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DOE OSTI2020

High Effectiveness, Compact, High Pressure and Low-Cost Recuperator, Presented at The Fifth International Symposium – Super-Critical CO2 Power Cycles, San Antonio, Texas, March 28-31, 2016, by Dr. John Kelly, President, Altex Technologies Corporation

Closed Brayton super-critical CO2 power cycles are well suited to waste heat bottoming cycles, due to their increased efficiency and compactness, relative to Rankine steam bottoming cycles. Since waste heat applications would be retrofits, the power system compactness is important. To achieve high efficiency, these power cycles require high pressure recuperative type heat exchangers, of substantial heat duty. Current Printed Circuit Heat Exchangers (PCHE), originally developed for high pressure gas and oil applications, can be used as recuperators, but costs are higher than desired. Altex is developing a purpose-built high pressure and effectiveness recuperator to provide the reliability, compactness, performance and pressure capability of current recuperators, but at a reduced cost. The High Effectiveness Low Cost (HELC) recuperative heat exchanger design yields volume and weight metrics of .0024 m3/UA and 10.2 kg/UA, which are 4% and 77.3% below recuperator target metrics, respectively. A 50 kW test article was designed and fabricated. Performance tests on water and oil showed that the HELC design model could predict heat transfer, to within 10% of the measured value. This model was then used to project HELC performance, when operating on supercritical CO2. Besides performance tests, the test article was hydrostatically tested, for integrity at up to 4,000 psi pressure. At these conditions, some distortion of channels was encountered. To mitigate distortion, the inserts were redesigned and these results were used to project the cost of 500 kW and 5,083 kW HELC units. The cost metric for the 5,083 kW unit was determined to be $1,349/UA, which is 10% lower than the recuperator desired cost metric desired target of $1,500/UA. In addition, the 5,083 kW unit HELC cost of $61.09/kW is 33.6% lower than the $92/kW estimated cost for a PCHE. Hydrostatic pressure tests, at up to 4,000psi, showed that the unit did not leak. However, channels were distorted at this pressure differential. Design updates to minimize stress concentrations and distortion were prepared and analyzed, to show that distortion could be controlled, but to date tests have not been run to prove the design. Project results show the potential of the HELC approach, but more work is required to confirm this potential, at the larger scales of interest.

14 SOLAR ENERGY↗

DOE OSTI2020

High Effectiveness, Compact, High Pressure and Low Cost Recuperator for Super-Critical CO2 Power Cycles, Paper Presented at The Fifth International Symposium – Super-Critical CO2 Power Cycles, San Antonio, Texas, March 28-31, 2016, by Dr. John Kelly, President, Altex Technologies Corporation

14 SOLAR ENERGY↗

DOE OSTI2022

Energy Northwest - Horn Rapids Solar and Storage: An Assessment of Battery Technical Performance

Chartered in 1957 as a joint action agency of the state, Energy Northwest (ENW) is a consortium of 27 public utility districts and municipalities across Washington state. ENW takes advantage of economies of scale and shared services to help utilities run their operations more efficiently and at lower cost, to the benefit of more than 1.5 million customers. ENW develops, owns, and operates a diverse mix of electricity generating resources, including hydro, solar, and wind projects – and the Northwest’s only active nuclear energy facility. These projects provide enough reliable, affordable, and environmentally responsible energy to power more than a million homes each year, and that carbon-free electricity is provided at the cost of generation. The agency continually explores new generation projects to meet its members’ needs. In 2017, as part of the second round of funding from the Washington state Clean Energy Fund, the Washington State Department of Commerce granted up to $3 million in matching funds to develop an estimated $6.5 million project that deployed a 4-MW, 20-acre solar generating array of photovoltaic (PV) panels coupled with a 1 MW/5.5 MWh lithium-iron-phosphate battery energy storage system (BESS) in Richland, Washington. The combination of PV and BESS will provide a predictable, renewable generating source and will also serve as a training ground for solar and battery technicians throughout the nation. The City of Richland will purchase the power from the project and utilize the benefits of the energy storage. The project provides Washington state with its first opportunity to integrate a large-scale solar and storage facility into its clean mix of hydro, nuclear, and wind resources. This first-of-its-kind facility combines solar generation with battery storage and technician training. In 2019, Pacific Northwest National Laboratory (PNNL) worked with ENW to assess the integrated PV and BESS in representative use cases that could benefit the City of Richland. Between March and May 2022, extensive testing was conducted, and the results were used to assess the technical performance of the BESS subjected to actual field operations. Both reference performance and use case tests were performed: (A) Reference performance tests assess the general technical capabilities of the BESS, such as energy capacity, round-trip efficiency (RTE), ramp rate, and signal tracking capability. These are the first tests performed (baseline), and they are repeated after use case tests (post cycle). A standardized U.S. Department of Energy (DOE) energy storage performance protocol was used to characterize the BESS, including representative duty cycle profiles, test procedure guidance, and calculation guidance for determining key characteristics. (B) Use case tests examine the performance of the BESS for specific use cases using duty cycles developed by PNNL in collaboration with ENW. Five use cases were selected for testing: 1) demand charge reduction, 2) load shaping, 3) transmission charge reduction, 4) Volt-VAR service, and 5) outage mitigation. The use case duty cycles were developed based on utility and site-specific characteristics in addition to the technical characteristics and physical capabilities of the BESS. Use case tests were performed between the baseline and post cycle tests. This report describes the BESS and its components, presents testing and performance analysis results, and shares key insights and lessons learned from this project. Outcomes of the tests and analyses will help ENW understand the performance of the Horn Rapids BESS in its current state and design appropriate operational strategies for this and other BESSs over the long term.

14 SOLAR ENERGY↗

DOE OSTI2022

Improving energy performance metrics to maximize the benefits of disruptive technologies

Advances in appliance and equipment systems' technologies also cause changes in their technical characteristics that can affect energy consumption and associated greenhouse gas emissions. Energy performance evaluation methods that use testing and metrics can evolve to account for energy consumption contributed from new technological characteristics. However, there is no systematic effort to enable the advancement of test procedures and performance metrics to maximize the energy, climate, and financial benefits of disruptive technologies. Therefore, it is important for countries to regularly update their energy-efficiency policy programs, such as standards and labels, by improving test procedures and metrics to reflect the innovation in emerging technologies as well as to mitigate the risk of deploying obsolete technology. This paper shows how energy performance metrics have been improving in selected appliances and equipment and provides insights to design a systematic effort to improve metrics and test procedures at the speed of ongoing changes in technologies and markets.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2023

Solute effects upon dislocation motion and recovery in Mg alloys (Final Report)

The objective the research was to develop a firmer understanding of the interactions between substitutional solute atoms and dislocations within Mg alloys. These interactions govern the absolute and relative mobilities of various types of dislocations in Mg (e.g., basal < a>, non-basal < a>, and pyramidal < c+a>). Furthermore, they have an impact on dislocation recovery processes (e.g., cross-glide, climb, rearrangement, and annihilation). Ultimately, solute-dislocation interactions strongly impact a) strain hardening, b) strain rate sensitivity, c) plastic anisotropy of textured polycrystals, d) texture evolution, e) dislocation substructures evolution, and even f) recrystallization behavior. It is broadly known that Mg alloys exhibit poor low temperature formability. Since formability is largely governed by properties (a) – (c) in this list, it is critical to develop a better understanding of solute-dislocation interactions, if one hopes to improve the situation. While the theory of static solute strengthening is well developed, especially for alloys with face centered cubic (FCC) crystal structures, there are outstanding questions related to applications to hexagonal close packed (HCP) crystal structures and dynamic strain aging (DSA) in materials of various structures. DSA has far-reaching implications for metal formability and, in the case of Mg alloys, appears to correlate with the so-called rare-earth (RE) texture which has been shown to benefit formability. The Portevin-Le Chatelier (PLC) effect, and associated negative strain rate sensitivity, occur at higher temperatures (>100℃) in Mg alloys as compared with similar Al alloys, even though they have similar melting points and solute diffusivities. Our preliminary research has shown that modern, physics-based models of DSA can be tuned to describe the behavior of Mg alloys if a rather higher activation enthalpy is assumed for cross-core diffusivity. While this partially explains the delay in DSA to higher temperatures, it is also hypothesized that this delay is due in part to the intrinsically more thermally activated (rate sensitive) nature of non-basal < a> dislocation motion which is required for macroscopic flow of Mg alloys, whereas octahedral slip in many FCC metals like aluminum is essentially athermal at room temperature. It was originally proposed to employ a combination of in-situ diffraction-based experimental characterization to validate existing theory. It was envisioned to perform in-situ transmission electron microscopy (TEM) to assess individual dislocation behavior and in-situ high-energy X-ray diffraction (HEXRD) techniques which were showing great promise for elucidating collective dislocation behavior, 2 including recovery, especially if the contributions to various forms of diffraction peak broadening (𝜂𝜂,𝜔𝜔,and 2𝜃𝜃) can be effectively integrated. Finally, it was envisioned to perform discrete dislocation dynamics (DDD) modeling approaches to aide in the interpretation of both TEM and HEXRD experiments. In the end, mechanical tests were performed on more complex Mg alloys which exhibited evidence of dynamic strain aging, and this led to the establishment of another project. Mechanical test data obtained at McMaster University served as the basis of an assessment of the applicability of Bazinski’s “stress equivalence” theory of solute strengthening to polycrystalline alloys of Mg. Although we did not succeed in applying the approach to Mg alloys, we did develop expertise with the HEXRD approach using a BCC, β-Ti alloy and demonstrated numerous new capabilities that may be applied to any polycrystalline material in collaboration with researchers at CHESS and around the world: (1) assessment of details of the elastoplastic transition (yielding) using a combination of HEXRD and full-field polycrystal plasticity modeling, (2) the first-ever experimental observation of strong stress rotation within the individual grains of a polycrystalline material, and (3) a comprehensive analysis of the grain-level dislocation density evolution based upon diffraction peak broadening along 𝜂𝜂,𝜔𝜔,and 2𝜃𝜃 directions. This final aspect allowed us to confirm that dislocations were gliding on multiple plane types and not restricted to {110} type planes, and it also provided clues as to why some grains were unloading during straining, with surprising implications for our understanding of the effects of geometrically necessary dislocations (GNDs). Finally, graduate student, Mohammed Shabana, developed a MATLAB code which confirmed the conclusions of Prof. Catalin Picu (Rensallear Polytechnic Institute, RPI) regarding the effect of solute-trapped, forest dislocations on the breaking stress of Lomer lock junctions in FCC metal alloys. He applied the same anisotropic line-tension model to a variety of dislocation junction configurations and found an inconsistency in the widely cited results of Dupuy and Fivel regarding the Hirth Lock, and he outlined an approach to extend these finding to HCP Mg alloys that we are still pursuing with discretionary fundings at UVA.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Surface properties and RF performance of Vapor Diffused Nb3Sn on Nb after sequential anneals below 1000 °C

Nb3Sn is a next-generation superconducting material that can be used for future superconducting radiofrequency (SRF) accelerator cavities, promising better performance, cost reduction, and higher operating temperature than Nb. The Sn vapor diffusion method is currently the most preferred and successful technique to coat niobium cavi-ties with Nb3Sn. Among post-coating treatments to opti-mize the coating quality, higher temperature annealing without Sn is known to degrade Nb3Sn because of Sn loss. We have investigated Nb3Sn/Nb samples briefly annealed at 800-1000 °C for 10 and 20 minutes to poten-tially improve the surface to enhance the performance of Nb3Sn-coated cavities. Following the sample studies, a coated single-cell cavity was sequentially annealed at 900 °C and tested its performance each time, improving the cavity's quality factor relatively. This paper summarizes the sample studies and discusses the RF test results from sequentially annealed SRF Nb3Sn/Nb cavity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Surface Properties and RF Performance of Vapor Diffused Nb3Sn on NB After Sequential Anneals Below 1000°C

Nb3Sn is a next-generation superconducting material that can be used for future superconducting radiofrequency (SRF) accelerator cavities, promising better performance, cost reduction, and higher operating temperature than Nb. The Sn vapor diffusion method is currently the most preferred and successful technique to coat niobium cavi-ties with Nb3Sn. Among post-coating treatments to opti-mize the coating quality, higher temperature annealing without Sn is known to degrade Nb3Sn because of Sn loss. We have investigated Nb3Sn/Nb samples briefly annealed at 800-1000°C for 10 and 20 minutes to poten-tially improve the surface to enhance the performance of Nb3Sn-coated cavities. Following the sample studies, a coated single-cell cavity was sequentially annealed at 900°C and tested its performance each time, improving the cavity's quality factor relatively. This paper summarizes the sample studies and discusses the RF test results from sequentially annealed SRF Nb3Sn/Nb cavity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

High pressure effects on EBC systems in high temperature environments

Environmental barrier coatings (EBCs) are designed to protect SiCfiber/SiCmatrix ceramic matrix composites (CMCs) in turbine engines by mitigating wear in high-temperature water vapor environments. The failure of EBCs is frequently attributed to the accelerated oxidation of the silicon bond coating layer when exposed to high-temperature steam, leading to the formation of a thickened thermally grown oxide (TGO). TGO growth increases interfacial stress, weakens adhesion, and results in coating spallation. Understanding the impact of high-temperature oxidation of EBC systems is essential for developing accurate lifespan models for turbine components, although pressurized oxidation testing is extremely sparse in the open literature. In this work, oxidation tests were performed on rare earth silicate EBCs coated onto SiC substrates under increased pressure conditions. The coated specimens were tested at 1100°C, 1200°C, and 1300°C at both 1 atm and 10 atm total pressure in steam environments. Subsequent characterization focused on the microstructural evolution of the EBC/Si/SiC system. The experimental findings indicated that TGO behavior is dependent on high-pressure conditions, with elevated pressure leading to an increase in oxide scale thickness and modifications in its morphology.

Ardrey, Kristyn [ORNL] (ORCID:0000000184407796)↗

DOE OSTI2022

A Framework for Error-Bounded Approximate Computing, with an Application to Dot Products

Approximate computing techniques, which trade off the computation accuracy of an algorithm for better performance and energy efficiency, have been successful in reducing computation and power costs in several domains. However, error sensitive applications in high-performance computing are unable to benefit from existing approximate computing strategies that are not developed with guaranteed error bounds. While approximate computing techniques can be developed for individual high-performance computing applications by domain specialists, this often requires additional theoretical analysis and potentially extensive software modification. Hence, the development of low-level error-bounded approximate computing strategies that can be introduced into any high-performance computing application without requiring additional analysis or significant software alterations is desirable. In this paper, we provide a contribution in this direction by proposing a general framework for designing error-bounded approximate computing strategies and apply it to the dot product kernel to develop \bf qdot---an error-bounded approximate dot product kernel. Following the introduction of qdot, here we perform a theoretical analysis that yields a deterministic bound on the relative approximation error introduced by qdot. Empirical tests are performed to illustrate the tightness of the derived error bound and to demonstrate the effectiveness of qdot on a synthetic dataset, as well as two scientific benchmarks---the conjugate gradient (CG) and power methods. In some instances, using qdot for the dot products in CG can result in many components being quantized to half precision without increasing the iteration count required for convergence to the same solution as CG using a double precision dot product.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Durability testing of actual Hanford waste glasses and their non-radioactive simulant glasses

The low-activity waste (LAW) fraction of Hanford tank waste will be converted to glass at the Waste Treatment and Immobilization Plant (WTP) and disposed on the Hanford site. The chemical durability of LAW glasses has been researched for decades to satisfy contract requirements. Most LAW glass durability data has been generated on non-radioactive simulant glasses fabricated via crucible melts. These non-radioactive glasses were chosen due to safety and cost reasons with confidence that radioactive waste glasses would exhibit similar behavior. To reduce the risk of significant differences in laboratory test response data between WTP melter waste glass and simulant glass, Product Consistency Tests (PCT, i.e., ASTM C1285-21) and Environmental Protection Agency (EPA) 1313 durability tests were performed on actual and simulant LAW glasses fabricated using laboratory-scaled melters. Actual and simulant glass durability test results are presented and statistically compared. Finally, differences in test responses were found to be within experimental uncertainty.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2020

Markforged Continuous Fiber Composite Material Testing

Continuous fiber composite 3D printing promises to greatly expand the design space of polymer additive manufacturing (AM). A series of mechanical tests were performed to attempt to fully characterize the composite materials built from feedstock provided by the Markforged company. These tests included tensile, compression, Charpy impact, three point bending, coefficient of thermal expansion, and calorimetry tests. Specimens were prepared on the Mark Two 3D printer at LANL during the spring and summer of 2019. These samples were then shipped to New Mexico Institute of Mining and Technology’s Thermo-Mechanical Lab for testing during the summer and fall of 2019. Test data are reported and analyzed for each of the tests.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Domain Adaptive Graph Neural Networks for Constraining Cosmological Parameters Across Multiple Data Sets

Deep learning models have been shown to outperform methods that rely on summary statistics, like the power spectrum, in extracting information from complex cosmological data sets. However, due to differences in the subgrid physics implementation and numerical approximations across different simulation suites, models trained on data from one cosmological simulation show a drop in performance when tested on another. Similarly, models trained on any of the simulations would also likely experience a drop in performance when applied to observational data. Training on data from two different suites of the CAMELS hydrodynamic cosmological simulations, we examine the generalization capabilities of Domain Adaptive Graph Neural Networks (DA-GNNs). By utilizing GNNs, we capitalize on their capacity to capture structured scale-free cosmological information from galaxy distributions. Moreover, by including unsupervised domain adaptation via Maximum Mean Discrepancy (MMD), we enable our models to extract domain-invariant features. We demonstrate that DA-GNN achieves higher accuracy and robustness on cross-dataset tasks. Using data visualizations, we show the effects of domain adaptation on proper latent space data alignment. This shows that DA-GNNs are a promising method for extracting domain-independent cosmological information, a vital step toward robust deep learning for real cosmic survey data.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Bridging the Gap between Cosmological Simulations with Graph Neural Networks and Domain Adaptation

Deep learning models have been shown to outperform methods that rely on summary statistics, like the power spectrum, in extracting information from complex cosmological data sets. However, due to differences in the subgrid physics implementation and numerical approximations across different simulation suites, models trained on data from one cosmological simulation show a drop in performance when tested on another. Similarly, models trained on any of the simulations would also likely experience a drop in performance when applied to observational data. Training on data from two different suites of the CAMELS hydrodynamic cosmological simulations, we examine the generalization capabilities of Domain Adaptive Graph Neural Networks (DA-GNNs). By utilizing GNNs, we capitalize on their capacity to capture structured scale-free cosmological information from galaxy distributions. Moreover, by including unsupervised domain adaptation via Maximum Mean Discrepancy (MMD), we enable our models to extract domain-invariant features. We demonstrate that DA-GNN achieves higher accuracy and robustness on cross dataset tasks (up to 28% better relative error and up to almost an order of magnitude better χ 2 ). Using data visualizations, we show the effects of domain adaptation on proper latent space data alignment. This shows that DA-GNNs are a promising method for extracting domain-independent cosmological information, a vital step toward robust deep learning for real cosmic survey data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Review of Shock, Vibration, and Other Tests for Type IV Hydrogen Composite Pressure Vessels for Rail Use

Requirements specific to hydrogen rail transportation and its unique components are currently not well represented in safety codes and standards. Notably, one of the most important components of the system, the hydrogen storage vessel, may be subject to entirely different shock and vibration conditions compared to hydrogen tanks on road vehicles. This report focuses on how composite hydrogen tanks are tested for performance and how this may relate to these tanks being used on rail systems. The shock and vibration testing procedures that are relevant for hydrogen composite tanks used for rail applications have been identified, as well as some general testing requirements for hydrogen tanks and composite tanks.

42 ENGINEERING↗

DOE OSTI2023

Domain Adaptive Graph Neural Networks for Constraining Cosmological Parameters Across Multiple Data Sets

Deep learning models have been shown to outperform methods that rely on summary statistics, like the power spectrum, in extracting information from complex cosmological data sets. However, due to differences in the subgrid physics implementation and numerical approximations across different simulation suites, models trained on data from one cosmological simulation show a drop in performance when tested on another. Similarly, models trained on any of the simulations would also likely experience a drop in performance when applied to observational data. Training on data from two different suites of the CAMELS hydrodynamic cosmological simulations, we examine the generalization capabilities of Domain Adaptive Graph Neural Networks (DA-GNNs). By utilizing GNNs, we capitalize on their capacity to capture structured scale-free cosmological information from galaxy distributions. Moreover, by including unsupervised domain adaptation via Maximum Mean Discrepancy (MMD), we enable our models to extract domain-invariant features. We demonstrate that DA-GNN achieves higher accuracy and robustness on cross-dataset tasks (up to $28\%$ better relative error and up to almost an order of magnitude better $\chi^2$). Using data visualizations, we show the effects of domain adaptation on proper latent space data alignment. This shows that DA-GNNs are a promising method for extracting domain-independent cosmological information, a vital step toward robust deep learning for real cosmic survey data.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

The Role of Pentaerythritol Tetranitrate (PETN) Aging in Determining Detonator Firing Characteristics

Pentaerythritol tetranitrate (PETN) is one of the most commonly used explosives for both military and mining applications. PETN is used in EBW (exploding bridge wire) and EFI (exploding foil initiator) detonator devices. Due the widespread usage of PETN, studies focusing on how the explosive changes with age, primarily its function in detonators has received particular interest. Aging studies have identified several factors that affect PETN detonator function over time, most notably the specific surface area of the explosive powder. Though small-scale studies have been performed on specific detonator systems with isolated batches of material, what is missing is a large statistically-significant study focusing on PETN aging characteristics - such as powder coarsening - and their influence on detonator performance. Herein we report the first large statistically viable PETN aging study focusing on four batches of PETN powder from the same stock of PETN using two stabilizers, polysaccharide and TriPEON. PETN was aged both as a free-flowing powder as well as in modified EBW RP-2 detonators, for one month at 75 °C. The PETN powder has been analyzed chemically using Fisher specific surface area analysis, SEM imaging and light scattering particle size analysis. Additionally the detonators were tested for performance through voltage-sweep threshold testing and function time measurements. Findings from the study indicate that aging at 75 °C for one month significantly changes the specific surface area and particle size of unstabilized PETN, leading to increases in detonator function time, but not detonator threshold values. Powders stabilized with TriPEON displayed less significant increases in function time, while powder stabilized with polysaccharide exhibited no aging effects, despite the high temperature aging.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2020

Measurements of enhanced performance in an indirect drive inertial confinement fusion experiment when reducing the contact area of the capsule support

Experimental results from indirectly driven inertial confinement fusion experiments testing the performance gained from using an alternate capsule tent support are reported. The polar tent describes an alternate geometry for the thin membrane used to support the Deuterium–Tritium (DT) filled capsule. In this work, the contact area is reduced by 23 times by locating the tent support close to the poles of the capsule. The polar tent experiments are repeats of previous 3 shock 1.63 MJ, 400 TW high foot experiments and use a 165 μm thick silicon doped carbon hydrogen plastic (CH) shell. Using the polar tent support, we report a DT neutron yield of 1.07 ×1016, 76% higher than the expected Y DT ∝V 7.7 scaling. This is, at the time of writing, the highest neutron yield to date from a CH shell implosion. Furthermore, we find that the inferred pressure when using the polar tent is significantly above the model based on analytic scaling even when accounting for tent effects. Analysis of x-ray and neutron images shows the reduction of lobes produced by nominal tent features. The reduction of these features in the polar tent experiments leads to decreased low mode (P2 and P4) asymmetry compared to the nominal tent results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

The Grassmann interpolation method for spin-unrestricted open-shell systems

The recently reported Grassmann interpolation (G-Int) method [J. A. Tan and K. U. Lao, J. Chem. Phys. 158, 051101 (2023)] has been extended to spin-unrestricted open-shell systems. In contrast to closed-shell systems, where G-Int has to be performed only once since the α and β density matrices are the same, spin-unrestricted open-shell systems require G-Int to be performed twice—one for the α spin and another for the β spin density matrix. In this work, we tested the performance of G-Int to the carbon monoxide radical cation CO●+ and nickelocene complex, which have the doublet and triple ground states, respectively. We found that the Frobenius norm errors associated with the interpolations for the α and β spin density matrices are comparable for a given molecular geometry. These G-Int density matrices, when used as an initial guess for a self-consistent field (SCF) calculation, outperform the conventional SCF guess schemes, such as the superposition of atomic densities, purified superposition of atomic densities, core Hamiltonian, and generalized Wolfsberg–Helmholtz approximation. Depending on the desired accuracy, these G-Int density matrices can be used to directly evaluate the SCF energy without performing SCF iterations. In addition, the spin-unrestricted G-Int density matrices have been used for the first time to directly calculate the atomic charges using the Mulliken and ChElPG population analysis.

Chemistry↗