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Extending the Gutzwiller approximation to intersite interactions

In this work, we develop an extension of the Gutzwiller approximation (GA) formalism that includes the effects of Coulomb interactions of arbitrary range (including density density, exchange, pair hopping, and Coulomb-assisted hopping terms). This formalism reduces to the ordinary GA formalism for the multiband Hubbard models in the presence of only local interactions. This is accomplished by combining the 1 / z expansion—where z is the coordination number, and only the leading-order terms contribute in the limit of infinite dimensions—with a P R † P R - I expansion, where P R is the Gutzwiller projector on the site R . Furthermore, the method is conveniently formulated in terms of a Gutzwiller Lagrange function. We apply our theory to the extended single-band Hubbard model. Similarly to the usual Brinkman-Rice mechanism, we find a Mott transition. A valence skipping transition is observed, where the occupation of the empty and doubly occupied states for the Gutzwiller wave function is enhanced with respect to the uncorrelated Slater determinant wave function.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Relativistic self-consistent G W : Exact two-component formalism with one-electron approximation for solids

We present a formulation of relativistic self-consistent GW for solids based on the exact two-component formalism with one-electron approximation (X2C1e) and nonrelativistic Coulomb interactions. Our theory allows us to study scalar relativistic effects, spin-orbit coupling, and the interplay of relativistic effects with electron correlation without adjustable parameters. Our all-electron implementation is fully ab initio and does not require a pseudopotential constructed from atomic calculations. We examine the effect of the X2C1e approximation by comparison to the established four-component formalism and reach an excellent agreement. The simplicity of X2C1e enables the construction of higher order theories, such as embedding theories, on top of perturbative calculations.

36 MATERIALS SCIENCE↗

An extension to artifact-free projection overlaps

Purpose: In multipinhole single photon emission computed tomography, the overlapping of projections has been used to increase sensitivity. Avoiding artifacts in the reconstructed image associated with projection overlaps (multiplexing) is a critical issue. In our previous report, two types of artifact-free projection overlaps, i.e., projection overlaps that do not lead to artifacts in the reconstructed image, were formally defined and proved, and were validated via simulations. In this work, a new proposition is introduced to extend the previously defined type-II artifact-free projection overlaps so that a broader range of artifact-free overlaps is accommodated. One practical purpose of the new extension is to design a baffle window multipinhole system with artifact-free projection overlaps. Methods: First, the extended type-II artifact-free overlap was theoretically defined and proved. The new proposition accommodates the situation where the extended type-II artifact-free projection overlaps can be produced with incorrectly reconstructed portions in the reconstructed image. Next, to validate the theory, the extended-type-II artifact-free overlaps were employed in designing the multiplexing multipinhole spiral orbit imaging systems with a baffle window. Numerical validations were performed via simulations, where the corresponding 1-pinhole nonmultiplexing reconstruction results were used as the benchmark for artifact-free reconstructions. The mean square error (MSE) was the metric used for comparisons of noise-free reconstructed images. Noisy reconstructions were also performed as part of the validations. Results: Simulation results show that for noise-free reconstructions, the MSEs of the reconstructed images of the artifact-free multiplexing systems are very similar to those of the corresponding 1-pinhole systems. No artifacts were observed in the reconstructed images. Therefore, the testing results for artifact-free multiplexing systems designed using the extended type-II artifact-free overlaps numerically validated the developed theory. Conclusions: First, the extension itself is of theoretical importance because it broadens the selection range for optimizing multiplexing multipinhole designs. Second, the extension has an immediate application: using a baffle window to design a special spiral orbit multipinhole imaging system with projection overlaps in the orbit axial direction. Such an artifact-free baffle window design makes it possible for us to image any axial portion of interest of a long object with projection overlaps to increase sensitivity.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Rad-Hydro with a High-Order, Low-Order Method

Moment-based acceleration via the development of “high-order, low-order” (HO-LO) algorithms has provided substantial accuracy and efficiency enhancements for solutions of the nonlinear, thermal radiative transfer equations by CCS-2 and T-3 staff members. Accuracy enhancements over traditional, linearized methods are obtained by solving a nonlinear, time-implicit HO-LO system via a Jacobian-free Newton Krylov procedure. This also prevents the appearance of non-physical maximum principle violations (“temperature spikes”) associated with linearization. Efficiency enhancements are obtained in part by removing “effective scattering” from the linearized system. In this highlight, we summarize recent work in which we formally extended the HO-LO radiation algorithm to include operator-split radiation-hydrodynamics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Continuum stress intensity factors from atomistic fracture simulations

Stress intensity factors (SIFs) are utilized in continuum fracture mechanics to quantify the stress fields surrounding a crack in a homogeneous material in the linear elastic regime. Critical values of the SIFs define an intrinsic measure of the resistance of a material to propagate a crack. At atomic scales, yet, fracture occurs as a series of atomic bonds breaking, differing from the continuum description. As a consequence, a formal analog of the continuum SIFs calculated from atomistic simulations can have spatially localized, microstructural contributions that originate from varying bond configurations. The ability to characterize fracture at the atomic scale in terms of the SIFs offers both an opportunity to probe the effects of chemistry, as well as how the addition of a microstructural component affects the accuracy. We present a novel numerical method to determine SIFs from molecular dynamics (MD) simulations. The accuracy of this approach is first examined for a simple model, and then applied to atomistic simulations of fracture in amorphous silica. MD simulations provide time and spatially dependent SIFs, with results that are shown to be in good agreement with experimental values for fracture toughness in silica glass.

42 ENGINEERING↗

A review of ptychographic techniques for ultrashort pulse measurement

The measurement of optical ultrafast laser pulses is done indirectly because the required bandwidth to measure these pulses exceeds the bandwidth of current electronics. As a result, this measurement problem is often posed as a 1-D phase retrieval problem, which is fraught with ambiguities. The phase retrieval method known as ptychography solves this problem by making it possible to measure ultrafast pulses in either the time domain or the frequency domain. One well known algorithm is the principal components generalized projections algorithm (PCGPA) for extracting pulses from Frequency-Resolved Optical Gating (FROG) measurements. In this work, we discuss the development of the PCPGA and introduce new developments including an operator formalism that allows for the convenient addition of external constraints and the development of more robust algorithms. A close cousin, the ptychographic iterative engine will also be covered and compared to the PCGPA. Additional developments using other algorithmic strategies will also be discussed along with new developments combining optics and high-speed electronics to achieve megahertz measurement rates.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Sparse-Stochastic Fragmented Exchange for Large-Scale Hybrid Time-Dependent Density Functional Theory Calculations

Here we extend our recently developed sparse-stochastic fragmented exchange formalism for ground-state near-gap hybrid DFT to calculate absorption spectra within linear-response time-dependent generalized Kohn-Sham DFT (LR-GKS-TDDFT) for systems consisting of thousands of valence electrons within a grid-based/plane-wave representation. A mixed deterministic/fragmented-stochastic compression of the exchange kernel, here using long-range explicit exchange functionals, provides an efficient method for accurate optical spectra. Both real-time propagation as well as frequency-resolved Casida-equation-type approaches for spectra are presented, and the method is applied to large molecular dyes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Time-Dependent Coupled Cluster Theory on the Keldysh Contour for Nonequilibrium Systems

In this work, we leverage the Keldysh formalism to extend our implementation of finite temperature coupled cluster theory [J. Chem. Theory Comput.2018,14, 5690–5700] to thermal systems that have been driven out of equilibrium. The resulting Keldysh coupled cluster theory is discussed in detail. We describe the implementation of the equations necessary to perform Keldysh coupled cluster singles and doubles calculations of finite-temperature dynamics, and we apply the method to some simple systems including a Hubbard model with a Peierls phase and an ab initio model of warm-dense silicon subject to an ultrafast XUV pulse.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electrochemical solvent reorganization energies in the framework of the polarizable continuum model

Electron transfer reactions at electrochemical interfaces play a critical role in a wide range of catalytic processes. A key parameter in the rate constant expressions for such processes is the reorganization energy, which reflects the energetic cost of the solute and solvent rearrangements upon electron transfer. In this paper, we present dielectric continuum methods for calculating the solvent reorganization energy for electrochemical processes. We extend the simple approach in which the solute is represented as a point charge located a specified distance from the electrode surface to the representation of the solute as a collection of point charges corresponding to the partial atomic charges of the molecule. We also develop a method for calculating the electrochemical solvent reorganization energies with molecular-shaped cavities within the framework of the polarizable continuum model (PCM). The electronic and inertial responses of the solvent are separated according to their respective time scales, and two limiting cases of the relation between the solute and solvent electrons are examined. The effects of the electrode are included with the integral equations formalism PCM (IEF-PCM), in which the molecule-solvent boundary is treated explicitly, but the effects of the electrode-solvent boundary are included through an external Green’s function. This approach accounts for the effects of detailed molecular charge redistribution in a molecular-shaped cavity, as well as the electronic and inertial solvent responses and the effects of the electrode. The calculated total reorganization energies are in reasonable agreement with experimental measurements for a series of electrochemical systems. Inclusion of the effects of the electrode is found to be essential for obtaining even qualitatively accurate solvent reorganization energies. These approaches are applicable to a wide range of systems and can be extended to include other types of boundaries, such as a self-assembled monolayer or double layer separating the electrode and the molecule. This research was supported as part of the Center for Molecular Electrocatalysis, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences.

Ghosh, Soumya↗

Investigation of secondary γ -ray angular distributions using the N 15 ( p , α 1 γ ) C * 12 reaction

The observation of secondary γ-rays provides an alternative method of measuring cross sections that populate excited final states in nuclear reactions. The angular distributions of these γ-rays also provide information on the underlying reaction mechanism. Despite a large amount of data of this type in the literature, publicly available R-matrix codes do not have the ability to calculate these types of angular distributions. In this report, the mathematical formalism derived in Brune and deBoer is implemented in the R-matrix code AZURE2 and calculations are compared with previous data from the literature for the 15 N( p, α1γ ) 12 C* reaction. In addition, new measurements, made at the University of Notre Dame Nuclear Science Laboratory using the Hybrid Array of Gamma Ray Detectors (HAGRiD), are reported that span an energy range from E p = 0.88 to 4.0 MeV. Excellent agreement between data and the phenomenological fit is obtained up to the limit of the previous fit at E p = 2.0 MeV and the R-matrix fit is extended from E x ≈ 13.5 up to E x ≈ 15.3 MeV, where 15 N+p and 12 C+α reactions are fit simultaneously for the first time. An excellent reproduction of the 15 N( p, α1γ ) 12 C* and 12 C(α, α) 12 C data is achieved, but inconsistencies and difficulty in fitting other data is encountered and discussed.

6 ≤ A ≤ 19↗

Ab initio Bogoliubov coupled cluster theory for open-shell nuclei

Background: Ab initio many-body methods have been developed over the past 10 yr to address closed-shell nuclei up to mass A≈130 on the basis of realistic two- and three-nucleon interactions. A current frontier relates to the extension of those many-body methods to the description of open-shell nuclei. Several routes to address open-shell nuclei are currently under investigation, including ideas that exploit spontaneous symmetry breaking. Purpose: Singly open-shell nuclei can be efficiently described via the sole breaking of U(1) gauge symmetry associated with particle-number conservation as a way to account for their superfluid character. While this route was recently followed within the framework of self-consistent Green's function theory, the goal of the present work is to formulate a similar extension within the framework of coupled cluster theory. Methods: We formulate and apply Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-state wave function of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the ground-state energy and the cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes three-nucleon forces at the normal-ordered two-body level. The first BCC code is implemented in m scheme, which will permit the treatment of doubly open-shell nuclei via the further breaking of SU(2) symmetry associated with angular momentum conservation. Results: Proof-of-principle calculations in an N max =6 spherical harmonic oscillator basis for 16,18 O and 18 Ne in the BCCD approximation are in good agreement with standard coupled cluster results with the same chiral two-nucleon interaction, while 20 O and 20 Mg display underbinding relative to experiment. The breaking of U(1) symmetry, monitored by computing the variance associated with the particle-number operator, is relatively constant for all five nuclei, in both the Hartree-Fock-Bogoliubov and BCCD approximations. Conclusions: The newly developed many-body formalism increases the potential span of ab initio calculations based on single-reference coupled cluster techniques tremendously, i.e., potentially to reach several hundred additional midmass nuclei. The new formalism offers a wealth of potential applications and further extensions dedicated to the description of ground and excited states of open-shell nuclei. Short-term goals include the implementation of three-nucleon forces at the normal-ordered two-body level. Midterm extensions include the approximate treatment of triples corrections and the development of the equation-of-motion methodology to treat both excited states and odd nuclei. Long-term extensions include exact restoration of U(1) and SU(2) symmetries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

TU-G-BRD-04: A Round Robin Dosimetry Intercomparison of Gamma Stereotactic Radiosurgery Calibration Protocols

Purpose: The purpose of this multi-institutional study was to compare two new gamma stereotactic radiosurgery (GSRS) dosimetry protocols to existing calibration methods. The ultimate goal was to guide AAPM Task Group 178 in recommending a standard GSRS dosimetry protocol. Methods: Nine centers (ten GSRS units) participated in the study. Each institution made eight sets of dose rate measurements: six with two different ionization chambers in three different 160mm-diameter spherical phantoms (ABS plastic, Solid Water and liquid water), and two using the same ionization chambers with a custom in-air positioning jig. Absolute dose rates were calculated using a newly proposed formalism by the IAEA working group for small and non-standard radiation fields and with a new air-kerma based protocol. The new IAEA protocol requires an in-water ionization chamber calibration and uses previously reported Monte-Carlo generated factors to account for the material composition of the phantom, the type of ionization chamber, and the unique GSRS beam configuration. Results obtained with the new dose calibration protocols were compared to dose rates determined by the AAPM TG-21 and TG-51 protocols, with TG-21 considered as the standard. Results: Averaged over all institutions, ionization chambers and phantoms, the mean dose rate determined with the new IAEA protocol relative to that determined with TG-21 in the ABS phantom was 1.000 with a standard deviation of 0.008. For TG-51, the average ratio was 0.991 with a standard deviation of 0.013, and for the new in-air formalism it was 1.008 with a standard deviation of 0.012. Conclusion: Average results with both of the new protocols agreed with TG-21 to within one standard deviation. TG-51, which does not take into account the unique GSRS beam configuration or phantom material, was not expected to perform as well as the new protocols. The new IAEA protocol showed remarkably good agreement with TG-21. Conflict of Interests: Paula Petti, Josef Novotny, Gennady Neyman and Steve Goetsch are consultants for Elekta Instrument A/B; Elekta Instrument AB, PTW Freiburg GmbH, Standard Imaging, Inc., and The Phantom Laboratory, Inc. loaned equipment for use in these experiments; The University of Wisconsin Accredited Dosimetry Calibration Laboratory provided calibration services.

60 APPLIED LIFE SCIENCES↗

An Exchange-Correlation Functional Capturing 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 semilocal approximations to the exchange-correlation energy of density functional theory break down for materials containing d and f electrons. In this report we summarize our progress in addressing this issue. We describe the construction of the BSC exchange-correlation functional within the subsystem functional formalism which enables us to capture bulk, surface, and confinement physics with a single exchange-correlation functional. We report on the initial assessment of this functional within the jellium surface system and demonstrate that the BSC functional captures the confinement physics more accurately than standard semilocal exchange-correlation functionals. We conclude by outlining our future research objectives which focus on refining the functional form of the BSC functional and achieving significantly more accurate energetics of materials containing f and d electrons than existing semilocal functionals.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Benchmarking Adaptive Variational Quantum Eigensolvers

By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is indirectly assessed by the value of the associated energy. Novel adaptive derivative-assembled pseudo-trotter (ADAPT) ansatz approaches and recent formal advances now establish a clear connection between the theory of quantum chemistry and the quantum state ansatz used to solve the electronic structure problem. Here we benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves for a few selected diatomic molecules, namely H 2 , NaH, and KH. Using numerical simulation, we find both methods provide good estimates of the energy and ground state, but only ADAPT-VQE proves to be robust to particularities in optimization methods. Another relevant finding is that gradient-based optimization is overall more economical and delivers superior performance than analogous simulations carried out with gradient-free optimizers. The results also identify small errors in the prepared state fidelity which show an increasing trend with molecular size.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Glass structure and crystallization in boro-alumino-silicate glasses containing rare earth and transition metal cations: a US-UK collaborative program

Nuclear wastes generated from reprocessing of used nuclear fuel tend to contain a large fraction of rare earth (RE, e.g., Nd3+), transition (TM, e.g., Mo6+, Zr4+), alkali (A, e.g., Cs+), and alkaline earth cations (AE, e.g., Ba2+, Sr2+). Various strategies have been considered for immobilizing such waste streams, varying from nominally crystal-free glass to glass-ceramic to multi-phase ceramic waste forms. For glass and glass-ceramic waste forms, the added glass-forming system is generally alkali-alkaline earth-aluminoborosilicate (i.e., Na-Ca-Al-B-Si oxide). In a US-UK collaborative project, summarized here, we investigated the glass structure and crystallization dependence on compositional changes in simulated nuclear waste glasses and glass-ceramics. Compositions ranged in complexity from five – to – eight oxides. Specifically, the roles of Mo and rare earths are investigated, since a proposed glass-ceramic waste form contains crystalline phases such as powellite [(AE,A,RE)MoO4] and oxyapatite [(RE,AE,A)10Si6O26], and the precipitation of molybdenum phases is known to be affected by the rare earth concentration in the glass. Additionally, the effects of other chemical additions have been systematically investigated, including Zr, Ru, P, and Ti. A series of studies were also undertaken to ascertain the effect of the RE size on glass structure and on partitioning to crystal phases, investigating similarities and differences in glasses containing single RE oxides of Sc, Y, La, Ce, Nd, Sm, Er, Yb, or Lu. Finally, the effect of charge compensation was investigated by considering not only the commonly assessed peralkaline glass but also metaluminous and peraluminous compositions. Glass structure and crystallization studies were conducted by spectroscopic methods (i.e., Raman, X-ray absorption, nuclear magnetic resonance (NMR), optical absorption, photoluminescence, photoluminescence excitation, X-ray photoelectron spectroscopy), microscopy (i.e., scanning electron microscopy, transmission electron microscopy, electron probe microanalysis), scattering (i.e., X-ray and neutron diffraction, small angle measurements), and physical characterization (i.e., differential thermal analysis, liquidus, viscosity, density). This paper will give an overview of the research program and some example unpublished results on glass-ceramic crystallization kinetics, microstructure, and Raman spectra, as well as some examples of the effects of rare earths on the absorption, luminescence, and NMR spectra of starting glasses. The formal collaboration described here has resulted in the generation of a large number of results, some of which are still in the process of being published as separate studies.

McCloy, John S.↗

Efficient Temperature-Dependent Green’s Functions Methods for Realistic Systems: Compact Grids for Orthogonal Polynomial Transforms

The Matsubara Green’s function that is used to describe temperature-dependent behavior is expressed on a numerical grid. While such a grid usually has a couple of hundred points for low-energy model systems, for realistic systems with large basis sets the size of an accurate grid can be tens of thousands of points, constituting a severe computational and memory bottleneck. In this paper, we determine efficient imaginary time grids for the temperature-dependent Matsubara Green’s function formalism that can be used for calculations on realistic systems. Here we show that, because of the use of an orthogonal polynomial transform, we can restrict the imaginary time grid to a few hundred points and reach micro-Hartree accuracy in the electronic energy evaluation. Moreover, we show that only a limited number of orthogonal polynomial expansion coefficients are necessary to preserve accuracy when working with a dual representation of the Green’s function or self-energy and transforming between the imaginary time and frequency domain.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multi-level coupled cluster theory

We present a general formalism where different levels of coupled cluster theory can be applied to different parts of the molecular system. The system is partitioned into subsystems by Cholesky decomposition of the one-electron Hartree-Fock density matrix. In this way the system can be divided across chemical bonds without discontinuities arising. The coupled cluster wave function is defined in terms of cluster operators for each part and these are determined from a set of coupled equations. The total wave function fulfills the Pauli-principle across all borders and levels of electron correlation. We develop the associated response theory for this multi-level coupled cluster theory and present proof of principle applications. The formalism is an essential tool in order to obtain size-intensive complexity in the calculation of local molecular properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The significance of structural power in Strategic Environmental Assessment

This article presents a study of how power dynamics enables and constrains the influence of actors upon decision-making and Strategic Environmental Assessment (SEA). Based on structuration theory, a model for studying power dynamics in strategic decision-making processes is developed. The model is used to map and analyse key decision arenas in the decision process of aluminium production in Greenland. The analysis shows that communication lines are an important resource through which actors exercise power and influence decision-making on the location of the aluminium production. The SEA process involved not only reproduction of formal communication and decision competence but also production of alternative informal communication structures in which the SEA had capability to influence. It is concluded, that actors influence strategic decision making, and attention needs to be on not only the formal interactions between SEA process and strategic decision-making process but also on informal interaction and communication between actors as the informal structures, which can be crucial to the outcome of the decision-making process. This article is meant as a supplement to the understanding of power dynamics influence in IA processes and as a contribution to the IA research field with a method to analyse power dynamics in strategic decision-making processes. The article also brings reflections of strengths and weaknesses of using the structuration theory as an approach to power analysis. - Highlights: Black-Right-Pointing-Pointer Informal interaction influenced process despite the presence of formalised rules. Black-Right-Pointing-Pointer Interdependence of actors influenced SEA effectiveness. Black-Right-Pointing-Pointer SEA practitioners successfully exercised power to influence decision-making. Black-Right-Pointing-Pointer Power dynamics are properties of actors' interactions in decision-making. Black-Right-Pointing-Pointer Power structures can be enabling and not solely limiting.

54 ENVIRONMENTAL SCIENCES↗