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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 NTRS2011

Development of an Open Rotor Cycle Model in NPSS Using a Multi-Design Point Approach

NASA's Environmentally Responsible Aviation Project and Subsonic Fixed Wing Project are focused on developing concepts and technologies which may enable dramatic reductions to the environmental impact of future generation subsonic aircraft (Refs. 1 and 2). The open rotor concept (also referred to as the Unducted Fan or advanced turboprop) may allow the achievement of this objective by reducing engine emissions and fuel consumption. To evaluate its potential impact, an open rotor cycle modeling capability is needed. This paper presents the initial development of an open rotor cycle model in the Numerical Propulsion System Simulation (NPSS) computer program which can then be used to evaluate the potential benefit of this engine. The development of this open rotor model necessitated addressing two modeling needs within NPSS. First, a method for evaluating the performance of counter-rotating propellers was needed. Therefore, a new counter-rotating propeller NPSS component was created. This component uses propeller performance maps developed from historic counter-rotating propeller experiments to determine the thrust delivered and power required. Second, several methods for modeling a counter-rotating power turbine within NPSS were explored. These techniques used several combinations of turbine components within NPSS to provide the necessary power to the propellers. Ultimately, a single turbine component with a conventional turbine map was selected. Using these modeling enhancements, an open rotor cycle model was developed in NPSS using a multi-design point approach. The multi-design point (MDP) approach improves the engine cycle analysis process by making it easier to properly size the engine to meet a variety of thrust targets throughout the flight envelope. A number of design points are considered including an aerodynamic design point, sea-level static, takeoff and top of climb. The development of this MDP model was also enabled by the selection of a simple power management scheme which schedules propeller blade angles with the freestream Mach number. Finally, sample open rotor performance results and areas for further model improvements are presented.

Hendricks, Eric S.↗
NASA NTRS1992

Performance Evaluation and Modeling Techniques for Parallel Processors

In practice, the performance evaluation of supercomputers is still substantially driven by singlepoint estimates of metrics (e.g., MFLOPS) obtained by running characteristic benchmarks or workloads. With the rapid increase in the use of time-shared multiprogramming in these systems, such measurements are clearly inadequate. This is because multiprogramming and system overhead, as well as other degradations in performance due to time varying characteristics of workloads, are not taken into account. In multiprogrammed environments, multiple jobs and users can dramatically increase the amount of system overhead and degrade the performance of the machine. Performance techniques, such as benchmarking, which characterize performance on a dedicated machine ignore this major component of true computer performance. Due to the complexity of analysis, there has been little work done in analyzing, modeling, and predicting the performance of applications in multiprogrammed environments. This is especially true for parallel processors, where the costs and benefits of multi-user workloads are exacerbated. While some may claim that the issue of multiprogramming is not a viable one in the supercomputer market, experience shows otherwise. Even in recent massively parallel machines, multiprogramming is a key component. It has even been claimed that a partial cause of the demise of the CM2 was the fact that it did not efficiently support time-sharing. In the same paper, Gordon Bell postulates that, multicomputers will evolve to multiprocessors in order to support efficient multiprogramming. Therefore, it is clear that parallel processors of the future will be required to offer the user a time-shared environment with reasonable response times for the applications. In this type of environment, the most important performance metric is the completion of response time of a given application. However, there are a few evaluation efforts addressing this issue.

Dimpsey, Robert Tod↗
DOE OSTI2016

Hierarchical Multi-Scale Approach To Validation and Uncertainty Quantification of Hyper-Spectral Image Modeling

Validating predictive models and quantifying uncertainties inherent in the modeling process is a critical component of the HARD Solids Venture program [1]. Our current research focuses on validating physics-based models predicting the optical properties of solid materials for arbitrary surface morphologies and characterizing the uncertainties in these models. We employ a systematic and hierarchical approach by designing physical experiments and comparing the experimental results with the outputs of computational predictive models. We illustrate this approach through an example comparing a micro-scale forward model to an idealized solid-material system and then propagating the results through a system model to the sensor level. Our efforts should enhance detection reliability of the hyper-spectral imaging technique and the confidence in model utilization and model outputs by users and stakeholders.

Engel, David W.↗
NASA NTRS1989

Color composite processing of multi-wavelength, multi-polarization airborne radar imagery

Multiwavelength, multipolarization radar image data can be processed to allow the clear depiction of most information in color composite displays. The first principal component, depicted as variations in image intensity, captures the dominant variation in the data and reduces noise without degradation of spatial detail. Other principal components, depicted primarily as variations in image chromaticity, are derived from spatially filtered data so that image colors can be attributed to significant wavelength and polarization contrasts, and not to speckle. Processing paths can be designed to emphasize wavelength contrasts, polarization contrasts, or overall discrimination of surface features.

Crippen, Robert E.↗
NASA NTRS1997

Comparison of Orbiter PRCS Plume Flow Fields Using CFD and Modified Source Flow Codes

The Space Shuttle Orbiter will use Reaction Control System (RCS) jets for docking with the planned International Space Station (ISS). During approach and backout maneuvers, plumes from these jets could cause high pressure, heating, and thermal loads on ISS components. The object of this paper is to present comparisons of RCS plume flow fields used to calculate these ISS environments. Because of the complexities of 3-D plumes with variable scarf-angle and multi-jet combinations, NASA/JSC developed a plume flow-field methodology for all of these Orbiter jets. The RCS Plume Model (RPM), which includes effects of scarfed nozzles and dual jets, was developed as a modified source-flow engineering tool to rapidly generate plume properties and impingement environments on ISS components. This paper presents flow-field properties from four PRCS jets: F3U low scarf-angle single jet, F3F high scarf-angle single jet, DTU zero scarf-angle dual jet, and F1F/F2F high scarf-angle dual jet. The RPM results compared well with plume flow fields using four CFD programs: General Aerodynamic Simulation Program (GASP), Cartesian (CART), Unified Solution Algorithm (USA), and Reacting and Multi-phase Program (RAMP). Good comparisons of predicted pressures are shown with STS 64 Shuttle Plume Impingement Flight Experiment (SPIFEX) data.

Rochelle, Wm. C.↗
DOE OSTI2019

The Additive Approximation for Heat Transfer and for Stability Calculations in a Multi-filamentary Superconductor - part A

This paper addresses the applicability of the “additive approximation” of total thermal conductivity in heat transfer and in superconductor stability calculations. If cases (a), (b) and (c) denote total (conductive plus radiative), or only conductive or only radiative heat flux, respectively, each flux q-dot calculated with Fourier’s conduction law using the corresponding thermal conductivity (λ{sub a}, λ{sub b}, λ{sub c}), the additive approximation would be confirmed if the heat flux difference Δ q-dot = q-dot {sub a}− q-dot {sub b}− q-dot {sub c}, at any position of an investigated object, and at any time, converges to zero. This is not trivial because of the strong, non-linear temperature dependence of the radiation component. Heat transfer calculations including radiative transfer are presented in this paper, first for simple, homogeneous, thin film test samples and later for a multi-filamentary BSCCO 2223 superconductor. The simulated heat sources either result from a sudden increase of conductor boundary temperature or from flux flow and Ohmic resistances in the superconductor under a disturbance (like transport current exceeding critcal current density). The conductors, though very thin, are non-transparent to mid-IR radiation. Validity of the additive approximation is critical for superconductor stability against quench. Based on the applied numerical scheme, a hypothesis is suggested concerning correlation of the results of the simulation (the “numerical space”) with the experimental situation (the “physical reality”): Non-convergence of the numerical scheme might tightly be correlated with occurrence of a quench in the simulated superconductor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1994

Cooperative control theory and integrated flight and propulsion control

This report documents the activities and research results obtained under a grant (NAG3-998) from the NASA Lewis Research Center. The focus of the research was the investigation of dynamic interactions between airframe and engines for advanced ASTOVL aircraft configurations, and the analysis of the implications of these interactions on the stability and performance of the airframe and engine control systems. In addition, the need for integrated flight and propulsion control for such aircraft was addressed. The major contribution of this research was the exposition of the fact that airframe and engine interactions could be present, and their effects could include loss of stability and performance of the control systems. Also, the significance of two directional, as opposed to one-directional, coupling was identified and explained. A multi variable stability and performance analysis methodology was developed, and applied to several candidate aircraft configurations. Also exposed was the fact that with interactions present along with some integrated control approaches, the engine command/limiting logic (which represents an important non-linear component of the engine control system) can impact closed-loop airframe/engine system stability. Finally, a brief investigation of control-law synthesis techniques appropriate for the class of systems was pursued, and it was determined that multi variable techniques, included model-following formulations of LQG and/or H (infinity) methods showed promise. However, for practical reasons, decentralized control architectures are preferred, which is an architecture incompatible with these synthesis methods.

Schmidt, David K.↗
DOE OSTI2017

Multi-color pyrometry imaging system and method of operating the same

A multi-color pyrometry imaging system for a high-temperature asset includes at least one viewing port in optical communication with at least one high-temperature component of the high-temperature asset. The system also includes at least one camera device in optical communication with the at least one viewing port. The at least one camera device includes a camera enclosure and at least one camera aperture defined in the camera enclosure, The at least one camera aperture is in optical communication with the at least one viewing port. The at least one camera device also includes a multi-color filtering mechanism coupled to the enclosure. The multi-color filtering mechanism is configured to sequentially transmit photons within a first predetermined wavelength band and transmit photons within a second predetermined wavelength band that is different than the first predetermined wavelength band.

42 ENGINEERING↗
DOE OSTI2017

Multi-scale modelling to relate beryllium surface temperature, deuterium concentration and erosion in fusion reactor environment

Beryllium (Be) has been chosen as the plasma-facing material for the main wall of ITER, the next generation fusion reactor. Identifying the key parameters that determine Be erosion under reactor relevant conditions is vital to predict the ITER plasma-facing component lifetime and viability. To date, a certain prediction of Be erosion, focusing on the effect of two such parameters, surface temperature and D surface content, has not been achieved. In this paper, we develop the first multi-scale KMC-MD modeling approach for Be to provide a more accurate database for its erosion, as well as investigating parameters that affect erosion. First, we calculate the complex relationship between surface temperature and D concentration precisely by simulating the time evolution of the system using an object kinetic Monte Carlo (OKMC) technique. These simulations provide a D surface concentration profile for any surface temperature and incoming D energy. We then describe how this profile can be implemented as a starting configuration in molecular dynamics (MD) simulations. We finally use MD simulations to investigate the effect of temperature (300–800 K) and impact energy (10–200 eV) on the erosion of Be due to D plasma irradiations. The results reveal a strong dependency of the D surface content on temperature. Increasing the surface temperature leads to a lower D concentration at the surface, because of the tendency of D atoms to avoid being accommodated in a vacancy, and de-trapping from impurity sites diffuse fast toward bulk. At the next step, total and molecular Be erosion yields due to D irradiations are analyzed using MD simulations. The results show a strong dependency of erosion yields on surface temperature and incoming ion energy. The total Be erosion yield increases with temperature for impact energies up to 100 eV. However, increasing temperature and impact energy results in a lower fraction of Be atoms being sputtered as BeD molecules due to the lower D surface concentrations at higher temperatures. Finally, these findings correlate well with different experiments performed at JET and PISCES-B devices.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Multi-Objective Hyperparameter Optimization for Spiking Neural Network Neuroevolution

Neuroevolution has had significant success over recent years, but there has been relatively little work applying neuroevolution approaches to spiking neural networks (SNNs). SNNs are a type of neural network that includes temporal processing component, are not easily trained using other methods, and can be deployed into energy-efficient neuromorphic hardware. In this work, we investigate two evolutionary approaches for training SNNs. We explore the impact of the hyperparameters of the evolutionary approaches, including tournament size, population size, and representation type, on the performance of the algorithms. We present a multi-objective Bayesian-based hyperparameter optimization approach to tune the hyperparameters to produce the most accurate and smallest SNNs. We show that the hyperparameters can significantly affect the performance of these algorithms. We also perform sensitivity analysis and demonstrate that every hyperparameter value has the potential to perform well, assuming other hyperparameter values are set correctly.

Parsa, Maryam↗
DOE OSTI2024

Multi-Level Structural Damage Characterization Using Sparse Acoustic Sensor Networks and Knowledge Transferred Deep Learning

Standard structural health monitoring techniques face well-known difficulties for comprehensive defect diagnosis in real-world structures that have structural, material, or geometric complexity. This motivates the exploration of machine-learning-based structural health monitoring methods in complex structures. However, creating sufficient training data sets with various defects is an ongoing challenge for data-driven machine (deep) learning algorithms. The ability to transfer the knowledge of a trained neural network from one component to another or to other sections of the same component would drastically reduce the required training data set. Also, it would facilitate computationally inexpensive machine learning based inspection systems. In this work, a machine-learning-based multi-level damage characterization is demonstrated with the ability to transfer trained knowledge within the sparse sensor network. A novel network spatial assistance and an adaptive convolution technique are proposed for efficient knowledge transfer within the deep learning algorithm. Proposed structural health monitoring method is experimentally evaluated on an aluminum plate with artificially induced defects. It was observed that the method improves the performance of knowledge transferred damage characterization by 50% during localization and 24% during severity assessment. Further, experiments using time windows with and without multiple edge reflections are studied. Results reveal that multiply scattered waves contain rich and deterministic defect signatures that can be mined using deep learning neural networks, improving the accuracy of both identification and quantification. In the case of a fixed sensor network, using multiply scattered waves shows 100% prediction accuracy at all levels of damage characterization.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Validating a Model for Welding Induced Residual Stress Using High-Energy X-ray Diffraction

Integrated computational materials engineering (ICME) provides a pathway to advance performance in structures through the use of physically-based models to better understand how manufacturing processes influence product performance. As one particular challenge, consider that residual stresses induced in fabrication are pervasive and directly impact the life of structures. For ICME to be an effective strategy, it is essential that predictive capability be developed in conjunction with critical experiments. In the present paper, simulation results from a multi-physics model for gas metal arc welding are evaluated through x-ray diffraction using synchrotron radiation. A test component was designed with intent to develop significant gradients in residual stress, be representative of real-world engineering application, yet remain tractable for finely spaced strain measurements with positioning equipment available at synchrotron facilities. Finally, the experimental validation lends confidence to model predictions, facilitating the explicit consideration of residual stress distribution in prediction of fatigue life.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Digital-twin-based improvements to diagnosis, prognosis, strategy assessment, and discrepancy checking in a nearly autonomous management and control system

We report the Nearly Autonomous Management And Control System (NAMAC) is a comprehensive control system to assist plant operations by furnishing control recommendations to operators in a broad class of situations. This study refines a NAMAC system for making reasonable recommendations during complex loss of flow (LOF) scenarios with a validated EBR-II simulator, digital twins improved by machine-learning algorithms, a multi-attribute decision-making scheme, and a discrepancy checker for identifying unexpected recommendation effects. The performance of each NAMAC component is assessed, while the capability of NAMAC is demonstrated and evaluated in a class of LOF scenarios.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

NMR-based serum metabolomics study reveals a innovative diagnostic model for missed abortion

A missed abortion (MA) is an in-utero death of the embryo or fetus before the 20th week of gestation with retained products of conception. In order to discover novel biomarkers for MA, a {sup 1}H NMR spectroscopy-based metabolomics approach was applied to detect human MA serum metabolic profiles. Serum samples were obtained from patients with MA (n = 15) and healthy controls (n = 9) for study. The NOESYPR1D spectrum combined with multi-variate pattern recognition analysis was used to cluster the groups and establish a disease-specific metabolites phenotype. Principal component analysis (PCA) and orthogonal partial least-squares discriminant analysis (OPLS-DA) models were capable of distinguishing MA patients from healthy subjects. The results revealed that 24 metabolites altered in MA patients compared with the control population. Metabolomic pathway analysis demonstrated that alanine, aspartate and glutamate metabolism, citrate cycle (TCA cycle), taurine and hypotaurine metabolism were significantly altered in MA. The results indicated that serum NMR-based metabolomic profiling method is sensitive and specific enough to distinguish MA and from healthy controls, this method could be developed as a clinically useful diagnostic tool for MA. The finding from the MA serum metabolic profiling shed a new light on further understanding of MA disease mechanisms.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Highly resolved Eulerian simulations of fuel spray transients in single and multi-hole injectors: Nozzle flow and near-exit dynamics

In high pressure fuel injectors, needle opening and closing transients cause complex off-design fluid dynamics behaviors that profoundly impact the spray and mixture formation processes. These dynamics are completely different from what is known to occur in steady state conditions. In this study, diesel spray transients have been investigated in single-hole and 3-hole nozzles, encompassing internal and external nozzle flow and including needle motion, performing highly resolved (2.5 μm) computational fluid dynamics (CFD) simulations. We focused on end-of-injection (EOI) and start-of-injection (SOI) processes, in order to provide insights in to the physics. The liquid fuel, vapor and gas species are modeled with a single-fluid multiphase mixture approach, with diffuse interface, and with large eddy simulations (LES) of the turbulence. Occurrence of phase change due to cavitation is accounted for, and the spray dispersion is described with a turbulent dispersion model. Detailed needle motion data and orifice internal surface are available from xray synchrotron source measurements carried out at Argonne National Laboratory, and shared through the Engine Combustion Network (ECN) community. Simulations are compared against x-ray phase contrast imaging and radiography of the internal and near-exit flow, in addition to optical microscopy data of the near-exit sprays. Simulation results are found to agree well with available experimental data, and are able to realistically capture local and global features. The simulations allow to gain insight into the physics of gas ingestion and dribbles at EOI, for different hole diameters, operating conditions and number of holes. At SOI, timing of liquid appearance out of the injector and spray tip penetration are adequately predicted, by using the EOI flow field as in-nozzle initialization, and by prescribing the measured tip needle displacement with an informed effective valve opening point inferred from the x-ray observations. Lastly, the variation of spreading angle over time is also discussed in detail for the multi-hole case, including hole-to-hole variations. Due to real geometry features and asymmetric needle motion with eccentric components, it is found that the three holes exhibit swirling flows of increasing intensity as the lift decreases, causing the near cone angle to open and spread, in a quasi-hollow cone structure. These features are not observed in axial single-hole injectors because of their relative simplicity and intrinsic symmetry.

42 ENGINEERING↗
DOE OSTI2023

How does uncertainty of soil organic carbon stock affect the calculation of carbon budgets and soil carbon credits for croplands in the U.S. Midwest?

Cropland carbon budget depicts the amount of carbon flowing in and out of agroecosystems and the changes in carbon stocks of soil and living biomass during the same period. Soil carbon credit is the additional change in soil carbon stock under certain farming practices compared with the business-as-usual practices. Accurately calculating cropland carbon budget and soil carbon credit is critical to assessing climate change mitigation potential in agroecosystems. The calculation of cropland carbon budget and soil carbon credit is sensitive to local soil and climatic conditions, especially initial soil organic carbon (SOC) stock, which is determined by both SOC concentration (SOC%) and bulk density (Bulk_Density). SOC stock data are either from soil sampling or gridded public survey data. In agroecosystem models, SOC stock data are a key model input for quantifying cropland carbon budget and soil carbon credit. However, various types and degrees of uncertainties exist in SOC stock datasets, which propagate to the quantification of SOC stock change. In particular, a large discrepancy is found in two widely used SOC stock datasets — Rapid Carbon Assessment dataset (RaCA) and Gridded Soil Survey Geographic Database (gSSURGO) — in the U.S. Midwest, with a relative difference (quantified using Normalized Root Mean Square Error, NRMSE) of 48.0% for 0–30 cm SOC stock between the two datasets. It remains largely unclear how uncertainty in SOC stocks affects the calculation of cropland carbon budget and soil carbon credit. To address this question, we used a well-validated process-based agroecosystem model, ecosys, to assess the impacts of SOC stock uncertainty on carbon budget and soil carbon credit calculation in the U.S. Midwestern corn-soybean rotation systems. Our results reveal the following findings: (1) A sizable discrepancy exists in simulated cropland carbon budget between using gSSURGO and using RaCA for their SOC% and Bulk_Density as model inputs, with a Pearson correlation coefficient (r) of only 0.4 for simulated change of SOC stock (ΔSOC) using these two different soil datasets. (2) Simulated cropland carbon budget components were more sensitive to initial SOC% than to Bulk_Density. For example, the upper and lower quartiles of multi-year averaged ΔSOC were –29.8 and 4.8 gC/m 2 /year for the selected counties respectively, with an uncertainty of 13.7 and 0.7 gC/m 2 /year induced by uncertainties in initial SOC% and Bulk_Density, respectively. (3) Both simulated ΔSOC and its uncertainty were negatively correlated with initial SOC%, whereas ΔSOC was negatively correlated with air temperature, and ΔSOC uncertainty was positively correlated with air temperature. (4) The uncertainty of calculated soil carbon credits was much smaller compared with the uncertainty of calculated absolute carbon budgets assuming the same SOC stock uncertainty level in the inputs. Specifically, in our assessment comparing planting cover crops vs no cover crop, the uncertainty of calculated soil carbon credits induced by initial SOC% uncertainty was less than 4% (relative to the quantified value of the soil carbon credits) for 90% of the cases. Our analysis highlights that high accuracy measurement of SOC% as inputs is needed for the calculation of cropland carbon budgets; however, soil carbon credit quantification is much less sensitive to the initial SOC% inputs, and the current publicly available soil datasets (e.g., gSSURGO) are largely suitable for the calculation of soil

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Advective gas flow in bentonite: Development and comparison of enhanced multi-phase numerical approaches

Understanding the impact of repository gas, generated from degradation of waste and its interaction with the host rock, is essential when assessing the performance and safety function of long-term disposal systems for radioactive waste. Numerical models based on conventional multi-phase flow theory have historically been applied to predict the outcome and impact of gas flow on different repository components. However, they remain unable to describe the full complexity of the physical processes observed in water-saturated experiments (e.g., creation of dilatant pathways) and thus, the development of novel representations for their description is required when assessing fully saturated clay-based systems. This was the primary focus of Task A within the international cooperative project DECOVALEX-2019 (D-2019) and refinement of these approaches is the primary focus of this study (Task B in the current phase of DECOVALEX-2023). This paper summarises development of enhanced numerical representations of key processes and compares the performance of each model against high-quality laboratory test data. Experimental data reveals that gas percolation in water-saturated compacted bentonite is characterised by four key features: (i) a quiescence phase, followed by (ii) the gas breakthrough, which leads to a (iii) peak value, which is then followed by (iv) a negative decay. Three models based on the multiphase flow theory have been developed. These models can provide good initial values and reasonable responses for gas breakthrough (although some of them still predict a too-smooth response). Peak gas pressure values are in general reasonably well captured, although maximum radial stress differences are observed at 48 mm from the base of the sample. Here, numerical peak values of 12.8 MPa are predicted, whereas experimental values are about 11 MPa. These models are also capable of providing a reasonable representation of the negative pressure decay following peak pressure. However, other key specific features (such as the timing of gas breakthrough) still require a better representation. The model simulations and their comparison with experimental data show that these models need to be further improved with respect to model parameter calibration, the numerical representation of spatial heterogeneities in material properties and flow localisation, and the upscaling of the related physical processes and parameters. To further understand gas flow localisation, a new conceptual model has been developed, which shows that discrete channels can possibly be induced through the instability of gas-bentonite interface during gas injection, thus providing a new perspective for modeling gas percolation in low-permeability deformable media.

58 GEOSCIENCES↗
DOE OSTI2021

Electron–Nucleus Hyperfine Coupling Calculated from Restricted Active Space Wavefunctions and an Exact Two-Component Hamiltonian

Exact two-component (X2C) relativistic nuclear hyperfine magnetic field operators were incorporated in X2C ab-initio wavefunction calculations at the multi-reference restricted active space (RAS) level for calculations of nuclear hyperfine magnetic properties. Spin-orbit coupling was treated via RAS state interaction (SO-RASSI). The method was tested by calculations of electron – nucleus hyperfine coupling constants. The approach, implemented in the OpenMolcas program, overcomes a major limitation of a previous SO-RASSI implementation for hyperfine coupling that relied on non-relativistic hyperfine operators [J. Chem. Theor. Comput. 2015, 11, 538–549] and therefore had only limited applicability. Furthermore, results from calculations on systems with light and heavy main group elements, transition metals, lanthanides, and one actinide complex, demonstrate reasonably good agreement with experimental data, where available, as long as the active space can generate sufficient spin polarization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗