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At least 55 records · Page 3

Capabilities of the Natural Environments Branch at NASA's Marshall Space Flight Center

The Natural Environment Branch at NASA s Marshall Space Flight Center (MSFC) has the responsibility to provide engineering support to programs and projects in natural environments. The Natural Environments Branch (EV13) is responsible for natural environments definitions, modelling, database development and effects assessments. EV13 personnel develop requirements for flight projects and provide operational support for space and launch vehicle systems. To accomplish these responsibilities, Branch . personnel have developed modelling and analytical tools which include planetary atmospheres, meteoroids, ionizing radiation, plasmas and ionospheres, magnetic and gravitational fields, spacecraft charging modelling, and radiation effects on electronic parts. NASA s Meteoroid Environment Office is operated within the EV13 and provides meteoroid engineering models and shower forecasts to spacecraft designers and operators. This paper will describe the capabilities within the Natural Environments Effects Branch including; examples of natural environment definitions, radiation transport, output from the Global Reference Atmosphere Models for Earth, Venus, Mars, Titan, and Neptune), recent NASCAP 2K results from solar sail modelling, and meteor stream models

Edwards, David L.↗

Capabilities of the Natural Environments Branch at NASA's Marshall Space Flight Center, Revised 2009

The Natural Environment Branch at NASA's Marshall Space Flight Center (MSFC) has the responsibility to provide natural environments engineering support to programs and projects. The Natural Environments Branch is responsible for natural environments definitions, modeling, database development, and analytical assessments of effects. Natural Environments Branch personnel develop requirements for flight projects and provide operational support for space and launch vehicle systems. To accomplish these responsibilities, models and analytical tools have been developed in the areas of planetary atmospheres, meteoroids, ionizing radiation, plasmas and ionospheres, magnetic and gravitational fields, spacecraft charging modeling, and radiation effects on electronic parts. This paper will build on a previous paper published in 2006 and provide updated descriptions of the capabilities within the Natural Environments Branch1. Updates describing improvements and new releases of several analytical tools and models will be presented. Separate sections will specifically describe modifications in the Meteoroid Engineering Model (MEM), and the Marshall Solar Activity Future Estimation (MSAFE) capabilities.

Edwards, David L.↗

Analyzing the Impacts of Natural Environments on Launch and Landing Availability for NASA's Eploration Systems Development Programs

NASA is developing new capabilities for human and scientific exploration beyond Earth orbit. Natural environments information is an important asset for NASA's development of the next generation space transportation system as part of the Exploration Systems Development Program, which includes the Space Launch System (SLS) and MultiPurpose Crew Vehicle (MPCV) Programs. Natural terrestrial environment conditions - such as wind, lightning and sea states - can affect vehicle safety and performance during multiple mission phases ranging from prelaunch ground processing to landing and recovery operations, including all potential abort scenarios. Space vehicles are particularly sensitive to these environments during the launch/ascent and the entry/landing phases of mission operations. The Marshall Space Flight Center (MSFC) Natural Environments Branch provides engineering design support for NASA space vehicle projects and programs by providing design engineers and mission planners with natural environments definitions as well as performing custom analyses to help characterize the impacts the natural environment may have on vehicle performance. One such analysis involves assessing the impact of natural environments to operational availability. Climatological time series of operational surface weather observations are used to calculate probabilities of meeting or exceeding various sets of hypothetical vehicle-specific parametric constraint thresholds.

Altino, Karen M.↗

Natural sunlight-driven oxidation of Mn 2+ (aq) and heterogeneous formation of Mn oxides on hematite

The oxidation of dissolved Mn 2+ (aq) plays a critical role in driving manganese cycles and regulating the fate of essential elements and contaminants in environmental systems. Based on sluggish oxidation rate, abiotic processes have been considered less effective oxidation pathway for manganese oxidation in environmental systems. Interestingly, a recent study (Jung et al., 2021) has shown that the rapid photochemical oxidation of Mn 2+ (aq) could be a feasible scenario to uncover the potential significance of abiotic Mn 2+ (aq) oxidation. Nevertheless, the significance of photochemical oxidation of Mn 2+ (aq) under natural sunlight exposure remains unclear. Here, we demonstrate the rapid photocatalytic oxidation of Mn 2+ (aq) and the heterogeneous growth of tunnel-structured Mn oxides under simulated freshwater and seawater conditions in the presence of natural sunlight and hematite. The natural sunlight-driven photocatalytic oxidation of Mn 2+ (aq) by hematite showed kinetic constants of 1.02 h -−1 and 0.342 h −1 under freshwater and seawater conditions, respectively. The natural sunlight-driven photocatalytic oxidation rates are quite comparable to the results obtained from the previous laboratory test using artificial sunlight, which has ∼4.5 times stronger light intensity. It is likely because of ∼5.5 times larger light exposure area in the natural sunlight-driven photocatalytic oxidation than that of the laboratory test using artificial sunlight. We also elucidate the roles of cation species in controlling the oxidation rate of Mn 2+ (aq) and the crystalline structure of Mn oxide products. Specifically, in the presence of large amounts of cations, the oxidation rate of Mn 2+ (aq) was slower likely because of competitive adsorption. Furthermore, our findings highlight that Mn 2+ contributes significantly to the formation of large-tunneled Mn oxides. These results illuminate the importance of abiotic photocatalytic processes in controlling the redox chemistry of Mn in real environmental aqueous systems on the oxidation of Mn 2+ (aq), and provide an environmentally sustainable approach to effectively remediate water contaminated with Mn 2+ (aq) using natural sunlight.

Junyeong Choi↗

Solid-State Mixed-Potential Electrochemical Sensors for Natural Gas Leak Detection and Quality Control (Final Technical Report)

Mitigation of methane emissions are a critical factor to limiting the impact of the natural gas industry on global climate change. Throughout the period of 2020-2024, the University of New Mexico and its commercialization partner and subcontractor, SensorComm Technologies, Inc. (SCT), have worked together to develop a low-cost Artificial Intelligence (AI)-driven Internet of Things (IoT)-based multi-gas sensor platform for methane emissions detection. In the final year of the project, we extended this work to include hydrogen detection in support of a transition to a hydrogen economy where hydrogen could be transported through existing natural gas infrastructure. Mixed potential electrochemical sensors were first prototyped by ceramic additive manufacturing and then transitioned to conventional ceramic manufacturing tape casting and screen-printing technologies in preparation for mass production. Demonstrated limits of detection of 5 ppm of methane in natural gas and 1 ppm of hydrogen were measured. These limits of detection are among the lowest of solid-state electrochemical sensors that have been reported in the literature or available in the industry. Machine learning algorithms were developed to identify natural gas mixtures with > 98% accuracy level and quantify methane concentrations at 97% accuracy. The presence of hydrogen could also be identified, and its concentration quantified at these accuracy levels. These algorithms were optimized for running on portable computing hardware which enabled > 1 Hz processing rates. A portable packaged IoT system was integrated with the electrochemical sensor in collaboration with SCT. The package consists of readout electronics with < 1 mV resolution, sensor temperature control, and data transmission over cellular wireless and/or Wi-Fi networks. Field testing was performed in two rounds at Colorado State University’s Methane Emissions Technology Evaluation Center (CSU METEC). The first round of testing demonstrated successful measurements of methane from an underground natural gas leak of 20 standard liters per minute (SLPM), which agreed with previously published literature using more sophisticated and expensive analytical equipment. The second round of testing showed that an above ground leak of 2 SLPM of hydrogen could be detected at 32 ft. This project has resulted in six published peer reviewed journal articles, over ten presentations at professional conferences, and one full patent application filed in 2023. Future work on this project includes increased sensitivity, higher production yields, and applications in the hydrogen safety and flare emissions monitoring spaces.

03 NATURAL GAS↗

Life Cycle Analysis of Natural Gas Extraction and Power Generation: U.S. 2020 Emissions Profile

This analysis expands upon previous life cycle analyses (LCAs) of natural gas systems performed by the National Energy Technology Laboratory (NETL). It provides a complete inventory of emissions to air and water, water consumption, and land use change. These environmental burdens are detailed for all supply chain steps from natural gas production through natural gas distribution. This package includes the report, the NETL Natural Gas Model, and appendices that include several Excel workbooks and a python script to provide transparent access to the calculations and resulting data.<p>To access the NETL Natural Gas Lifecycle model, visit https://doi.org/10.18141/2476250.</p><p>To access the 2020 Report Appendices, visit https://doi.org/10.18141/2438472.</p>

03 NATURAL GAS↗

Life Cycle Analysis of Natural Gas Extraction and Power Generation: U.S. 2020 Emissions Profile

This analysis expands upon previous life cycle analyses (LCAs) of natural gas systems performed by the National Energy Technology Laboratory (NETL). It provides a complete inventory of emissions to air and water, water consumption, and land use change. These environmental burdens are detailed for all supply chain steps from natural gas production through natural gas distribution. This package includes the report, the NETL Natural Gas Model, and appendices that include several Excel workbooks and a python script to provide transparent access to the calculations and resulting data. This is revision 1 of the 2024 study (published December 17, 2024 and updated on January 24, 2025) and corrects a modeling error in natural gas composition. See the errata on page 2 for more information.

03 NATURAL GAS↗

Recovery of Natural Gas Equipment Emissions into Gas Compression Engines for the Reduction of Potential Greenhouse Gas Emissions

Since the turn of the millennium, the United States (U.S.) oil and natural gas (ONG) industry has nearly doubled its natural gas production rate. As a result, the ONG industry has recently come under increasing scrutiny for its contributions to greenhouse gas (GHG) emissions. Consequently, various solutions to this problem have been proposed and formulated to reduce the impacts of GHG emissions on the environment. West Virginia University (WVU) have found it important to research the impacts of recovering vented gas streams into prime-mover engines. The U.S. Department of Energy (DOE) and National Energy Technology Laboratory (NETL) have granted WVU funding to research and develop a “Methane Mitigator” (M2) - a “Scalable Vent Mitigation Strategy to Simultaneously Reduce Methane Emissions and Fuel Consumption from the Compression Industry.” One of the main areas of interest for this research was the collection of emissions from natural gas equipment into a Caterpillar G3508J natural gas compression engine. The parameters being analyzed from the engine were brake-specific emissions and power output. The emissions sources considered for this research were pneumatic controllers (PCs), reciprocating compressor vents, and the engine’s open crankcase breather. The compressor vent and PC emissions were simulated using a mass flow controller (MFC) and flowed into the engine using two separate methods: (1) directly into the air intake, and (2) through a retrofitted closed crankcase ventilation system (CCV), serving as a buffer volume. The crankcase emissions were quantified without the CCV, and the impact on exhaust emissions from circulating the crankcase gases into the intake was measured. The simulated compressor vent and PC flows from the MFC had limited effect on the steady state operation of the engine and resulting performance. When the simulated flows were fed directly into the engine’s air intake, the changes within the engine’s continuous performance and emission parameters were larger but lasted for shorter durations. Conversely, when the simulated flows were fed into the CCV before entering the air intake, the changes in the engine’s performance and emission parameters were less pronounced for continuous analysis but lasted for longer durations. In either case, the continuous emission changes in both emissions and performance varied in size depending on the test scenario being run, but the cycle average changes in emissions and performance showed little impact overall compared to the engine’s baseline operation. As a result, the inclusion of a CCV shows a decrease in baseline carbon dioxide equivalent (CO2-eq.) engine emissions (from combined exhaust and open crankcase) of almost 4%. Likewise, the CCV inclusion reduced baseline total methane (CH4) from combined exhaust and open crankcase by upwards of 16%. These atmospheric emissions only decreased further with the inclusions of collected PC and compressor vent flows. The resulting changes in time-averaged rated exhaust behavior (or lack thereof) prove that the proposed M2 system could likely be deployed at sites with modern lean-burn natural gas engines as a viable option for reducing and eliminating potential GHG sources that would have otherwise been unutilized as energy sources.

03 NATURAL GAS↗

Natural fibers as promising core materials of vacuum insulation panels

To reduce energy consumption in buildings, this paper investigates the feasibility of using natural fibers as cost-effective, environmentally sustainable core materials for vacuum insulation panels (VIPs). First, a comprehensive experimental study was conducted for 10 potential natural fiber candidates. The thermal conductivities of the 10 natural fiber mats at various vacuum pressures were measured; their compression and morphology properties were quantified. In addition, an analytical model was used to explore the major factors that influence the thermal conductivity of natural fibers as a function of internal air pressure. Results show that recycled cotton, kapok, and bamboo fibers are ideal candidates for VIP core materials; at <0.05 Pa, their thermal conductivities varied between 2 and 4 mW/(m∙K). Furthermore, for some fibers, thermal conductivity was inversely proportional to fiber density. For the selection of fiber materials for VIP cores, the ideal fiber candidate has a small fiber diameter and a low fiber mat density. Based on thermal measurements, even though the internal air pressure of 5 Pa was enough to attain the minimum thermal conductivity, obtaining internal air pressure below 5 Pa is recommended for prolonged service life, considering small leaks of VIP package barrier films and potential off-gassing from fibers. The simulation results predicting the effective thermal conductivities matched the experimental results well. These findings indicate that natural fiber–based VIPs have the potential to be a sustainable, inexpensive alternative to the current technologies in building insulation materials.

36 MATERIALS SCIENCE↗

Joint Management and Optimization of Residential Natural Gas and Electricity Distribution Networks Coupled via Fuel Cells

The interesting properties of natural gas as well as the growing electric power demand worldwide have led to increasing attention to natural-gas-based distributed generation applications in electric distribution systems. This paper goes over the interdependency between a residential natural gas network and an electric distribution network that are coupled via fuel cells. The modeling of the gas network is introduced first, and then the algorithm for gas flow study is presented. The optimal placement and sizing of fuel cell based distributed generation systems are formulated to minimize the losses in both the gas and electric distribution networks, subject to their model constraints. In addition to this, in order to capture the probabilistic nature of the optimization problem under study, the K-means clustering algorithm is applied to the gas and electricity demands to determine hourly load states and their corresponding probabilities. Furthermore, simulation studies are carried out on an integrated system consisting of the IEEE 69-bus distribution feeder and a radial 27-node natural gas network to verify the developed optimization model and the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗

FECM/NETL Natural Gas with Hydrogen Pipeline Cost Model (2024): Description and User’s Manual

This is the user’s manual for The FECM/NETL Natural Gas with Hydrogen Pipeline Cost Model (NG-H2_P_COM) that estimates costs for transporting gaseous hydrogen with natural gas in a pipeline from a source, such as a hydrogen production facility, to a final destination which may be a user of the hydrogen and natural gas or a distribution center where hydrogen in the pipeline with natural gas is diverted to multiple end users. This user’s manual provides two main functions. First, the detailed statement describes the equations and algorithms that are used by the model to calculate technical quantities (such as blend hydrogen percentage, reuse percentage of the pipeline and stations, the pipe diameter size and length needed to transport a user-specified hydrogen with natural gas rate in a specified distance) and engineering-economic quantities (such as capital costs, operating costs, and cash flows). Second, the document is a user’s manual for the model that describes the procedures the user must follow to configure and setup the model, run the model, analyze the results, and visualize the outcomes. Such details offer user a quick and handy way to utilize the model for their application and decision making. The model can be accessed at this URL: https://www.netl.doe.gov/energy-analysis/details?id=cf3f6564-3c55-4aa5-b712-7160e558d9f6. The Model Results and Comparative Analysis can be accessed here: https://www.netl.doe.gov/energy-analysis/details?id=83862799-a28c-4944-a809-90b7e23d4af6.

03 NATURAL GAS↗

Let Our Powers Combine! Harnessing NASA's Earth Observatory Natural Event Tracker (EONET) in Worldview

Constellations of NASA Earth Observing System (EOS) satellites orbit the earth to collect images and data about the planet in near real-time. Within hours of satellite overpass, you can discover where the latest wildfires, severe storms, volcanic eruptions, and dust and haze events are occurring using NASA's Worldview web application. By harnessing a repository of curated natural event metadata from NASA Earth Observatory's Natural Event Tracker (EONET), Worldview has moved natural event discovery to the forefront and allows users to select events-of-interest from a curated list, zooms to the area, and adds the most relevant imagery layers for that type of natural event. This poster will highlight NASA Worldviews new natural event feed functionality.

earth science↗

Cruise Slotted Wing Design with Natural Laminar Flow for Transonic Commercial Transport Aircraft

The present computational study investigates the aerodynamic design and analysis of cruise slotted wings with natural laminar flow for transonic transport aircraft. The cruise slotted wing is a multielement wing concept that features an intermediate slot to achieve greater aft loading relative to supercritical wings for the potential benefit of reduced shock strength and pressure drag. Transonic near-cruise, off-design assessments have also shown improved drag rise characteristics due to the ability of the slot to mitigate boundary layer separation on the aft flap component. However, due to the decreased Reynolds number of the flap, the cruise slotted wing has historically incurred a skin-friction drag penalty relative to a conventional supercritical wing. To offset this penalty, a cruise slotted wing with the forward main element and aft flap element shaped to achieve natural laminar flow is desired. Toward this effort, a knowledge-based aerodynamic design method, CDISC, has been leveraged to design a partial-span cruise slotted wing with natural laminar flow for a Mach-0.8 variant of the Common Research Model. Drag comparisons will be provided at cruise and near-cruise, off-design conditions relative to both fully turbulent and natural laminar flow conventional wing designs. It is anticipated that pairing natural laminar flow technology with the cruise slotted wing architecture will allow for cruise drag performance similar to conventional laminar flow wings with improved drag rise characteristics and more limited laminar-flow sensitivity at off-design conditions. Preliminary results for a cruise slotted wing with laminar flow on the outboard wing section only have shown a 10-ct cruise drag reduction relative to a conventional supercritical wing, but a 8-ct penalty relative to the conventional NLF wing. The final paper will include results for a cruise slotted wing design with laminar flow on both the inboard and outboard wing sections.

CFD↗

Cruise Slotted Wing Design with Natural Laminar Flow for Transonic Commercial Transport Aircraft

The present computational study investigates the aerodynamic design and analysis of cruise slotted wings with natural laminar flow for transonic transport aircraft. The cruise slotted wing is a multielement wing concept that features an intermediate slot to achieve greater aft loading relative to supercritical wings for the potential benefit of reduced shock strength and pressure drag. Transonic near-cruise, off-design assessments have also shown improved drag rise characteristics due to the ability of the slot to mitigate boundary layer separation on the aft flap component. However, due to the decreased Reynolds number of the flap, the cruise slotted wing has historically incurred a skin-friction drag penalty relative to a conventional supercritical wing. To offset this penalty, a cruise slotted wing with the forward main element and aft flap element shaped to achieve natural laminar flow is desired. Toward this effort, a knowledge-based aerodynamic design method, CDISC, has been leveraged to design a partial-span cruise slotted wing with natural laminar flow for a Mach-0.8 variant of the Common Research Model. Drag comparisons will be provided at cruise and near-cruise, off-design conditions relative to both fully turbulent and natural laminar flow conventional wing designs. It is anticipated that pairing natural laminar flow technology with the cruise slotted wing architecture will allow for cruise drag performance similar to conventional laminar flow wings with improved drag rise characteristics and more limited laminar-flow sensitivity at off-design conditions. Preliminary results for a cruise slotted wing with laminar flow on the outboard wing section only have shown a 10-ct cruise drag reduction relative to a conventional supercritical wing, but a 8-ct penalty relative to the conventional NLF wing. The final paper will include results for a cruise slotted wing design with laminar flow on both the inboard and outboard wing sections.

Natural Laminar Flow↗

A Global Methane Observation System to Reduce Uncertainty for Anthropogenic and Natural Sources and Sinks for Detecting and Attributing Climate Feedbacks

Atmospheric methane (CH4) concentrations are accelerating global warming as net emissions increase. Observing systems that quantify sources remain too sparse and fragmented to detect trends—especially in remote regions where climate‐driven natural emissions may be rising. We provide a framework for quantifying uncertainty reductions through the implementation of a global ecosystem‐methane observing system designed to: (i) substantially lower uncertainty in sectoral and regional emissions, (ii) separate co‐occurring anthropogenic and natural fluxes, and (iii) trend detection at regional scales to verify mitigation progress and provide early warning of natural feedbacks. Using bottom‐up inventories and process‐model ensembles for 2014–2023, we show that anthropogenic emissions remain uncertain by ∼32% globally, while natural sources—tropical and boreal‐arctic wetlands, fires, and inland waters—carry far larger uncertainties (+ 70%) and trend uncertainties reaching ∼200%. Additional observations must match spatial emission structure to increase observability of emissions: high‐resolution satellite constellations for point sources combined with expanded flux networks and wetland mapping for diffuse sources, and denser ground‐based atmospheric column measurements to restore observability in under‐sampled tropics and high latitudes. Notional analyses indicate that targeted additions of flux towers and ∼20 in situ atmospheric column concentration instruments per key tropical region could reduce continental‐scale uncertainties at modest cost. Conceptual illustration of a Global Ecosystem Methane Observing System (GEM‐OS) integrating satellites, aircraft, atmospheric networks, and ecosystem measurements to quantify methane emissions from anthropogenic and natural sources. The multi‐scale observing framework improves source attribution, reduces uncertainty in regional methane budgets, and enables early detection of climate‐driven feedbacks from wetlands, fires, permafrost, agriculture, and fossil‐fuel emissions.

Ciais, P↗

Nature-based climate solutions can help mitigate the radiative forcing that follows deforestation

Widespread expansion of agriculture and forestry has altered the surface of the Earth, the composition of the atmosphere, and as a result, the climate. Here we quantify the radiative forcing caused by the historical deforestation of an ecoregion in the U.S. Upper Midwest and the adoption of eight nature-based climate solutions. We combined regional forest inventory data with over three decades of remote sensing and in situ data from a replicated land use change experiment. Deforestation of the region caused net global warming (1626 ± 44 µW m -2 ), mainly from the 76 % reduction of ecosystem carbon stocks, but also from the 84 % reduction of the soil methane sink and the 115 % increase in soil nitrous oxide emissions. The associated albedo increase offset 24 % of this greenhouse gas induced warming. For the adoption of nature-based climate solutions, we found that conservation agriculture can provide -39 to -76 ± 31 µW m -2 of climate mitigation over a 100-year time period while short/medium length forestry rotations can provide more at -296 to -881 ± 44 µW m -2 and natural forest regeneration can provide the most at -1555 ± 44 µW m -2 . As the impacts of climate change on nature and society intensify, consideration should be given to the climate mitigation, habitat, and ecosystem services that nature-based climate solutions can provide.

54 ENVIRONMENTAL SCIENCES↗

Cell-free synthetic biology for natural product biosynthesis and discovery

Natural products have applications as biopharmaceuticals, agrochemicals, and other high-value chemicals. However, there are challenges in isolating natural products from their native producers (e.g. bacteria, fungi, plants). In many cases, synthetic chemistry or heterologous expression must be used to access these important molecules. The biosynthetic machinery to generate these compounds is found within biosynthetic gene clusters, primarily consisting of the enzymes that biosynthesise a range of natural product classes (including, but not limited to ribosomal and nonribosomal peptides, polyketides, and terpenoids). Cell-free synthetic biology has emerged in recent years as a bottom-up technology applied towards both prototyping pathways and producing molecules. Recently, it has been applied to natural products, both to characterise biosynthetic pathways and produce new metabolites. This review discusses the core biochemistry of cell-free synthetic biology applied to metabolite production and critiques its advantages and disadvantages compared to whole cell and/or chemical production routes. Specifically, we review the advances in cell-free biosynthesis of ribosomal peptides, analyse the rapid prototyping of natural product biosynthetic enzymes and pathways, highlight advances in novel antimicrobial discovery, and discuss the rising use of cell-free technologies in industrial biotechnology and synthetic biology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Linear-scaling quadruple excitations in local pair natural orbital coupled-cluster theory

Here, we present a fast, asymptotically linear-scaling implementation of the perturbative quadruples energy correction in coupled-cluster theory using local natural orbitals. Our work follows the domain-based local pair natural orbital (DLPNO) approach previously applied to lower levels of excitations in coupled-cluster theory. Our DLPNO-CCSDT(Q) algorithm uses converged doubles and triples amplitudes from a preceding DLPNO-CCSDT computation to compute the quadruples amplitude and energy in the quadruples natural orbital (QNO) basis. We demonstrate the compactness of the QNO space, showing that more than 95% of the (Q) correction can be recovered using relatively loose natural orbital cutoffs, compared to the tighter cutoffs used in pair and triples natural orbitals at lower levels of coupled-cluster theory. We also highlight the accuracy of our algorithm in the computation of relative energies, which yields deviations of sub-kJ mol −1 in relative energy compared to the canonical CCSDT(Q). Timings are conducted on a series of growing linear alkanes (up to 10 carbons and 608 basis functions) and water clusters (up to 49 water molecules and 2842 basis functions) to establish the asymptotic linear-scaling of our DLPNO-(Q) algorithm.

Auxiliary functions↗