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DOE OSTI2021

Statistical learning for predicting density–matrix-based electron dynamics

In this study, we consider the problem of learning density-dependent molecular Hamiltonian matrices from time series of electron density matrices, all in the context of Hartree–Fock theory. Prior work developed a solution to this problem for small molecular systems with density and Hamiltonian matrices of size at most 6 × 6. Here, using a battery of techniques, we scale prior methods to larger molecular systems with, for example, 29 × 29 matrices. This includes systems that either have more electrons or are expressed in large basis sets such as 6-311++G**. Scaling the method to larger systems enhances its relevance for realistic applications in chemistry and physics. To achieve this scaling, we apply dimensionality reduction, ridge regression and analytic computation of Hessians. Through the combination of these techniques, we are able to learn Hamiltonians by minimizing an objective function that encodes local propagation error. Importantly, these learned Hamiltonians can then be used to predict electron dynamics for thousands of steps: When we use our learned Hamiltonians to numerically solve the time-dependent Hartree–Fock equation, we obtain predicted dynamics that are in close quantitative agreement with ground truth dynamics. This includes field-off trajectories similar to the training data and field-on trajectories outside of the training data.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Classical and quantum simulations of 1+1-dimensional ${\mathbb{Z}}_{2}$ gauge theory at finite temperature and density

Simulating strongly coupled gauge theories at finite temperature and density is a longstanding challenge in nuclear and high-energy physics with fundamental implications for condensed matter physics. Here, we simulate such systems using minimally entangled typical thermal state (METTS) approaches, which combine classical random sampling with imaginary-time evolution, implementable on either classical or quantum computers, to estimate thermal averages of observables. We study 1+1-dimensional ${\mathbb{Z}}_{2}$ gauge theory coupled to spinless fermionic matter, which maps onto a local quantum spin chain. We benchmark both a classical matrix-product-state implementation of METTS and a recently proposed adaptive variational approach for near-term quantum devices, focusing on the equation of state and measures of fermion confinement. Of particular importance is the choice of basis for METTS sampling, which impacts both the sampling overhead and quantum circuit complexity. Our work sets the stage for future studies of strongly coupled gauge theories using classical and quantum hardware.

Chen, I-Chi [Iowa State Univ., Ames, IA (United St↗

DOE OSTI2021

Numerical Evidence for Many-Body Localization in Two and Three Dimensions

Disorder and interactions can lead to the breakdown of statistical mechanics in certain quantum systems, a phenomenon known as many-body localization (MBL). Much of the phenomenology of MBL emerges from the existence of localized-bits, or l-bits, a set of conserved quantities that are spatially localized and binary (i.e., possess only ±1 eigenvalues). While MBL and l-bits are known to exist in one-dimensional systems, their existence in dimensions greater than one is a key open question. To tackle this question, we develop an algorithm that can find approximate binary l-bits in arbitrary dimensions by adaptively generating a basis of operators in which to represent the l-bit. We use the algorithm to study four models: the one-, two-, and three-dimensional disordered Heisenberg models and the two-dimensional disordered hard-core Bose-Hubbard model. For all four of the models studied, our algorithm finds high-quality l-bits at large disorder strength and rapid qualitative changes in the distributions of l-bits in particular ranges of disorder strengths, suggesting the existence of MBL transitions. Furthermore, these transitions in the one-dimensional Heisenberg model and two-dimensional Bose-Hubbard model coincide well with past estimates of the critical disorder strengths in these models which further validates the evidence of MBL-like behavior in the other two and three-dimensional models we examine. In addition to finding MBL-like behavior in higher dimensions, our algorithm can be used to probe MBL in various geometries and dimensionality.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

The effect of hydrogen-bonding on flavin’s infrared absorption spectrum

Cluster and continuum solvation computational models are employed to model the effect of hydrogen bonding interactions on the vibrational modes of lumiflavin. Calculated spectra were compared to experimental Fourier-transform infrared (FTIR) spectra in the diagnostic 1450–1800 cm –1 range, where intense V C=C , V C=N , V C 2 =O , and V C 4 =O stretching modes of flavin’s isoalloxazine ring are found. Local mode analysis is used to describe the strength of hydrogen-bonding in cluster models. The computations indicate that V C=C and V C=N mode frequencies are relatively insensitive to intermolecular interactions while the V C 2 =O and V C 4 =O modes are sensitive to direct (and also indirect for V C 2 =O ) hydrogen-bonding interactions. Although flavin is neutral, basis sets without the diffuse functions provide incorrect relative frequencies and intensities. The 6-31+G* basis set is found to be adequate for this system, and there is limited benefit to considering larger basis sets. Calculated vibrational mode frequencies agree with experimentally determined frequencies in solution when cluster models with multiple water molecules are used. Accurate simulation of relative FTIR band intensities, on the other hand, requires a continuum (or possibly quantum mechanical/molecular mechanical) model that accounts for long-range electrostatic effects. Lastly, an experimental peak at ca. 1624 cm –1 that is typically assigned to the V C 2 =O vibrational stretching mode has a complicated shape that suggests multiple underlying contributions. Our calculations show that this band has contributions from both the C 6 –C 7 and C 2 = O stretching vibrations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Commercial Energy Code Compliance – Just the Facts, Ma’am

What percent of newly constructed commercial buildings comply with the energy code? How much energy and cost could be saved if the compliance increased? Which code requirements have both low compliance rates and high savings potential? These are the questions U.S. Department of Energy (DOE) is trying to answer through its Commercial Energy Code Field Study. Previous commercial studies have been very limited and did not result in a widely accepted and tested methodology. DOE’s goal is to create a standardized methodology that can produce actionable results at a reasonable study cost, that can be used by state and local governments and utilities and provides valuable information to policy makers. This paper builds on the methodology presented at the 2016 Summer Study and provides a first glimpse of the results as seen in the field. The field study team has implemented the pilot methodology, compiling a data set of over 200 office and retail buildings in climate zones 2A and 5A. The approach is based on identifying lost savings on a total energy cost basis rather than simply counting the quantity of measures that do not meet code. This paper will review the findings of that analysis, discuss critical aspects of the methodology, such as sampling and recruitment strategies, and identify areas where the greatest return—bang for the buck—exists in improving compliance with codes in commercial buildings. In addition, the team will make specific recommendations for jurisdictions looking to use the methodology to maximize energy code savings achieved in the field.

Cheslak, Kimberly↗

DOE OSTI2026

Custom-trained Machine-learning Interatomic Potentials: ZnCl2 Aqueous Solution

This dataset was generated using an iterative active-learning strategy implemented in the ArcaNN software package (https://github.com/arcann-chem/arcann_training) to train machine-learning interatomic potentials for aqueous ZnCl2 solutions. Each active-learning cycle consisted of three stages: training, exploration, and labeling. The initial training set combined configurations generated in this work from enhanced-sampling ab initio molecular dynamics simulations with configurations from a previously reported neural-network-potential study of aqueous ZnCl2. The enhanced-sampling ab initio molecular dynamics simulations involved Zn–Cl separation and the chloride coordination number around Zn²? as collective variables. These configurations served as the seed dataset. Subsequent active-learning cycles expanded the training set by identifying and labeling configurations that were poorly represented by the current models, thereby improving coverage of ion-association states and changes in local coordination and charge-state environments relevant to the solution free-energy landscape. For all selected configurations, single-point calculations of the total energies and atomic forces were performed within density functional theory using the CP2K Quickstep module. Reference calculations employed the revPBE-D3 and r2SCAN exchange-correlation functionals. Motivated by recent work on aqueous Zn²?, the main revPBE calculations omitted D3 dispersion contributions involving Zn²?, while retaining the D3 correction for water and chloride. For comparison, fully dispersion-corrected revPBE-D3 reference calculations were also performed, with D3 applied to all species, including Zn²?. Valence electrons were treated explicitly, while core electrons were represented using norm-conserving Goedecker–Teter–Hutter pseudopotentials. The wave functions were expanded using the mixed Gaussian-and-plane-wave scheme with TZV2P-MOLOPT basis sets for all elements and a 600 Ry auxiliary plane-wave cutoff for the electron density. Self-consistent-field convergence was accelerated using the orbital-transformation and Direct Inversion in the Iterative Subspace algorithms, with a convergence threshold of 10?6. All single-point calculations were performed in periodic orthorhombic cells. The CELL_REF keyword in CP2K was used to define a fixed reference cell with a box length of 25 Å. This treatment ensured a consistent reference for configurations extracted from NpT trajectories with fluctuating cell dimensions. The resulting DFT energies and atomic forces constitute the ground-truth labels used to train the MLIPs. The resulting MLIP was trained for aqueous ZnCl2 solutions spanning concentrations from 0 to 30 molal and a broad pH range, from strongly acidic to strongly basic conditions. Representative examples of configurations included in the MLIP training dataset are provided below. These include 1) Representative configurations from the dataset labeled at the revPBE-D3 level, with D3 dispersion interactions involving Zn2+ excluded (revPBE-wo-D3). 2) Representative configurations from the dataset labeled at the fully dispersion-corrected revPBE-D3 level, with D3 interactions applied to all species, including Zn2+ (revPBE-D3). 3) Representative configurations from the dataset labeled at the r2SCAN level of theory (r2SCAN).

Dinpajooh, Mohammadhasan [Pacific Northwest Nation↗

DOE OSTI2025

Design Basis Document / Owner’s Technical Specification for Nitrate Salt Systems in CSP Projects (Final Technical Report)

The number of commercial coal, gas, and nuclear projects built over the past 100 years number in the thousands. As such, there is a large database, available to a wide range of commercial engineering contractors, on proven designs. In essence, unsuccessful designs have, through generations of iterations, been identified and then deleted from further consideration. In contrast, the number of commercial parabolic trough projects using nitrate salt for the thermal storage media is perhaps 60. Further, the number of commercial central receiver projects using nitrate salt as the working fluid is on the order of 20, including estimates for China. Given the relative immaturity of salt technology, and commercial pressures to successfully bid new solar projects into a mature electricity market, solar projects often promise more than has been delivered. The Design Basis Document / Owner’s Technical Specification is a first step in the iteration process. The report describes the successful features of commercial projects, outlines a range equipment and system failures in projects that didn’t operate as intended, and provides a draft set of design changes intended to correct the known problems. The product of the study is 3 volumes of technical material; one volume is on parabolic trough technologies; a second is on central receiver technologies, and the third is on potential design changes to parabolic trough and central receiver projects. The 3 volumes, which total some 590 pages, can be found at https://www.solardynllc.com/csp-plant-technologies. One of the principal topics in the report is the use of functional or prescriptive specifications. Functional specifications describe what the equipment needs to do, consistent with the minimum legal requirements of the local jurisdictions. The details of how this is to be accomplished is developed by the engineering contractor. Prescriptive specifications, which are developed by the Owner, prescribe to the engineering contractor how the functional requirements are to be met. This arrangement ensures that the favorable experience from a previous project is repeated. One example is the design code for the hot salt tank in central receiver projects. The closest design basis is API Standard 650 Welded Steel Tanks for Oil Storage. However, the maximum design temperature in API 650 is 260 °C. As such, solar projects have typically adopted a hybrid Code approach, in which allowable material stresses are taken from ASME Section II Materials. Further, since the tanks experience daily changes in temperature and in (static) pressure, and since portions of the tank can operate at stresses beyond the elastic range, the low cycle fatigue life of the tank is conducted using the rules of Section VIII Division 2. However, in a recent study by NREL, the principal damage mechanism was identified as creep rather than fatigue. Further, design stresses permitted under Section VIII Division 2, corresponding to a fatigue life of 30 years, result in projected creep lifetimes of only 2 to 5 years. An alternate design approach, prescribed by the Owner, would be based on Code sections intended for high temperature service in the creep regime. A candidate is Section III Division 5. Granted, this is a nuclear code section, and it’s use would not likely be mandated by local jurisdictions. However, the effects of creep have been deemed to be of sufficient importance that one nuclear project developer, and one central receiver project developer, have stipulated in the tank design specification that the equipment be designed to the requirements of Section III Division 5.

14 SOLAR ENERGY↗

DOE OSTI2023

Density Matrix Implementation of the Fermi–Löwdin Orbital Self-Interaction Correction Method

The Fermi–Löwdin orbital self-interaction correction (FLOSIC) method effectively provides a transformation from canonical orbitals to localized Fermi–Löwdin orbitals which are used to remove the self-interaction error in the Perdew–Zunger (PZ) framework. This transformation is solely determined by a set of points in space, called Fermi–Löwdin descriptors (FODs), and the occupied canonical orbitals or the density matrix. In this work, we provide a detailed workflow for the implementation of the FLOSIC method for removal of self-interaction error in DFT calculations in an orbital-by-orbital basis that takes advantage of the unitary invariant nature of the FLOSIC method. In this way, it is possible to cast the self-consistent energy minimization at fixed FODs in the same manner than standard Kohn–Sham with one additional term in the Kohn–Sham Hamiltonian that introduces the PZ self-interaction correction. Each energy minimization iteration is divided in two substeps, one for the density matrix and one for the FODs. Expressions for the effective Kohn–Sham matrix and FOD gradients are provided such that its implementation is suitable for most electronic structure codes. Here, we analyze the convergence characteristics of the algorithm and present applications for the evaluation of NMR shielding constants and real-time time-dependent DFT simulations based on the Liouville–von Neumann equation to calculate excitation energies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Explicitly correlated coupled cluster method for accurate treatment of open-shell molecules with hundreds of atoms

We present a near-linear scaling formulation of the explicitly correlated coupled-cluster singles and doubles with the perturbative triples method [CCSD(T)F12¯] for high-spin states of open-shell species. The approach is based on the conventional open-shell CCSD formalism [M. Saitow et al., J. Chem. Phys. 146, 164105 (2017)] utilizing the domain local pair-natural orbitals (DLPNO) framework. The use of spin-independent set of pair-natural orbitals ensures exact agreement with the closed-shell formalism reported previously, with only marginally impact on the cost (e.g., the open-shell formalism is only 1.5 times slower than the closed-shell counterpart for the C160H322 n-alkane, with the measured size complexity of ≈1.2). Evaluation of coupled-cluster energies near the complete-basis-set (CBS) limit for open-shell systems with more than 550 atoms and 5000 basis functions is feasible on a single multi-core computer in less than 3 days. The aug-cc-pVTZ DLPNO-CCSD(T)F12¯ contribution to the heat of formation for the 50 largest molecules among the 348 core combustion species benchmark set [J. Klippenstein et al., J. Phys. Chem. A 121, 6580–6602 (2017)] had root-mean-square deviation (RMSD) from the extrapolated CBS CCSD(T) reference values of 0.3 kcal/mol. For a more challenging set of 50 reactions involving small closed- and open-shell molecules [G. Knizia et al., J. Chem. Phys. 130, 054104 (2009)], the aug-cc-pVQ(+d)Z DLPNO-CCSD(T)F12¯ yielded a RMSD of ∼0.4 kcal/mol with respect to the CBS CCSD(T) estimate.

Kumar, Ashutosh (ORCID:0000000175896030)↗

DOE OSTI2021

Rules of Use Report Engineering evaluations of nuclear material storage containers against the packaging requirements at TA-55

A set of obligations in the yearly storage container surveillance program, ensures that a retrospective approach is applied with loaded containers in inventory to confirm compliance with all “users” to ensure nuclear material storage container requirements are being followed. Validation that packaged containers are properly used, within a specific set of container types prescribed “bounding conditions of use,” is based on meeting requirements as identified in operating procedures associated with TA55-DOP-091, TA-55 Nuclear Material Packaging, and PA-RD-01022, Nuclear Material Packaging Requirements. The surveillance plan obligation requires the application of local area nuclear material accountability software or (LANMAS) to produce queries. The data queries are used to assess attributes of containers in storage these investigations are conducted on a bi-annual basis. This rules of use (ROU) compliance process ensures proper usage of storage containers as containment systems and therefore provides effective worker protection. It is structured as a supporting effort by implementing aspects of PA-AP-01207, Nuclear Material Container Safety Management at TA-55.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Engineering evaluations of nuclear material storage containers against the packaging requirements at TA-55 (FY22 Rules of Use Report)

36 MATERIALS SCIENCE↗

DOE OSTI2025

AI-Assisted Conceptual Development of a Pre-Geometric Cosmological Model - An Exercise in AI-Assisted Conceptual Framework Generation, Paper II: Local Geometry and Metric Structure

This paper develops the geometric sector of the replication-driven cosmogenesis framework introduced in Paper I. Starting from a pre-geometric spectral substrate and a minimal set of replication axioms, we show how coherent self-replicating units generate a spatial adjacency graph whose continuum limit acquires an effective Riemannian structure. The replication dynamics determines a characteristic correlation length that seeds the local metric, while overlap relations among coherent units produce an isotropic neighborhood geometry with an emergent dimensionality $d_{\rm eff}\simeq 3$ across a broad range of replication factors. As replication slows and causal order stabilizes, a limiting signal speed $c_\ast$ appears, providing the basis for the Lorentzian structure of spacetime without assuming a pre-existing light cone. We derive conditions under which the adjacency graph converges to a smooth three-dimensional manifold, describe the transition from Euclidean to Lorentzian propagation, and identify geometric invariants controlled by the replication parameters. This work establishes the geometric and causal layer of the replication cosmogenesis program, bridging the spectral axioms of Paper I to the cosmological dynamics explored in Paper III.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

A Scalable Space-Time Domain Decomposition Approach for Solving Large Scale Nonlinear Regularized Inverse Ill Posed Problems in 4D Variational Data Assimilation

We address the development of innovative algorithms designed to solve the strong-constraint Four Dimensional Variational Data Assimilation (4DVar DA) problems in large scale applications. We present a space-time decomposition approach which employs the whole domain decomposition, i.e. both along the spacial and temporal direction in the overlapping case, and the partitioning of both the solution and the operator. Starting from the global functional defined on the entire domain, we get to a sort of regularized local functionals on the set of sub domains providing the order reduction of both the predictive and the Data Assimilation models. The algorithm convergence is developed. Performance in terms of reduction of time complexity and algorithmic scalability is discussed on the Shallow Water Equations on the sphere. The number of state variables in the model, the number of observations in an assimilation cycle, as well as numerical parameters as the discretization step in time and in space domain are defined on the basis of discretization grid used by data available at repository Ocean Synthesis/Reanalysis Directory of Hamburg University.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Alternative approach to quantum imaginary time evolution

There is increasing interest in quantum algorithms (QAs) that are based on the imaginary time evolution (ITE), a successful classical numerical approach to obtain ground states. However, most of the proposals so far require heavy postprocessing computational steps on a classical computer, such as solving linear equations. Here we provide an alternative approach to implement ITE. A key feature in our approach is the use of an orthogonal basis set: the propagated state is efficiently expressed in terms of orthogonal basis states at every step of the evolution. We argue that the number of basis states needed at those steps to achieve an accurate solution can be kept on the order of n , the number of qubits, by controlling the precision (number of significant digits) and the imaginary time increment. The number of quantum gates per imaginary time step is estimated to be polynomial in n . Additionally, while in many QAs the locality of the Hamiltonian is a key assumption, in our algorithm this restriction is not required. This characteristic of our algorithm renders it useful for studying highly nonlocal systems, such as the occupation-representation nuclear shell model. Here, we illustrate our algorithm through numerical implementation on an IBM quantum simulator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Langevin dynamics of generalized spins as SU( N ) coherent states

Classical models of spin systems traditionally retain only the dipole moments, but a quantum spin state will frequently have additional structure. Spins of magnitude S have N = 2⁢S + 1 levels. Alternatively, the spin state is fully characterized by a set of N 2 - 1 local physical observables, which we interpret as generalized spin components. For example, a spin with S = 1 has three dipole components and five quadrupole components. Further, these components evolve under a generalization of the classical Landau-Lifshitz dynamics, which can be extended with noise and damping terms. In this paper, we reformulate the dynamical equations of motion as a Langevin dynamics of SU(N) coherent states in the Schrödinger picture. This viewpoint is especially useful as the basis for an efficient numerical method to sample spin configurations in thermal equilibrium and to simulate the relaxation and driven motion of topological solitons. To illustrate the approach, we simulate a nonequilibrium relaxation process that creates CP 2 skyrmions, which are topological defects with both dipole and quadrupole character.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Interpreting the Operando X-ray Absorption Near-Edge Structure of Supported Cu and CuPd Clusters in Conditions of Oxidative Dehydrogenation of Propane: Dynamic Changes in Composition and Size

Supported subnano-cluster catalysts are highly dynamic, developing true active sites only under the pressures and temperatures of reaction conditions. Operando X-ray absorption near-edge structure (XANES) spectroscopy can track changes in the oxidation state and the local environment of cluster atoms, providing insight into the development of these active sites. While bulk metal, oxide, and hydroxide standards are often used for fitting experimental XANES spectra to obtain average oxidation states, we recently showed that computed cluster standards of relevant compositions are a more suitable basis, producing more accurate fits. Here, we theoretically interpret the operando XANES of supported Cu 3 Pd and Cu 4 clusters during temperature-programmed reaction (TPRx) of oxidative dehydrogenation of propane. We use an expanded basis set including both globally optimized computed clusters and bulk standards. Not only can we track reversible composition/oxidation state change with temperature, but also the irreversible growth of the bulk fraction upon heating, which we attribute to cluster sintering. This has important implications for the mechanism of the catalyzed reaction and the nature of the available active sites. Here, we propose that operando XANES provides most significant insight into the nature of supported cluster catalysts in reaction conditions when interpreted using mixed computed cluster and bulk standards.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Exact constraints and appropriate norms in machine-learned exchange-correlation functionals

Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human-designed functionals derived to obey mathematical constraints known for the exact exchange-correlation functional. More recently, efforts have been made to reconcile the two techniques, integrating machine learning and exact-constraint satisfaction. We continue this integrated approach, designing a deep neural network that exploits the exact constraint and appropriate norm philosophy to de-orbitalize the strongly constrained and appropriately normed (SCAN) functional. The deep neural network is trained to replicate the SCAN functional from only electron density and local derivative information, avoiding the use of the orbital-dependent kinetic energy density. The performance and transferability of the machine-learned functional are demonstrated for molecular and periodic systems.

Artificial neural networks↗

DOE OSTI2024

Hybrid particle-spectral method for kinetic plasma simulations

A hybrid model for numerical solutions of the Vlasov–Poisson equations is presented, which blends spectral and particle approaches. The model splits the distribution function for plasma species into both spectral and particle representations in the velocity space to combine the advantages of each approach. The spectral representation leverages asymmetrically weighted Hermite basis, whereas the particle representation leverages the particle-in-cell method. Configuration phase space is decomposed with the Fourier method, which is well suited for periodic problems. We derive conservation equations for mass, momentum, and energy for the proposed combined method. It is shown that the coupling error between the two methods is absent in the semi-discrete setting (not taking into account time discretization). Finally, numerical test cases are presented simulating a weak electron beam interaction with plasma, leading to beam–plasma instability. The initially localized electron beam evolved into a highly non-equilibrium distribution function in the velocity space. A small growth rate and the resonance nature of instability make it difficult to obtain accurate solutions for purely particle methods due to noise, which falls as ∼1/Np with a number of particles. At the same time, purely spectral methods may require a large number of modes to capture the highly non-equilibrium state of the evolved beam. We show that the hybrid method is well suited for such problems: it reproduces the linear stage as well as nonlinear dynamics with sufficient accuracy using a highly non-equilibrium distribution function.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗