continuum phase-space grids on 1X + 1V Vlasov-Poisson models of Landau damping and two-stream instability, the method is well-suited to unstructured grids. Stable long time dynamics are demonstrated up to time T = 500. Reproducibility artifacts and data are publicly available.

Kinetic methods↗
DOE OSTI2026

Magnus method for electronic structure calculations at extreme conditions

We present the application of Magnus based methods to the solution of first order coupled ordinary differential equations in High Energy Density (HED) physics applications. Our focus is on the application to quantum mechanical methods, specifically on the solution of the radial Dirac equation for real and complex energies. HED applications require accurate solutions across a wide range of spatial and energy domains, including regimes where the solutions exhibit pronounced oscillatory behavior. Such cases pose significant computational challenges. We demonstrate that Magnus-based integrators can efficiently and accurately address these challenges. We discuss the implementation of the Magnus method for the solution of the radial Dirac equation, including practical considerations such as the evaluation of matrix exponentials, numerical integration, error estimation, and adaptive step size control. We also discuss the application of these methods to complex energy Green’s function techniques and the efficient approximation of integrals of the solutions relevant to HED electronic structure calculations. Here, we demonstrate the accuracy and robustness of the resulting method in applications to the free-particle case, for which analytic solutions are available for comparison, as well as the challenging case of gold at HED conditions.

general physics↗
DOE OSTI2021

An adaptive Hessian approximated stochastic gradient MCMC method

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their ability to handle large datasets and the potential to avoid overfitting. Although standard SG-MCMC methods have shown great performance in a variety of problems, they may be inefficient when the random variables in the target posterior densities have scale differences or are highly correlated. Here, we present an adaptive Hessian approximated stochastic gradient MCMC method to incorporate local geometric information while sampling from the posterior. The idea is to apply stochastic approximation (SA) to sequentially update a preconditioning matrix at each iteration. The preconditioner possesses second-order information and can guide the random walk of a sampler efficiently. Instead of computing and saving the full Hessian of the log posterior, we use limited memory of the samples and their stochastic gradients to approximate the inverse Hessian-vector multiplication in the updating formula. Moreover, by smoothly optimizing the preconditioning matrix via SA, our proposed algorithm can asymptotically converge to the target distribution with a controllable bias under mild conditions. To reduce the training and testing computational burden, we adopt a magnitude-based weight pruning method to enforce the sparsity of the network. Our method is user-friendly and demonstrates better learning results compared to standard SG-MCMC updating rules. The approximation of inverse Hessian alleviates storage and computational complexities for large dimensional models. Numerical experiments are performed on several problems, including sampling from 2D correlated distribution, synthetic regression problems, and learning the numerical solutions of heterogeneous elliptic PDE. The numerical results demonstrate great improvement in both the convergence rate and accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A method for generating moving, orthogonal, area preserving polygonal meshes

A new method for generating locally orthogonal polygonal meshes from a set of generator points is presented in which polygon areas are a constraint. The area constraint property is particularly useful for particle methods where moving polygons track a discrete portion of material. Because Voronoi polygon meshes have some very attractive mathematical and numerical properties for numerical computation, a generalization of Voronoi polygon meshes was formulated that enforces a polygon area constraint. Area constrained moving polygonal meshes allow one to develop hybrid particle-mesh numerical methods that display some of the most attractive features of each approach. It is shown that this mesh construction method can continuously reconnect a moving, unstructured polygonal mesh in a pseudo-Lagrangian fashion without change in cell area/volume, and the method's ability to simulate various physical scenarios is shown. Overall, the advantages are identified for incompressible fluid flow calculations, with demonstration cases that include material discontinuities of all three phases of matter and large density jumps.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A high-order, localized-artificial-diffusivity method for Eulerian simulation of multi-material elastic-plastic deformation with strain hardening

A high-order method for Eulerian simulation of material undergoing large elastic–plastic deformation is developed. Thermodynamically consistent hyperelastic constitutive relations are assumed, facilitating the treatment of solids, liquids, and gases in a unified manner. Here, the method enables the simulation of multi-material interactions using a diffuse interface approach. Numerical capturing of material interfaces, shock waves, contact surfaces, and elastic-plastic strain discontinuities using high-order compact-difference schemes is assisted by Localized Artificial Diffusivity (LAD). In the new setting involving elastic–plastic deformation, the previously established terms for the artificial properties are verified to effectively regularize normal shocks. Additional LAD terms are introduced to the elastic and plastic kinematic equations to regularize shear shocks and other strain discontinuities, improving solution stability. Other important features of the method that improve robustness include the numerical treatment of compatibility terms in the kinematic equations, and the treatment of rotation. Particular emphasis is focused toward new advancements of the methods for plastic-deformation integration and the associated strain hardening of the material, including rate-dependent plasticity. The method is demonstrated on a variety of test problems, including 1-D impacts, a variant of the Shu-Osher problem, a Taylor impact, and a Richtmyer-Meshkov instability between two elastic–plastic solids with strain hardening.

42 ENGINEERING↗
DOE OSTI2025

A review of low-rank methods for time-dependent kinetic simulations

Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised of a six–dimensional phase space, making simulations of such phenomena extremely expensive. In this article we demonstrate that in many situations, the solution to kinetics problems lives on a low dimensional manifold that can be described by a low-rank matrix or tensor approximation. We then review the recent development of so-called low-rank methods that evolve the solution on this manifold. The two classes of methods we review are the dynamical low-rank (DLR) method, which derives differential equations for the low-rank factors, and a Step-and-Truncate (SAT) approach, which projects the solution onto the low-rank representation after each time step. Thorough discussions of time integrators, tensor decompositions, and method properties such as structure preservation and computational efficiency are included. We further show examples of low-rank methods as applied to particle transport and plasma dynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A hybrid Monte Carlo-deterministic second moment method with efficient variance reduction

In this work, we present a hybrid method that combines Monte Carlo with deterministic finite element methods to solve a linear Boltzmann transport equation. Our hybrid method runs orders of magnitude faster than Monte Carlo, without sacrificing accuracy, for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material. We believe that this is the first demonstration of a hybrid Second Moment Method in more than one spatial dimension, the first to consider more than one material, and the first to use variance reduction. Our variance reduction approach arises from an asymptotic analysis in which we show that the magnitude of the scattering source grows without bound. We transform the problem to compute the deviation of the radiation intensity from isotropy. The magnitude of the source in the transformed problem is bounded, and the quality of the hybrid method solution is dramatically improved by a substantial reduction in the variance.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

A new multi-model absolute difference-based sensitivity (MMADS) analysis method to screen non-influential processes under process model and parametric uncertainty

Process-based models have been widely used for hydrologic modeling, and it is a common practice to use sensitivity analysis methods for excluding non-influential hydrologic processes from further investigation and/or model improvement. This study develops a new method called multi-model absolute difference-based sensitivity (MMADS) analysis method to screen non-influential system processes and parameters. MMADS is conceptually similar to the Morris method for addressing parametric uncertainty, but has a unique feature to address both process model uncertainty (i.e., a process may be represented by multiple process models) and process model parameter uncertainty (i.e., parameters associated with a process model are random). MMADS first evaluates absolute differences of a quantity of interest (i.e., a system model output) by varying process models and/or process model parameter values, and then calculates the mean and variance of the differences for investigating process influence. The mean measures overall influence of the process on the quantity of interest, and the variance estimates influence of nonlinear effects of the process and/or its interactions with other processes. MMADS is an extension of the Morris method from a parameter space to a joint parameter-model space for explicitly addressing both process model uncertainty and model parameter uncertainty. The performance of MMADS is evaluated by using two numerical experiments. One experiment is based on Sobol’s G*-function with ten product elements, and has analytical solutions of the MMADS mean and variance of absolute differences. The other experiment is for groundwater flow modeling which considers three processes (i.e., recharge, geology, and snowmelt) that interact with each other. Finally, results indicate that MMADS is computationally efficient and can identify non-influential processes of complex hydrological systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Evaluation of sequence tracking methods for Compton cameras based on CdZnTe arrays

In this study, the performance of sequence tracking methods for multiple interaction events in specific CdZnTe Compton imagers was evaluated using Monte Carlo simulations. The Compton imager consisted of a 6 × 6 array of virtual Frisch-grid CZT crystals, where the dimensions of each crystal were 5 × 5 × 12 mm 3 . The sequence tracking methods for another Compton imager that consists of two identical CZT crystals arrays were also evaluated. When 662 keV radiation was incident on the detectors, the percentages of the correct sequences determined by the simple comparison and deterministic methods for two sequential interactions were identical (~80 %), while those evaluated using the minimum squared difference method (55-59 %) and Three Compton method (45-55 %) for three sequential interactions, differed from each other. The reconstructed images of a 662 keV point source detected using single and double arrays were evaluated based on their angular resolution and signal-to-noise ratio, and the results showed that the double arrays outperformed single arrays.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Ensemble methods for quantification of potassium oxide in ChemCam Mars and laboratory spectra

In this paper we test new approaches for predicting the amount of element oxides in rock samples from the ChemCam instrument suite onboard the NASA Curiosity rover by focusing on K 2 O. Using the expanded dataset compiled by Gasda et al. (2021) with and without the Earth to Mars (E2M and NoE2M) transformation discussed in Clegg et al. (2017) we trained blended submodels using the “double blending” technique and compared these to ensemble methods (Random Forest, ExtraTrees, and Gradient Boosting Regression). We found that ensemble methods performed similar to blended submodels when looking at RMSE-P on the laboratory spectra and provided significant advantages when looking at spectra coming from Mars. For the full model, blended submodels achieved an RMSE-P of 0.62 and 0.60 (E2M and NoE2M respectively) while Gradient Boosting Regression resulted in a slightly improved RMSE-P of 0.59 and 0.60. More importantly, by employing a local RMSE-P estimation technique where model performance is evaluated based on nearby test samples we found that using ensemble methods can lower the quantification limit for K 2 O from the current value of ≈0.6 wt% to ≈0.08 wt% using Extra Trees and Random Forest. This would allow for a much larger range of K 2 O values to be quantified on Mars with greater certainty given that most targets seen on Mars tend to have <1 wt% K2O. Finally, we used both Mean Decrease in Impurity (MDI) and permutation importance techniques to investigate the wavelengths used by the ensemble methods and found that they correspond to known potassium emission lines. This suggests that ensemble methods can provide an easier to train and improved alternative to blended submodels for predicting potassium compositions from Laser Induced Breakdown Spectroscopy (LIBS) data.

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

Intensity of sample processing methods impacts wastewater SARS-CoV-2 whole genome amplicon sequencing outcomes

Wastewater SARS-CoV-2 surveillance has been deployed since the beginning of the COVID-19 pandemic to monitor the dynamics in virus burden in local communities. Genomic surveillance of SARS-CoV-2 in wastewater, particularly efforts aimed at whole genome sequencing for variant tracking and identification, are still challenging due to low target concentration, complex microbial and chemical background, and lack of robust nucleic acid recovery experimental procedures. The intrinsic sample limitations are inherent to wastewater and are thus unavoidable. Here, we use a statistical approach that couples correlation analyses to a random forest-based machine learning algorithm to evaluate potentially important factors associated with wastewater SARS-CoV-2 whole genome amplicon sequencing outcomes, with a specific focus on the breadth of genome coverage. We collected 182 composite and grab wastewater samples from the Chicago area between November 2020 to October 2021. Samples were processed using a mixture of processing methods reflecting different homogenization intensities (HA + Zymo beads, HA + glass beads, and Nanotrap), and were sequenced using one of the two library preparation kits (the Illumina COVIDseq kit and the QIAseq DIRECT kit). Technical factors evaluated using statistical and machine learning approaches include sample types, certain sample intrinsic features, and processing and sequencing methods. The results suggested that sample processing methods could be a predominant factor affecting sequencing outcomes, and library preparation kits was considered a minor factor. Finally, a synthetic SARS-CoV-2 RNA spike-in experiment was performed to validate the impact from processing methods and suggested that the intensity of the processing methods could lead to different RNA fragmentation

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Improved Solid-State Reaction Method for Scaled-Up Synthesis of Ceramic Proton-Conducting Electrolyte Materials

Protonic ceramic electrochemical cells (PCECs) represent promising technologies in the production of clean electricity, decarbonized hydrogen, chemicals, and fuels at intermediate temperatures. One of the challenges in commercializing PCECs is to produce the electrolyte materials on a large scale. The conventional solid-state reaction (SSR) method suffers from tedious synthesis procedures and low phase purity of the products due to the formation of unwanted secondary phases. Herein, we report an improved SSR (i-SSR) method for kilogram-scale production of high phase-purity electrolyte material BaZr 0.4 Ce 0.4 Y 0.1 Yb 0.1 O 3–δ (BZCYYb4411). In this method, the ball-milled precursor powders are pelletized prior to calcination, which effectively reduces the length of the diffusion paths between the components during perovskite phase formation. In this study, the synthesis procedure and calcination temperature are carefully optimized for efficient and repeatable production based on the powder crystallization behavior. A combined technoeconomic analysis and life cycle assessment modeling suggest that the i-SSR method could reduce the total production cost and greenhouse gas emissions by up to 19% and 39%, respectively, compared to the conventional SSR method. The high quality of the synthesized electrolyte material is corroborated by the excellent electrical conductivity and electrochemical performance of the fabricated PCEC cells.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Systematic Assessment of Retrieval Methods for Canopy Far-Red Solar-Induced Chlorophyll Fluorescence Using High-Frequency Automated Field Spectroscopy

Remote sensing of solar-induced chlorophyll fluorescence (SIF) offers potential to infer photosynthesis across scales and biomes. Many retrieval methods have been developed to estimate top-of-canopy SIF using ground-based spectroscopy. However, inconsistencies among methods may confound interpretation of SIF dynamics, eco-physiological/environmental drivers, and its relationship with photosynthesis. Using high temporal- and spectral resolution ground-based spectroscopy, we aimed to (1) evaluate performance of SIF retrieval methods under diverse sky conditions using continuous field measurements; (2) assess method sensitivity to fluctuating light, reflectance, and fluorescence emission spectra; and (3) inform users for optimal ground-based SIF retrieval. Analysis included field measurements from bi-hemispherical and hemispherical-conical systems and synthetic upwelling radiance constructed from measured downwelling radiance, simulated reflectance, and simulated fluorescence for benchmarking. Fraunhofer-based differential optical absorption spectroscopy (DOAS) and singular vector decomposition (SVD) retrievals exhibit convergent SIF-PAR relationships and diurnal consistency across different sky conditions, while O2A-based spectral fitting method (SFM), SVD, and modified Fraunhofer line discrimination (3FLD) exhibit divergent SIF-PAR relationships across sky conditions. We find that such behavior holds across system configurations, though hemispherical-conical systems diverge less across sky conditions. O 2 A retrieval accuracy, influenced by atmospheric distortion, improves with a narrower fitting window and when training SVD with temporally local spectra. This may impact SIF-photosynthesis relationships interpreted by previous studies using O 2 A-based retrievals with standard (759–767.76 nm) fitting windows. Fraunhofer-based retrievals resist atmospheric impacts but are noisier and more sensitive to assumed SIF spectral shape than O 2 A-based retrievals. We recommend SVD or SFM using reduced fitting window (759.5–761.5 nm) for robust far-red SIF retrievals across sky conditions.

59 BASIC BIOLOGICAL SCIENCES↗
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↗