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A variational approach to the question of temporal stability of equilibrium models of solar prominences. I - The formal theory

A Lagrangian approach to the equations describing small amplitude departures from equilibrium of solar prominences is presented. Seven quantities are derived which, by analogy to the concepts of energy, momentum, and angular momentum, are conserved under conditions corresponding to ignorable coordinates of classical mechanics. It is expected that these conservation laws will be useful as criteria of accuracy in obtaining eigenfrequencies for the perturbation equations when numerical techniques are used. The method is capable of handling complicated spatial dependences and has internal criteria for assessing the accuracy of any given numerical convergence scheme.

Lerche, I.↗

Semi-local Density Functional Approximations for Bulk, Surface, and Confinement Physics

Due to its balance of accuracy and computational cost, density functional theory has become the method of choice for computing the electronic structure and related properties of materials. However, present-day semi-local approximations to the exchange-correlation energy of density functional theory break down for materials containing d and f electrons. In this report we summarize the results of our research efforts within the LDRD 200202 titled "Making density functional theory work for all materials" in addressing this issue. Our efforts are grouped into two research thrusts. In the first thrust, we develop an exchange-correlation functional (BSC functional) within the subsystem functional formalism. It enables us to capture bulk, surface, and confinement physics with a single, semi-local exchange-correlation functional in density functional theory calculations. We present the analytical properties of the BSC functional and demonstrate that the BSC functional is able to capture confinement physics more accurately than standard semi-local exchange-correlation functionals. The second research thrust focusses on developing a database for transition metal binary compounds. The database consists of materials properties (formation energies, ground-state energies, lattice constants, and elastic constants) of 26 transition metal elements and 89 transition metal alloys. It serves as a reference for benchmarking computational models (such as lower-level modeling methods and exchange-correlation functionals). We expect that our database will significantly impact the materials science community. We conclude with a brief discussion on the future research directions and impact of our results.

36 MATERIALS SCIENCE↗

ITAR: A modified TAR method to determine depth dose distribution for an ophthalmic device that performs kilovoltage x-ray pencil-beam stereotaxy

Purpose: New technology has been developed to treat age-related macular degeneration (AMD) using 100 kVp pencil-beams that enter the patient through the radio-resistant sclera with a depth of interest between 1.6 and 2.6 cm. Measurement of reference and relative dose in a kilovoltage x-ray beam with a 0.42 cm diameter field size and a 15 cm source to axis distance (SAD) is a challenge that is not fully addressed in current guidelines to medical physicists. AAPM's TG-61 gives dosimetry recommendations for low and medium energy x-rays, but not all of them are feasible to follow for this modality. Methods: An investigation was conducted to select appropriate equipment for the application. PTW's Type 34013 Soft X-Ray Chamber (Freiburg, Germany) and CIRS's Plastic Water LR (Norfolk, VA) were found to be the best available options. Attenuation curves were measured with minimal scatter contribution and thus called Low Scatter Tissue Air Ratio (LSTAR). A scatter conversion coefficient (C{sub scat}) was derived through Monte Carlo radiation transport simulation using MCNPX (LANL, Los Alamos, NM) to quantify the difference between a traditional TAR curve and the LSTAR curve. A material conversion coefficient (C{sub mat}) was determined through experimentation to evaluate the difference in attenuation properties between water and Plastic Water LR. Validity of performing direct dosimetry measurements with a source to detector distance other than the treatment distance, and therefore a different field size due to a fixed collimator, was explored. A method—Integrated Tissue Air Ratio (ITAR)—has been developed that isolates each of the three main radiological effects (distance from source, attenuation, and scatter) during measurement, and integrates them to determine the dose rate to the macula during treatment. Results: LSTAR curves were determined to be field size independent within the range explored, indicating that direct dosimetry measurements may be performed with a source to detector distance of 20 cm even though the SAD is 15 cm during treatment. C{sub scat} varied from 1.102 to 1.106 within the range of depths of interest. The experimental variance among repeated measurements of C{sub mat} was larger than depth dependence, so C{sub mat} was estimated as1.019 for all depths of interest. Conclusions: Equipment selection, measurement techniques, and formalism for the determination of dose rate to the macula during stereotaxy for AMD have been determined and are strongly recommended by the authors of this paper to be used by clinical medical physicists.

61 RADIATION PROTECTION AND DOSIMETRY↗

Development of a phantom to validate high-dose-rate brachytherapy treatment planning systems with heterogeneous algorithms

Purpose: This work presents the development of a phantom to verify the treatment planning system (TPS) algorithms used for high-dose-rate (HDR) brachytherapy. It is designed to measure the relative dose in a heterogeneous media. The experimental details used, simulation methods, and comparisons with a commercial TPS are also provided. Methods: To simulate heterogeneous conditions, four materials were used: Virtual Water™ (VM), BR50/50™, cork, and aluminum. The materials were arranged in 11 heterogeneity configurations. Three dosimeters were used to measure the relative response from a HDR {sup 192}Ir source: TLD-100™, Gafchromic{sup ®} EBT3 film, and an Exradin™ A1SL ionization chamber. To compare the results from the experimental measurements, the various configurations were modeled in the PENELOPE/penEasy Monte Carlo code. Images of each setup geometry were acquired from a CT scanner and imported into BrachyVision™ TPS software, which includes a grid-based Boltzmann solver Acuros™. The results of the measurements performed in the heterogeneous setups were normalized to the dose values measured in the homogeneous Virtual Water™ setup and the respective differences due to the heterogeneities were considered. Additionally, dose values calculated based on the American Association of Physicists in Medicine-Task Group 43 formalism were compared to dose values calculated with the Acuros™ algorithm in the phantom. Calculated doses were compared at the same points, where measurements have been performed. Results: Differences in the relative response as high as 11.5% were found from the homogeneous setup when the heterogeneous materials were inserted into the experimental phantom. The aluminum and cork materials produced larger differences than the plastic materials, with the BR50/50™ material producing results similar to the Virtual Water™ results. Our experimental methods agree with the PENELOPE/penEasy simulations for most setups and dosimeters. The TPS relative differences with the Acuros™ algorithm were similar in both experimental and simulated setups. The discrepancy between the BrachyVision™, Acuros™, and TG-43 dose responses in the phantom described by this work exceeded 12% for certain setups. Conclusions: The results derived from the phantom measurements show good agreement with the simulations and TPS calculations, using Acuros™ algorithm. Differences in the dose responses were evident in the experimental results when heterogeneous materials were introduced. These measurements prove the usefulness of the heterogeneous phantom for verification of HDR treatment planning systems based on model-based dose calculation algorithms.

07 ISOTOPE AND RADIATION SOURCES↗

TH-C-19A-01: Analytic Design Method to Make a 2D Planar, Segmented Ion Chamber Water-Equivalent for Proton Dose Measurements

Purpose: Quality Assurance (QA) measurements of proton therapy fields must accurately measure steep longitudinal dose gradients as well as characterize the dose distribution laterally. Currently, available devices for two-dimensional field measurements perturb the dose distribution such that routine QA measurements performed at multiple depths require multiple field deliveries and are time consuming. Methods: A design procedure for a two-dimensional detector array is introduced whereby the proton energy loss and scatter are adjusted so that the downstream dose distribution is maintained to be equivalent to that which would occur in uniform water. Starting with the design for an existing, functional two-dimensional segmented ion chamber prototype, a compensating material is introduced downstream of the detector to simultaneously equate the energy loss and lateral scatter in the detector assembly to the values in water. An analytic formalism and procedure is demonstrated to calculate the properties of the compensating material in the general case of multiple layers of arbitrary material. The resulting design is validated with Monte Carlo simulations. Results: With respect to the specific prototype design considered, the results indicate that a graphite compensating layer of the proper dimensions can yield proton beam range perturbation less than 0.1mm and beam sigma perturbation less than 2% across the energy range of therapeutic proton beams. Conclusion: We have shown that, for a 2D gas-filled detector array, a graphite-compensating layer can balance the energy loss and multiple Coulomb scattering relative to uniform water. We have demonstrated an analytic formalism and procedure to determine a compensating material in the general case of multiple layers of arbitrary material. This work was supported by the US Army Medical Research and Materiel Command under Contract Agreement No. DAMD17-W81XWH-04-2-0022. Opinions, interpretations, conclusions and recommendations are those of the author and are not necessarily endorsed by the US Army.

07 ISOTOPE AND RADIATION SOURCES↗

Metal–Metal Bonding in Actinide Dimers: U 2 and U 2 –

Understanding direct metal–metal bonding between actinide atoms has been an elusive goal in chemistry for years. Here we report for the first time the anion photoelectron spectrum of U 2 – . The threshold of the lowest electron binding energy (EBE) spectral band occurs at 1.0 eV, which corresponds to the electron affinity (EA) of U 2 , whereas the vertical detachment energy of U 2 – is found at EBE ~ 1.2 eV. Electronic structure calculations on U 2 and U 2 – were carried out with state-of-the-art theoretical methods. The computed values of EA(U 2 ) and EA(U) and the difference between the computed dissociation energies of U 2 and U 2 – are found to be internally consistent and consistent with experiment. Analysis of the bonds in U 2 and U 2 – shows that while U 2 has a formal quintuple bond, U 2 – has a quadruple bond, even if the effective bond orders differ only by 0.5 unit instead of one unit. Furthermore, the resulting experimental-computational synergy elucidates the nature of metal–metal bonding in U 2 and U 2 – .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Explicit inclusion of nonlocality in ( d , p ) transfer reactions

Traditionally, nucleon-nucleus optical potentials are made local for convenience. In recent work we studied the effects of including nonlocal interactions explicitly in the final state for (d,p) reactions, within the distorted wave Born approximation. Our goal in this work is to develop an improved formalism for nonlocal interactions that includes deuteron breakup and to use it to study the effects of including nonlocal interactions in transfer (d,p) reactions, in both the deuteron and the proton channel. We extend the finite-range adiabatic distorted wave approximation to include nonlocal nucleon optical potentials. We apply our method to (d,p) reactions on 16 O, 40 Ca, 48 Ca, 126 Sn, 132 Sn, and 208 Pb at 10, 20 and 50 MeV. Here, we find that nonlocality in the deuteron scattering state reduces the amplitude of the wave function in the nuclear interior, and shifts the wave function outward. In many cases, this has the effect of increasing the transfer cross section at the first peak of the angular distributions. This increase was most significant for heavy targets and for reactions at high energies. Lastly, our systematic study shows that, if only local optical potentials are used in the analysis of experimental (d, p) transfer cross sections, the extracted spectroscopic factors may be incorrect by up to 40% due to the local approximation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

TU-AB-201-02: An Automated Treatment Plan Quality Assurance Program for Tandem and Ovoid High Dose-Rate Brachytherapy

Purpose: For tandem and ovoid (T&O) HDR brachytherapy in our clinic, it is required that the planning physicist manually capture ∼10 images during planning, perform a secondary dose calculation and generate a report, combine them into a single PDF document, and upload it to a record- and-verify system to prove to an independent plan checker that the case was planned correctly. Not only does this slow down the already time-consuming clinical workflow, the PDF document also limits the number of parameters that can be checked. To solve these problems, we have developed a web-based automatic quality assurance (QA) program. Methods: We set up a QA server accessible through a web- interface. A T&O plan and CT images are exported as DICOMRT files and uploaded to the server. The software checks 13 geometric features, e.g. if the dwell positions are reasonable, and 10 dosimetric features, e.g. secondary dose calculations via TG43 formalism and D2cc to critical structures. A PDF report is automatically generated with errors and potential issues highlighted. It also contains images showing important geometric and dosimetric aspects to prove the plan was created following standard guidelines. Results: The program has been clinically implemented in our clinic. In each of the 58 T&O plans we tested, a 14- page QA report was automatically generated. It took ∼45 sec to export the plan and CT images and ∼30 sec to perform the QA tests and generate the report. In contrast, our manual QA document preparation tooks on average ∼7 minutes under optimal conditions and up to 20 minutes when mistakes were made during the document assembly. Conclusion: We have tested the efficiency and effectiveness of an automated process for treatment plan QA of HDR T&O cases. This software was shown to improve the workflow compared to our conventional manual approach.

60 APPLIED LIFE SCIENCES↗

Geothermal Fault Zone and Fluid Imaging through Joint Airborne ZTEM and Ground MT Data Inversion Analysis

This project has aimed to achieve detailed electrical resistivity resolution at geothermal reservoir scales by combining airborne natural electromagnetic (EM) field surveying (ZTEM) with ground magnetotelluric (MT) measurements to approximate an airborne MT geophysical method. MT alone is relatively expensive and may have permitting challenges in sensitive areas. Airborne ZTEM field data contains only the magnetic field, requires a background assumption, and has been limited to relatively high frequencies, thus suffering uniqueness problems. Based on proto-type 2D simulations, ZTEM ambiguities may be reduced through formal incorporation with possibly sparse ground MT soundings, which we pursued in full 3D for this project. The methodology was tested at the high-temperature Roosevelt Hot Springs geothermal system, Utah, which was considered advantageous given the near total exposure of crystalline reservoir rocks across the project area. ZTEM and ground MT survey data were acquired in 2017, subcontracted to outside parties with which we have worked in the past. These included 80 remote-referenced tensor MT soundings over the Mineral Mountains and adjacent Roosevelt Hot Spring producing geothermal system. These MT stations abut later coverage of a similar number of MT stations taken for the Utah FORGE project providing excellent total data aperture to re-solve structure beneath both project areas better than either set alone. The airborne ZTEM survey covered 704 line kilometers in E-W flight lines with a 250 m line spacing. Although this survey was timed during a maintenance-related shutdown of power production at the Roosevelt Hot Springs, other noise sources difficult to identify but including two high-voltage state-scale transmission lines compromised the ZTEM survey badly leading to unusable responses. Thus, with DOE management concurrence, the project proceeded to emphasize inversion and interpretation of the joint SubTER-FORGE MT data sets with regard to the Roosevelt Hot Springs reservoir recharge and to deep heat sources for both it and the Utah FORGE EGS project area. We also investigated the joint ZTEM-MT sampling concept with data sets from the Eleven Mile Canyon prospect area donated by the U.S. Navy (A. Sabin, PoC). Inversion of the SubTER-FORGE MT data using the HexMT 3D finite element algorithm reveals a large, low-resistivity anomaly extending sub-vertically through the depth range of the crust beneath the western Mineral Mountains. The steep conductive zone connects in the lower crust to a more tabular conductor characteristic of much of the Great Basin that generally is ascribed to current mafic magmatic underplating, hybridization and fluid release. The location of the resolved anomaly relative to the recent (0.5-0.8 Ma) eruptive centers of the Mineral Mountains implicates it as remnants of the magma body which fed these centers. This structure appears to be currently feeding heat and fluids upward into the Roosevelt Hot Springs hydrothermal system, as well as heat laterally to the FORGE project area. Separate and joint inversion models were carried out for the donated Eleven Mile Canyon MT-ZTEM data set to demonstrate concept. ZTEM only inversion showed two main alteration zones in the western portion of the project area known from geological mapping. Joint inversion including an E-W profile of MT soundings sharpened these features considerably. It also resolved in much greater detail the graben related normal faulting structure of the central project area which lies at depths exceeding the sensitivity of ZTEM alone. The sparse number of MT da-ta relative to the ZTEM required upweighting the former by a factor of several, but an exact procedure awaits future research. Our final impression is that sparse MT data can improve resolution of the subsurface over that of ZTEM alone. However, well sampled MT data are to be preferred and offer the simplicity of interpreting just one data type, and possess the superior resolution capability coming with the electric field everywhere, and from their high bandwidth.

15 GEOTHERMAL ENERGY↗

Validation of Image-Based Neural Network Controllersthrough Adaptive Stress Testing

Neural networks have become state-of-the-art for computer vision problems because of their ability to efficiently model complex functions from large amounts of data. While neural networks can be shown to perform well empirically fora variety of tasks, their performance is difficult to guarantee.Neural network verification tools have been developed that can certify robustness with respect to a given input image; however,for neural network systems used in closed-loop controllers,robustness with respect to individual images does not address multi-step properties of the neural network controller and itsenvironment. Furthermore, neural network systems interacting in the physical world and using natural images are operating in a black-box environment, making formal verification in-tractable. This work combines the adaptive stress testing (AST)framework with neural network verification tools to search for the most likely sequence of image disturbances that cause the neural network controlled system to reach a failure. Anautonomous aircraft taxi application is presented, and results show that the AST method finds failures with more likely image disturbances than baseline methods. Further analysis of AST results revealed an explainable cause of the failure, giving insight into the problematic scenarios that should be addressed.

Adaptive Stress Testing, Marabou, Deep Neural Netw↗

Using Likelihood for Combined Data Set Analysis

The joint likelihood is a simple extension of the standard likelihood formalism that enables the estimation of common parameters across disjoint datasets. Joining the likelihood, rather than the data itself, means nuisance parameters can be dealt with independently. Application of this technique, particularly to Fermi-LAT dwarf spheroidal analyses, has already been met with great success. We present a description of the method's general implementation along with a toy Monte-Carlo study of its properties and limitations.

Anderson, Brandon↗

MO-AB-BRA-02: A Novel Scatter Imaging Modality for Real-Time Image Guidance During Lung SBRT

Purpose: A novel scatter imaging modality is developed and its feasibility for image-guided radiation therapy (IGRT) during stereotactic body radiation therapy (SBRT) for lung cancer patients is assessed using analytic and Monte Carlo models as well as experimental testing. Methods: During treatment, incident radiation interacts and scatters from within the patient. The presented methodology forms an image of patient anatomy from the scattered radiation for real-time localization of the treatment target. A radiographic flat panel-based pinhole camera provides spatial information regarding the origin of detected scattered radiation. An analytical model is developed, which provides a mathematical formalism for describing the scatter imaging system. Experimental scatter images are acquired by irradiating an object using a Varian TrueBeam accelerator. The differentiation between tissue types is investigated by imaging simple objects of known compositions (water, lung, and cortical bone equivalent). A lung tumor phantom, simulating materials and geometry encountered during lung SBRT treatments, is fabricated and imaged to investigate image quality for various quantities of delivered radiation. Monte Carlo N-Particle (MCNP) code is used for validation and testing by simulating scatter image formation using the experimental pinhole camera setup. Results: Analytical calculations, MCNP simulations, and experimental results when imaging the water, lung, and cortical bone equivalent objects show close agreement, thus validating the proposed models and demonstrating that scatter imaging differentiates these materials well. Lung tumor phantom images have sufficient contrast-to-noise ratio (CNR) to clearly distinguish tumor from surrounding lung tissue. CNR=4.1 and CNR=29.1 for 10MU and 5000MU images (equivalent to 0.5 and 250 second images), respectively. Conclusion: Lung SBRT provides favorable treatment outcomes, but depends on accurate target localization. A comprehensive approach, employing multiple simulation techniques and experiments, is taken to demonstrate the feasibility of a novel scatter imaging modality for the necessary real-time image guidance.

60 APPLIED LIFE SCIENCES↗

Experimental evaluation of the extended Dytlewski-style dead time correction formalism for neutron multiplicity counting

Over the past few decades, neutron multiplicity counting has played an integral role in Special Nuclear Material (SNM) characterization pertaining to nuclear safeguards. Current neutron multiplicity analysis techniques use singles, doubles, and triples count rates because a methodology to extract and dead time correct higher order count rates (i.e. quads and pents) was not fully developed. This limitation is overcome by the recent extension of a popular dead time correction method developed by Dytlewski. This extended dead time correction algorithm, named Dytlewski-Croft-Favalli (DCF), is detailed in reference Croft and Favalli (2017), which gives an extensive explanation of the theory and implications of this new development. Dead time corrected results can then be used to assay SNM by inverting a set of extended point model equations which as well have only recently been formulated. Here, we discuss and present the experimental evaluation of practical feasibility of the DCF dead time correction algorithm to demonstrate its performance and applicability in nuclear safeguards applications. In order to test the validity and effectiveness of the dead time correction for quads and pents, 252 Cf and SNM sources were measured in high efficiency neutron multiplicity counters at the Los Alamos National Laboratory (LANL) and the count rates were extracted up to the fifth order and corrected for dead time. To assess the DCF dead time correction, the corrected data is compared to traditional dead time correction treatment within INCC. In conclusion, the DCF dead time correction is found to provide adequate dead time treatment for broad range of count rates available in practical applications.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

SELF-GRAVITY, RESONANCES AND ORBITAL DIFFUSION IN STELLAR DISKS

Fluctuations in a stellar system's gravitational field cause the orbits of stars to evolve. The resulting evolution of the system can be computed with the orbit-averaged Fokker–Planck equation once the diffusion tensor is known. We present the formalism that enables one to compute the diffusion tensor from a given source of noise in the gravitational field when the system's dynamical response to that noise is included. In the case of a cool stellar disk we are able to reduce the computation of the diffusion tensor to a one-dimensional integral. We implement this formula for a tapered Mestel disk that is exposed to shot noise and find that we are able to explain analytically the principal features of a numerical simulation of such a disk. In particular the formation of narrow ridges of enhanced density in action space is recovered. As the disk's value of Toomre's Q is reduced and the disk becomes more responsive, there is a transition from a regime of heating in the inner regions of the disk through the inner Lindblad resonance to one of radial migration of near-circular orbits via the corotation resonance in the intermediate regions of the disk. The formalism developed here provides the ideal framework in which to study the long-term evolution of all kinds of stellar disks.

79 ASTRONOMY AND ASTROPHYSICS↗

Availability of Neutronics Benchmarks in the ICSBEP and IRPhEP Handbooks for Computational Tools Testing

In the past several decades, numerous experiments have been performed worldwide to support reactor operations, measurements, design, and nuclear safety. Those experiments represent an extensive international investment in infrastructure, expertise, and cost, representing significantly valuable resources of data supporting past, current, and future research activities. Those valuable assets represent the basis for recording, development, and validation of our nuclear methods and integral nuclear data [1]. The loss of these experimental data, which has occurred all too much in the recent years, is tragic. The high cost to repeat many of these measurements can be prohibitive, if not impossible, to surmount. Two international projects were developed, and are under the direction of the Organisation for Co-operation and Development Nuclear Energy Agency (OECD NEA) to address the challenges of not just data preservation, but evaluation of the data to determine its merit for modern and future use. The International Criticality Safety Benchmark Evaluation Project (ICSBEP) was established to identify and verify comprehensive critical benchmark data sets; evaluate the data, including quantification of biases and uncertainties; compile the data and calculations in a standardized format; and formally document the effort into a single source of verified benchmark data [2]. Similarly, the International Reactor Physics Experiment Evaluation Project (IRPhEP) was established to preserve integral reactor physics experimental data, including separate or special effects data for nuclear energy and technology applications [3]. Annually, contributors from around the world continue to collaborate in the evaluation and review of select benchmark experiments for preservation and dissemination. The extensively peer-reviewed integral benchmark data can then be utilized to support nuclear design and safety analysts to validate the analytical tools, methods, and data needed for next-generation reactor design, safety analysis requirements, and all other front- and back-end activities contributing to the overall nuclear fuel cycle where quality neutronics calculations are paramount.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Theory of tunneling between two-dimensional electron layers driven by spin pumping: Adiabatic regime and beyond

Tunneling spectroscopy between parallel two-dimensional (2D) electronic systems provides a powerful method to probe the underlying electronic properties by measuring tunneling conductance. Here, in this work, we present a theoretical framework for spin transport in 2D-to-2D tunneling systems, driven by spin pumping. This theory applies to a vertical heterostructure where two layers of metallic 2D electron systems are separated by an insulating barrier, with one layer exchange coupled to a magnetic layer driven at resonance. Utilizing a nonperturbative Floquet-Keldysh formalism, we derive general expressions for the tunneling spin and charge currents across a broad range of driving frequencies, extending beyond the traditional adiabatic pumping regime. At low frequencies, we obtain analytical results that recover the known behaviors in the adiabatic regime. However, at higher frequencies, our numerical findings reveal significant deviations in the dependence of spin and charge currents on both frequency and precession angle. This work offers fresh insights into the role of magnetization dynamics in tunneling transport, opening up new avenues for exploring nonadiabatic spin pumping phenomena.

Green's function methods↗

Electronic Structure and Magnetic Properties of Cobalt-Doped Nonstoichiometric Rutile Thin Films

The coherent potential method has been applied for the investigation of Co substitutional doping influence on the spectral and magnetic properties of TiO{sub 2} rutile (100) surface. Both stoichiometric and nonstoichiometric oxygen compositions have been considered. For the stoichiometric case, the energy spectrum corresponds to half-metallic ferromagnet. The Co ions are in 2 + formal oxidation state with a spin magnetic moment of 0.8 μ{sub B}. The presence of oxygen vacancies makes the surface insulating and increases the Co spin magnetic moment value.

36 MATERIALS SCIENCE↗

Linear-Scaling Asymmetric Triples Correction through the Solution of the DLPNO–CCSD Lambda Equations: DLPNO–CCSD(T) Λ

In this research, we derive equations for solving for the stationary points of the DLPNO–CCSD Lagrangian, in the t 1 -transformed formalism introduced earlier and as currently implemented in the P SI 4 quantum chemistry software package. These lambda equations in the local pair natural orbital basis allow for the evaluation of CCSD(T) Λ energetics with linear-scaling computational effort, also known as the asymmetric triples correction. This DLPNO–CCSD(T) Λ method allows for accurate triples contributions to be computed for larger molecules, especially in cases that CCSD(T) is known to be insufficient, such as with multireference systems and bond-breaking systems. We showcase the accuracy of our code on reaction energies, barrier heights, and noncovalent interaction energies. Also showcased are the capabilities of our code by evaluating DLPNO–CCSD(T) Λ energetics on large noncovalent dimers up to 112 atoms, as well as a rhodium catalyst complex containing 66 atoms.

Cluster chemistry↗

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