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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Energy flexibility of residential buildings: A systematic review of characterization and quantification methods and applications

With building electric demand becoming increasingly dynamic, and a growing percentage of intermittent renewable power generation from solar photovoltaics and wind turbines, the power grid is facing increasing challenge to manage the real time balance between the supply and demand. With advancements in smart sensing and metering, smart appliances, electric vehicles, and energy storage technologies, demand side management of residential buildings can help the grid to improve stability by optimizing flexible loads. This paper reviews recent studies on residential building demand side management, with a focus on characterization and quantification of energy flexibility covering various types of flexible loads, metrics, methods, and applications. The reviewed studies showed four levels of applications: building level (45%), district or community level (29%), system level (19%), and building sector level (7%). Shifting loads is the dominant flexibility type in 60% of applications, followed by shedding (19%), generation (16%), and modulating (6%). Depending on the technology and application scope, flexible operations have a wide range of performance, with peak power reductions of 1%~65%, energy savings up to 60%, operational cost reduction of 1%~48%, and greenhouse gas emission reductions of up to29%. More than half (51%) of the studies employed control strategies to achieve flexibility; among those 72% used optimal controls, while 28% used rule-based controls. About 58% of the studies used mathematical formulation to quantify energy flexibility. Most studies were based on simulation, while less than 15% of the studies had measurements from experiments or field tests. The review reveals research opportunities to address significant gaps in the existing literature: (1) establishing a common definition and performance metrics for energy flexibility of buildings that are technology and application agnostic, (2) developing an ontology to standardize representation of flexibility resources for interoperability, (3) integrating occupant impacts into the quantification and optimization of energy flexibility, and (4) developing requirements and credits of energy flexibility in building energy codes and standards. Findings from the review can inform future research and development of energy flexible buildings which are essential to a reliable and resilient power grid.

Li, H↗
DOE OSTI2026

Optimizing district energy systems by integrating Borehole Thermal Energy Storage Using a Mixed-Integer Linear Programming g-function framework with a Multi-Timescale Rolling Horizon method

Shallow geothermal has gained increasing attention in recent years; however, a reliable framework for its accurate incorporation into large-scale energy system optimization remains lacking. This study proposes a Mixed-Integer Linear Programming (MILP) framework combined with the g-function approach to integrate Borehole Thermal Energy Storage (BTES) technology into energy system optimization. Validation against a Modelica-based reservoir network simulation demonstrates that the proposed framework effectively captures the ground thermal response under varying energy loads and accurately estimates the borefield energy supply. To enhance scalability, a Rolling Horizon with Multi-Timescale (RH-MTS) method is further introduced, reducing computational time by 73 % for the 1-year optimization model with only minor loss of optimality. The framework is demonstrated through the case study of the UC Berkeley campus. Results indicate that BTES is a cost-effective and low-carbon solution: two borefields comprising 382 boreholes can meet 8.0 % and 6.6 % of the total campus heating and cooling demand, respectively, at an average energy rate of 0.70–0.77 USD/kWh and carbon intensity of 0.54 kg-CO2/kWh. Short-term analysis reveals a 35%–65% decline in BTES energy flow after 3–6 months of continuous heating/cooling operation, while long-term simulation shows that annual energy production of BTES can vary by up to 12.0 % after four years before stabilizing. Overall, this study develops a novel optimization framework that couples physics-based g-function method with MILP optimization framework, thereby advancing methodological development for shallow-geothermal integration and providing actionable guidance for BTES deployment in district-energy systems.

Yang, Jiahui↗
DOE OSTI2025

Energy resolution and gain measurements in Argon-based gas mixtures: Exploring Ar:CF 4 for low energy measurements with TPCs

Time Projection Chambers (TPCs) are among the most advanced charged-particle detectors. Gas-filled TPCs have tracking capabilities that provide 3D-imaging of charged particles with a good energy resolution for spectroscopy. Different gas mixtures have different properties that determine the energy resolution as well as the spatial resolution. Therefore, optimization of operating conditions is required to simultaneously obtain adequate gain, energy resolution, spatial/track resolution, as well as higher drift velocities for high counting rates applications. Ar:CF 4 gas mixture has higher electron drift velocities and lower electron diffusion, which makes it an attractive candidate for TPC filling gas for low energy nuclear physics applications as compared to commonly used Ar:CH 4 and Ar:CO 2 gas mixtures, namely when tracking information is needed. However, other properties, including energy resolution and gain, remain largely unexplored in Ar:CF 4 especially at pressures and other operating conditions relevant for low-energy nuclear physics applications. Here, in this paper we report on gain and energy resolution measurements, using Gas Electron Multipliers (GEMs), in the less explored Ar:CF 4 mixture (Alfonsi et al., 2006), as well as in the more commonly used gas mixtures Ar:CH 4 and Ar:CO 2 . In addition to obtaining energy resolution and gain, we provide results from Garfield++ simulations for gain fluctuations, and their impact on energy resolution is discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Total energy in supernova neutrinos and the tidal deformability and binding energy of neutron stars

The energy radiated in supernova neutrinos is a fundamental quantity that is closely related to the gravitational binding energy of a neutron star. Recently the tidal deformability of neutron stars was constrained by gravitational wave observations. By considering several equations of state, we find a strong correlation between the tidal deformability and neutron star binding energy. We use this correlation to sharpen predictions of the binding energy of neutron stars and the total neutrino energy in supernovae. We find a minimum binding energy for a neutron star formed in a supernova of ~ 1.5 × 10 53 ergs . Should the neutrino energy in a supernova be significantly below this value, it would strongly suggest new unobserved particles are carrying away some of the supernova energy. Alternatively, if the neutrino energy is observed above ~ 6 × 10 53 ergs , it would strongly imply the formation of a (perhaps surprisingly) massive neutron star.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Analysis of Energy Justice and Equity Impacts from Replacing Peaker Plants with Energy Storage

Transitions to low-carbon energy systems are essential to mitigating and adapting to climate change. Energy storage systems are a key component in achieving a viable decarbonized electric grid. However, decarbonization alone does not guarantee a fairer, more inclusive, or socially just energy system. Energy equity and justice should be integrated in energy system transitions to ensure benefits and burdens are shared equitably. In this paper, we discuss the relationship between energy storage and social equity by assessing the use of energy storage to replace natural gas-fired (NG) peaker plants. Peaker plants are disproportionately located near disadvantaged communities and tend to be older and high emitters of health-affecting fine particulate matter and other pollutants. This paper investigates the equity implications of NG peaker plant replacements with battery energy storage in the context of Washington State’s peaker plants to highlight the human-centered values of retiring the plants. The study performed production cost simulations using the latest Western Electric Coordinating Council Anchor Dataset 2030 case and found that total generation cost, locational marginal price, and total annual emissions were reduced with the replacements. These reductions will have equity benefits on local communities including access to clean air, enhanced health outcomes, and energy burden reductions.

Tarekegne, Bethel W.↗
DOE OSTI2023

Energy Justice Framework for Marine Energy: Considerations from PacWave

To accelerate the energy transition while addressing land use conflicts and community opposition, federal policies and incentives require that new energy infrastructure provide direct benefits to communities, and ensure that these benefits remain in the community. The objective of this study is to develop a framework for collecting demographic, socioeconomic, and environmental data and supporting communities in understanding how such data can support more just and equitable outcomes. Specifically, this study addresses two research questions: (1) How can energy justice be incorporated into ME project life cycle, and (2) what social and economic data are needed to assess how marine energy development supports energy justice? Based on our literature review and the data collection template, a case study of PacWave, a wave energy testing facility located on the central Oregon Coast, is employed to draw more specific implications for how energy justice can be integrated into marine energy. PacWave represents a flagship investment by Oregon State University, the State of Oregon, and the Department of Energy. The facility is situated in Lincoln County, which is home to the Confederated Tribes of Siletz Indians and family-scale fishing enterprises. PacWave has strong community support as a testing site and holds potential to provide valuable lessons for other communities.

16 TIDAL AND WAVE POWER↗
DOE OSTI2024

Battery Energy Storage Systems: A Review of Energy Management Systems and Health Metrics

With increasing concerns about climate change, there is a transition from high-carbon-emitting fuels to green energy resources in various applications including household, commercial, transportation, and electric grid applications. Even though renewable energy resources are receiving traction for being carbon-neutral, their availability is intermittent. To address this issue to achieve extensive application, the integration of energy storage systems in conjunction with these resources is becoming a recommended practice. Additionally, in the transportation sector, the increased demand for EVs requires the development of energy storage systems that can deliver energy for rigorous driving cycles, with lithium-ion-based batteries emerging as the superior choice for energy storage due to their high power and energy densities, length of their life cycle, low self-discharge rates, and reasonable cost. As a result, battery energy storage systems (BESSs) are becoming a primary energy storage system. The high-performance demand on these BESS can have severe negative effects on their internal operations such as heating and catching on fire when operating in overcharge or undercharge states. Reduced efficiency and poor charge storage result in the battery operating at higher temperatures. To mitigate early battery degradation, battery management systems (BMSs) have been devised to enhance battery life and ensure normal operation under safe operating conditions. Some BMSs are capable of determining precise state estimations to ensure safe battery operation and reduce hazards. Precise estimation of battery health is computed by evaluating several metrics and is a central factor in effective battery management systems. In this scenario, the accurate estimation of the health indicators (HIs) of the battery becomes even more important within the framework of a BMS. This paper provides a comprehensive review and discussion of battery management systems and different health indicators for BESSs, with suitable classification based on key characteristics.

Nazaralizadeh, Solmaz (ORCID:0009000737004039)↗
NASA NTRS1981

Computer simulated building energy consumption for verification of energy conservation measures in network facilities

A computer program called ECPVER (Energy Consumption Program - Verification) was developed to simulate all energy loads for any number of buildings. The program computes simulated daily, monthly, and yearly energy consumption which can be compared with actual meter readings for the same time period. Such comparison can lead to validation of the model under a variety of conditions, which allows it to be used to predict future energy saving due to energy conservation measures. Predicted energy saving can then be compared with actual saving to verify the effectiveness of those energy conservation changes. This verification procedure is planned to be an important advancement in the Deep Space Network Energy Project, which seeks to reduce energy cost and consumption at all DSN Deep Space Stations.

Plankey, B.↗
NASA NTRS2007

On the use of Lineal Energy Measurements to Estimate Linear Energy Transfer Spectra

This paper examines the error resulting from using a lineal energy spectrum to represent a linear energy transfer spectrum for applications in the space radiation environment. Lineal energy and linear energy transfer spectra are compared in three diverse but typical space radiation environments. Different detector geometries are also studied to determine how they affect the error. LET spectra are typically used to compute dose equivalent for radiation hazard estimation and single event effect rates to estimate radiation effects on electronics. The errors in the estimations of dose equivalent and single event rates that result from substituting lineal energy spectra for linear energy spectra are examined. It is found that this substitution has little effect on dose equivalent estimates in interplanetary quiet-time environment regardless of detector shape. The substitution has more of an effect when the environment is dominated by solar energetic particles or trapped radiation, but even then the errors are minor especially if a spherical detector is used. For single event estimation, the effect of the substitution can be large if the threshold for the single event effect is near where the linear energy spectrum drops suddenly. It is judged that single event rate estimates made from lineal energy spectra are unreliable and the use of lineal energy spectra for single event rate estimation should be avoided.

Adams, David A.↗
NASA NTRS2022

Washington, D.C. & Maryland Energy: Estimating Solar Potential Using NASA POWER Data to Inform Renewable Energy Policy for Washington, D.C.

In line with the Sustainable D.C. 2.0 plan to combat climate change, Washington D.C. aims to decrease its greenhouse gas emissions by 100% by 2050. As solar energy is a clean, renewable energy form, its integration into the region’s power grids lowers energy costs and incentivizes sustainable development. We partnered with the Washington D.C. Department of Energy & Environment (DOEE) to determine how urban areas surrounding D.C. can better be incorporated into decisions regarding renewable energy policy. The team used NASA’s Prediction of Worldwide Energy Resources (POWER) solar data and a Light Detection and Ranging (LiDAR) derived digital surface model, to estimate and visualize rooftop solar potential for Maryland’s Prince George’s and Montgomery counties. POWER provided solar irradiance data adjusted for tilt angle while the digital surface model contributed aspect and slope data. This methodology factored out areas that were unsuitable for solar panel installation while displaying areas that possess a high potential for energy return. The team found the total rooftop solar potential for the study area to be almost 32 million kW, which is equivalent to roughly 660 kW per building. The methodology used to generate the solar potential maps can be applied to other regions of the country seeking to efficiently utilize solar energy. The end users at the DOEE can use our resulting solar potential map and data table to effectively target buildings that have the highest potential to generate solar energy.

Edward Cronin↗
DOE OSTI2020

Scaling Deep Energy Retrofits for Residential Walls - Energy, Cost, and Economic Assessment of Five Wall Systems

Providing strong economic and performance value is a primary challenge of convincing homeowners to implement deep energy retrofits to their wall systems. This study combines energy modeling and technoeconomic assessment of six experimental residential retrofit wall systems to typical existing homes in cold climates to evaluate their energy performance and cost effectiveness. Deep energy retrofits can significantly improve the energy performance of a home’s thermal envelope, help manage indoor environmental pollutants, increase homeowner comfort, increase building value, and register significant energy and cost savings in the process. We are evaluating exterior wall retrofit components and construction practices to measure and recommend steps to improve financial performance for manufacturers, installers and consumers. This study leverages a literature review, inputs from an advisory group made up of thermal enclosure experts, and simulations to identify state-of-the-art technologies for energy efficient wall systems that are suitable for cold and very cold climate zones. This paper will present results from energy modeling of six experimental wall systems compared to one baseline, that inform cost and energy performance of the subject wall systems.

Ganguli, Sumitrra↗
DOE OSTI2022

Chapter 2: Thermal Energy Storage for Energy Decarbonization

Thermal energy storage (TES) deployed with concentrating solar power (CSP) has shown value and capabilities in generating dispatchable power. It has attracted significant interest for potential roles in energy storage for various capacities and applications. Energy storage plays an important role in expanding renewable generation and is becoming indispensable in future carbon-free electric power. TES development and deployment provide various possibilities for electric storage and have shown advantages in capacity and flexibility to support renewable integration. In addition, renewable energy integrated with a low-cost TES system can potentially provide a reliable thermal energy supply to displace fossil fuels for broad decarbonization. Varieties of TES technologies and developments breed new areas of growth in TES materials, designs, components, and system configurations, which provide opportunities for substantial cost reduction and performance improvements to meet the technoeconomic challenges in practical applications. This chapter will describe recent progress in thermal energy storage research and development and primarily focus on sensible heat storage and its applications in supplying reliable electricity and industry process heat by integrating with variable renewable energy.

concentrating solar thermal power↗
DOE OSTI2022

Multilevel Analysis, Design, and Modeling of Coupling Advanced Nuclear Reactors and Thermal Energy Storage in an Integrated Energy System

This report discusses the different options for coupling thermal energy storage (TES) systems to advanced nuclear power plants (A-NPPs) in order to enable flexible and hybrid plant operation. An advanced light-water reactor (A LWR), a high-temperature gas-cooled reactor (HTGR) and a liquid-metal fast reactor (LMFR) were selected as the initial use cases for demonstrating a thermally balanced energy storage coupling design for thermal power extraction. The models presented herein showcase several design considerations, focusing on optimal deployment methodologies for achieving steady-state and transient-state operation with minimum disruption to the nuclear power cycle. This first part of the study presents steady-state models developed using Aspen HYSYS®, with the thermal energy bypass for NPP-TES coupling being varied at up to 50%. The various components were sized using the Aspen Process Economic Analyzer (APEA) and Aspen Exchanger Design and Rating (EDR), when applicable. Cost functions from these models were developed using the latest publicly available data obtained from APEA V11. The TES-coupled A-NPP steady-state models and cost functions then provided a baseline for dynamic operation and process optimization by using Idaho National Laboratory (INL)’s Framework for Optimization of Resources and Economics (FORCE) tools. A stochastic optimization of the various energy storage systems coupled to the A-NPPs was then performed using the Risk Analysis Virtual Environment (RAVEN) and its dispatch optimization plugin, the Holistic Energy Resource Optimization Network (HERON). The signal processing and synthetic history capabilities of RAVEN were used to account for the unpredictable behavior of electricity markets. An autoregressive moving average (ARMA) model was used to analyze price signals from the Pennsylvania-New Jersey-Maryland (PJM) market and were applied to the HERON analysis in order to optimize a system with the best economics. Transient modeling evaluation was then performed using Modelica models within the HYBRID repository, which was developed at INL for the Department of Energy Integrated Energy Systems program for the characterization of dynamic integrated system behavior and feedback. This includes evaluation of the TES-coupled A-LWR systems’ impact on physical and thermal system response during imposed system demands. Additional TES-coupled reactor types, coupling approaches, markets, and TES technologies will be evaluated in future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Multi-decade high-resolution regional hindcasts for wave energy resource characterization in U.S. coastal waters

Long-term, high-resolution, regional wave hindcast datasets were generated using unstructured-grid Simulating WAves Nearshore (SWAN) models for the U.S. coastal waters to support nearshore wave energy development in the U.S. including those bordering U.S. territorial islands. The model domains resolved the entire U.S. exclusive economic zones, with a spatial resolution of approximately 200 m nearshore. The regional SWAN models were driven by the global WAVEWATCH III® model outputs and run for a 42-year period from 1979 to 2020. Extensive model validations were performed using buoy observations and altimeter data. Regional resource characterization was performed based on hindcast data points at 2 km from shore and along the 100 m isobath. Aggregations of wave resource parameters were produced, and spatial and seasonal variations were analyzed for all the regions. Wave resource metrics recommended by international standards, including a 3-hour time series of six resource parameters, hourly frequency- and directionally resolved wave spectra at selected “virtual buoy” locations, and average-annual values of omni-directional wave power, significant wave height, and energy period are publicly disseminated through an Amazon Web Service and a Marine Energy Atlas web application tool to facilitate wave energy research and a wide range of coastal ocean applications.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

Tidal energy resource characterization measurements at Cook Inlet’s East Foreland: Velocity and turbulence

To characterize tidal current and turbulence at a top tidal energy site off the East Foreland in Cook Inlet, Alaska, United States, three moorings were deployed for two months between July and August 2021, and a transect survey was conducted over the course of two tidal cycles at the end of the deployment period. Measurements of velocity and turbulence were then analyzed to better understand the site's hydrodynamics and power potential. Analysis reveals that swift, north-flowing flood currents peak at 4~m/s, while south-flowing ebb currents reach just over 3~m/s. Turbulence intensity ranges from 23\% at the seafloor to 8\% near the surface, and the presence of the foreland creates more intense turbulence near-shore during ebb tide than flood. Power availability at the site could be as high as 720~MW, or 13~kW/m$^2$, though the energy available to a marine energy device will be smaller than this estimate because of water-to-wire efficiency and wake losses. The results from this measurement campaign will inform the validation of a high-resolution tidal hydrodynamic model, as well as early tidal energy projects that are beginning to move beyond the prototyping and demonstration stages to full-scale deployments.

McVey, James R.↗
DOE OSTI2024

Minimizing grid energy consumption in wastewater treatment plants: Towards green energy solutions, water sustainability, and cleaner environment

Wastewater treatment plants (WWTPs) consume significant amount of energy to sustain their operation. From this point, the current study aims to enhance the capacity of these facilities to meet their energy needs by integrating renewable energy sources. The study focused on the investigation of two primary solar energy systems in As Samra WWTP in Jordan. The first system combines parabolic trough collectors (PTCs) with thermal energy storage (TES). This system primarily serves to fulfill the thermal energy demands of the plant by reducing the demands from boiler units, which allows more biogas for electricity generation. The second system is a photovoltaic (PV) system with Lithium-Ion batteries, which directly produces electricity that will be used to cover part of the electrical energy demands of plant. To assess the optimal configuration, two distinct scenarios have been formulated and compared to the current case scenario (SC#1). The first scenario focuses on maximizing the net present value (NPV) and minimizing the levelized cost of electricity (LCOE). The second scenario is centred on minimizing the levelized cost of heat (LCOH). The findings indicate that both scenarios succeeded in reducing the reliance on the grid to a value that reach 1 %. Moreover, they both reduced biogas percentage in energy production from 88 % to approximately 65 % through the integration of the PV system. In terms of thermal demand, SC#2 reduced the reliance on biogas boiler units from 100 % to 25 %, while SC#3 achieved an even more impressive reduction to just 8 %. The best LCOE value was attained in SC#2, at 0.0895 USD/kWh, with an NPV of 10.54 million USD. Conversely, SC# 3 yielded an LCOH value of 0.0432 USD/kWh th compared to 0.0534 USD/kWh th USD for SC#2. In conclusion, despite their relatively high capital and operating costs, SC#2 and SC#3 managed to substantially decrease the annual electricity expenditure from approximately 2 million USD to 86,000 USD and 0 USD, respectively.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Comparison of the Energy-Transfer Rates in Structural and Spectral Variants of the B800–850 Complex from Purple Bacteria

Photosynthetic light harvesting can occur with a remarkable near-unity quantum efficiency. The B800–850 complex, also known as light-harvesting complex 2 (LH2), is the primary light-harvesting complex in purple bacteria and has been extensively studied as a model system. The bacteriochlorophylls of the B800–850 complex are organized into two concentric rings, known as the B800 and B850 rings. However, depending on the species and growth conditions, the number of constituent subunits, the pigment geometry, and the absorption energies vary. While the dynamics of some B800–850 variants have been exhaustively characterized, others have not been measured. Furthermore, a direct and simultaneous comparison of how both structural and spectral differences between variants affect these dynamics has not been performed. In this work, we utilize ultrafast transient absorption measurements to compare the B800 to B850 energy-transfer rates in the B800–850 complex as a function of the number of subunits, geometry, and absorption energies. The nonameric B800–850 complex from Rhodobacter (Rb.) sphaeroides is 40% faster than the octameric B800–850 complex from Rhodospirillum (Rs.) molischianum, consistent with structure-based predictions. In contrast, the blue-shifted B800–820 complex from Rs. molischianum is only 20% faster than the B800–850 complex from Rs. molischianum despite an increase in the spectral overlap between the rings that would be expected to produce a larger increase in the energy-transfer rate. These measurements support current models that contain dark, higher-lying excitonic states to bridge the energy gap between rings, thereby maintaining similar energy-transfer dynamics. Altogether, these results demonstrate that energy-transfer dynamics in the B800–850 complex are robust to the spectral and structural variations between species used to optimize energy capture and flow in purple bacteria.

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

Bond Dissociation Energy, Ionization Energy, and Electronic Structure of Thorium Dimer

Diatomic thorium, Th 2 , has been investigated using a laser ablation, supersonic expansion source to produce the molecule and resonant two-photon ionization spectroscopy to measure its bond dissociation energy (BDE) and ionization energy (IE). The molecule has a high density of states in the vicinity of its bond dissociation energy, leading to rapid predissociation as soon as this energy is exceeded. The BDE is identified from this predissociation threshold as D 0 (Th 2 ) = 2.857(7) eV, where the assigned error limit is provided in parentheses in units of the last quoted digit. Similarly, the one-photon ionization threshold has been measured, providing the ionization energy IE(Th 2 ) = 5.042(4) eV. Together with a thermochemical cycle and the atomic ionization energy, these values provide the BDE of the cation, giving D 0 (Th 2 + ) = 4.122(8) eV. Computations show that Th 2 has three nearly degenerate low-lying electronic states (1 3 Σ u + , 1 1 Σ g + , and 1 3 Δ g ) with bonding dominated by 7s and 6d orbitals, indicating predominantly transition-metal-like behavior. The 1 3 Σ u + state exhibits a triple bond, whereas the 1 1 Σ g + and 1 3 Δ g states possess quadruple-bond character and correspondingly shorter bonds. Although 1 3 Σ u + is predicted to be the lowest state without spin–orbit coupling, the large spin–orbit stabilization of the 1 3 Δ g state makes its Ω = 1 g component the ground state. Furthermore, the calculated dissociation energy (2.840 eV) and ionization energy of Th 2 (5.098 eV) are both in excellent agreement with experiment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗