Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Krylov”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 289 records · Page 16

Quantum computing and quantum information storage

Quantum storage, transmission, and processing is the future of information technology. Here, the promise of quantum hardware stems from the inherent complexity of an entangled quantum system—the size of the wave-function scales exponentially with the number of particles, whether represented in real space or in a parameter space. In contrast, a classical N-body system can be completely represented by only 6N variables (positions and momenta of all particles). This complexity of quantum systems creates a yet-unsolved challenge of modeling quantum systems by means of classical computing—the curse of dimensionality. Indeed, although we can easily write the Schrödinger equation for any system of interacting nuclei and electrons, we can only solve it exactly on classical computers for very small systems.

97 MATHEMATICS AND COMPUTING↗

Extension of frozen natural orbital approximation to open-shell references: Theory, implementation, and application to single-molecule magnets

Natural orbitals are often used to achieve a more compact representation of correlated wave-functions. Using natural orbitals computed as eigenstates of the virtual–virtual block of the state density matrix instead of the canonical Hartree–Fock orbitals results in smaller errors when the same fraction of virtual space is frozen. This strategy, termed frozen natural orbital (FNO) approach, is effective in reducing the cost of regular coupled-cluster (CC) calculations and some multistate methods, such as EOM-IP-CC (equation-of-motion CC for ionization potentials). This contribution extends the FNO approach to the EOM-SF-CC ansatz (EOM-CC with spin-flip). In contrast to EOM-IP-CCSD, EOM-SF-CCSD relies on high-spin open-shell references. Using FNOs computed for an open-shell reference leads to an erratic behavior of the EOM-SF-CC energies and properties due to an inconsistent truncation of the α and β orbital spaces. A general solution to problems arising in the EOM-CC calculations utilizing open-shell references, termed OSFNO (open-shell FNO), is proposed. Furthermore, by means of singular value decomposition (SVD) of the overlap matrix of the α and β orbitals, the OSFNO algorithm identifies the corresponding orbitals and determines virtual orbitals corresponding to the singly occupied space. This is followed by SVD of the singlet part of the state density matrix in the remaining virtual orbital subspace. The so-computed FNOs preserve the spin purity of the open-shell orbital subspace to the extent allowed by the original reference, thus facilitating a safe truncation of the virtual space. The performance of OSFNO is benchmarked for selected diradicals and triradicals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effective Hamiltonians derived from equation-of-motion coupled-cluster wave functions: Theory and application to the Hubbard and Heisenberg Hamiltonians

Effective Hamiltonians, which are commonly used for fitting experimental observables, provide a coarse-grained representation of exact many-electron states obtained in quantum chemistry calculations; however, the mapping between the two is not trivial. In this contribution, we apply Bloch’s formalism to equation-of-motion coupled-cluster (EOM-CC) wave functions to rigorously derive effective Hamiltonians in the Bloch’s and des Cloizeaux’ forms. We report the key equations and illustrate the theory by application to systems with two or three unpaired electrons, which give rise to electronic states of covalent and ionic characters. We show that the Hubbard and Heisenberg Hamiltonians can be extracted directly from the so-obtained effective Hamiltonians. By establishing a quantitative connection between many-body states and simple models, the approach facilitates the analysis of the correlated wave functions. We propose a simple diagnostic for assessing the validity of the model space choice based on the overlaps between the target- and model-space states. Finally, artifacts affecting the quality of electronic structure calculations such as spin contamination are also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Calculation of spin–orbit couplings using RASCI spinless one-particle density matrices: Theory and applications

Here we present the formalism and implementation for calculations of spin–orbit couplings (SOCs) using the Breit–Pauli Hamiltonian and non-relativistic wave functions described by the restricted active space configuration interaction (RASCI) method with general excitation operators of spin-conserving spin-flipping, ionizing, and electron-attaching types. The implementation is based on the application of the Wigner–Eckart theorem within the spin space, which enables the calculation of the entire SOC matrix based on the explicit calculation of just one transition between the two spin multiplets. Numeric results for a diverse set of atoms and molecules highlight the importance of a balanced treatment of correlation and adequate basis sets and illustrate the overall robust performance of RASCI SOCs. The new implementation is a useful addition to the methodological toolkit for studying spin-forbidden processes and molecular magnetism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Equation-of-motion coupled-cluster method with double electron-attaching operators: Theory, implementation, and benchmarks

We report a production-level implementation of the equation-of-motion (EOM) coupled-cluster (CC) method with double electron-attaching (DEA) EOM operators of 2 p and 3 p 1 h types, EOM-DEA-CCSD. This ansatz, suitable for treating electronic structure patterns that can be described as two-electrons-in-many orbitals, represents a useful addition to the EOM-CC family of methods. We analyze the performance of EOM-DEA-CCSD for energy differences and molecular properties. By considering reduced quantities, such as state and transition one-particle density matrices, we compare EOM-DEA-CCSD wave functions with wave functions computed by other EOM-CCSD methods. The benchmarks illustrate that EOM-DEA-CCSD is capable of treating diradicals, bond-breaking, and some types of conical intersections.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Simulating excited-state complex ensembles: Fluorescence and solvatochromism in amine-arene exciplexes

Exciplexes are excited-state complexes formed as a result of partial charge transfer from the donor to the acceptor species when one moiety of the donor–acceptor pair is electronically excited. The arene–amine exciplex formed between oligo-(p-phenylene) (OPP) and triethylamine (TEA) is of interest in the catalytic photoreduction of CO2 because it can compete with complete electron transfer to the OPP catalyst. Therefore, formation of the exciplex can hinder the generation of a radical anion OPP·− necessary for subsequent CO2 reduction. We report an implementation of a workflow automating quantum-chemistry calculations that generate and characterize an ensemble of structures to represent this exciplex state. We use FireWorks, Pymatgen, and Custodian Python packages for high-throughput ensemble generation. The workflow includes time-dependent density functional theory optimization, verification of excited-state minima, and exciplex characterization with natural transition orbitals, exciton analysis, excited-state Mulliken charges, and energy decomposition analysis. Fluorescence spectra computed for these ensembles using Boltzmann-weighted contributions of each structure agree better with experiment than our previous calculations based on a single representative exciplex structure [Kron et al., J. Phys. Chem. A 126, 2319–2329 (2022)]. The ensemble description of the exciplex state also reproduces an experimentally observed red shift of the emission spectrum of [OPP-4–TEA]* relative to [OPP-3–TEA]*. The workflow developed here streamlines otherwise labor-intensive calculations that would require significant user involvement and intervention.

Chemistry↗

Influence of birefringent fibre joints on the visibility drift in a Mach – Zehnder interferometer

It is shown that imperfect joints of linear birefringent fibres in a fibre interferometer may result in an uncontrolled visibility drift under varying environmental conditions even with a standard phase matching device. As an example, a double Mach – Zehnder interferometer is considered, which is employed in schemes of quantum key distribution. Results of numerical simulation demonstrate the standard deviation of the quantum bit error rate (QBER), which is comparable to an average QBER value. (paper)

36 MATERIALS SCIENCE↗

On the prospects of optical cycling in diatomic cations: effects of transition metals, spin–orbit couplings, and multiple bonds

Molecules with optical cycling centers (OCCs) are highly desirable in the context of fundamental studies as well as applications (e.g., quantum computing) because they can be effectively cooled to very low temperatures by repeated absorption and emission (hence, cycling). Charged species offer additional advantages for experimental control and manipulation. Here, we present a systematic computational study of a series of diatomic radical-cations made of a d-block metal and a p-block ligand, that are isoelectronic (in their valence shell) to the successfully laser-cooled neutral molecules. Using high-level electronic structure methods, we characterize state and transition properties of low-lying electronic states and compute Franck-Condon factors. The computed branching ratios and radiative lifetimes reveal that the electronic transitions analogous to those successfully used in the laser cooling of neutral molecules are less than optimal in the cations. We propose alternative transitions suitable for optical cycling and highlight trends that could assist future designs of OCCs in charged or neutral molecules.

74 ATOMIC AND MOLECULAR PHYSICS↗

Resonant Inelastic X-Ray Scattering Reveals Hidden Local Transitions of the Aqueous OH Radical

Resonant inelastic x-ray scattering (RIXS) provides remarkable opportunities to interrogate ultrafast dynamics in liquids. In this work we use RIXS to study the fundamentally and practically important hydroxyl radical in liquid water, OH ( a q ) . Impulsive ionization of pure liquid water produced a short-lived population of OH ( a q ) , which was probed using femtosecond x-rays from an x-ray free-electron laser. We find that RIXS reveals localized electronic transitions that are masked in the ultraviolet absorption spectrum by strong charge-transfer transitions—thus providing a means to investigate the evolving electronic structure and reactivity of the hydroxyl radical in aqueous and heterogeneous environments. First-principles calculations provide interpretation of the main spectral features.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Operation and performance of the MEG II detector

Abstract The MEG II experiment, located at the Paul Scherrer Institut (PSI) in Switzerland, is the successor to the MEG experiment, which completed data taking in 2013. MEG II started fully operational data taking in 2021, with the goal of improving the sensitivity of the$$\upmu ^+ \rightarrow {\textrm{e}}^+ \upgamma $$ μ + → e + γ decay down to$$\sim 6 \times 10^{-14}$$ ∼ 6 × 10 - 14 almost an order of magnitude better than the current limit. In this paper, we describe the operation and performance of the experiment and give a new estimate of its sensitivity versus data acquisition time.

Physics↗

A search for $$\upmu ^+ \rightarrow \textrm{e}^+ \upgamma $$ with the first dataset of the MEG II experiment

Abstract The MEG II experiment, based at the Paul Scherrer Institut in Switzerland, reports the result of a search for the decay$$\upmu ^+ \rightarrow {\textrm{e}}^+ \upgamma $$ μ + → e + γ from data taken in the first physics run in 2021. No excess of events over the expected background is observed, yielding an upper limit on the branching ratio of$${\mathcal {B}} (\upmu ^+ \rightarrow {\textrm{e}}^+ \upgamma ) < 7.5 \times 10^{-13}$$ B ( μ + → e + γ ) < 7.5 × 10 - 13 (90% CL). The combination of this result and the limit obtained by MEG gives$${\mathcal {B}} (\upmu ^+ \rightarrow {\textrm{e}}^+ \upgamma ) < 3.1 \times 10^{-13}$$ B ( μ + → e + γ ) < 3.1 × 10 - 13 (90% CL), which is the most stringent limit to date. A ten-fold larger sample of data is being collected during the years 2022–2023, and data-taking will continue in the coming years.

Physics↗

Replicated Computational Results (RCR) Report for “Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software”

The article by Flegar et al. titled “Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software” presents a novel, practical implementation of an adaptive precision block-Jacobi preconditioner. Performance results using state-of-the-art GPU architectures for the block-Jacobi preconditioner generation and application demonstrate the practical usability of the method, compared to a traditional full-precision block-Jacobi preconditioner. A production-ready implementation is provided in the Ginkgo numerical linear algebra library. In this report, the Ginkgo library is reinstalled and performance results are generated to perform a comparison to the original results when using Ginkgo’s Conjugate Gradient solver with either the full or the adaptive precision block-Jacobi preconditioner for a suite of test problems on an NVIDIA GPU accelerator. After completing this process, the published results are deemed reproducible.

97 MATHEMATICS AND COMPUTING↗

PyAMG: Algebraic Multigrid Solvers in Python

PyAMG is a Python package of algebraic multigrid (AMG) solvers and supporting tools for approximating the solution to large, sparse linear systems of algebraic equations, Ax = b, where A is an n × n sparse matrix. Sparse linear systems arise in a range of problems in science, from fluid flows to solid mechanics to data analysis. While the direct solvers available in SciPy’s sparse linear algebra package (scipy.sparse.linalg) are highly efficient, in many cases iterative methods are preferred due to overall complexity. However, the iterative methods in SciPy, such as CG and GMRES, often require an efficient preconditioner in order to achieve a lower complexity. Preconditioning is a powerful tool whereby the conditioning of the linear system and convergence rate of the iterative method are both dramatically improved. PyAMG constructs multigrid solvers for use as a preconditioner in this setting. A summary of multigrid and algebraic multigrid solvers can be found in Olson (2015a), in Olson (2015b), and in Falgout (2006); a detailed description can be found in Briggs et al. (2000) and Trottenberg et al. (2001).

97 MATHEMATICS AND COMPUTING↗

Molecules Functionalized with Cycling Centers for Quantum Information Science

The ability for a single molecule to produce enough laser-induced fluorescence to control and detect its quantum state is known as optical cycling. This property has been used to great effect in atoms, where the relatively small number of states promotes their ability to repeatedly fluoresce, for applications such as laser cooling, precision measurement, atomic clocks, and quantum information processing. The extension of this capability to molecular species, however, has been difficult, primarily due to their propensity to become vibrationally excited during illumination. This project brought together experts from atomic physics, physical chemistry, and computational quantum chemistry to develop means to create molecules capable of optical cycling. In particular, this program sought to produce an optical cycling center (OCC), a quantum functional group capable of chemical attachment to a wide variety of molecular hosts while retaining (and thereby furnishing to its host) the ability to optically cycle. Following our team’s theoretical identification of promising species, including alkaline-earth phenoxides, we then created these species and in many cases confirmed their optical cycle closure. We now not only know of the existence of a handful of large, molecular species that can be deployed for applications in quantum technologies and measurement, but have improved our knowledge of the molecular mechanisms leading to this discovery, which will enable generalization in the future. The extension of these ideas for informed chemical design of cycling molecules with bespoke properties is now being pursued by multiple groups.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Theoretical framework for new magnetic materials for quantum computing and information storage. Final report for the Award No. DE-SC0018910

The focus of this grant was on molecular magnetic materials for information storage and quantum computing. We have been developing robust, first-principle methods for computing relevant electronic and magnetic properties of molecular building blocks (SMMs) of novel magnetic materials and quantum computers. These tools enable theoretical modeling of SMMs’ behavior, facilitating the interpretation of experimental studies and aiding the design of novel magnetic materials. Our strategy is based on the spin-flip (SF) approach, which extends the hierarchy of black-box single-reference methods to strongly correlated systems. Specifically, we developed general scalable algorithms and computer codes for calculating molecular properties, with an emphasis on spin-related properties, such as zero-field splittings, hyperfine couplings, and g-tensors. While our primary focus was on SF wave functions and SF-TDDFT, the underlying theory and computer codes were formulated using reduced density matrices, such that these tools are applicable to a broader class of methods. To extend the scope of applicability of wave-function-based SF methods to larger systems, we developed reduced-scaling approaches for the equation-of-motion coupled-cluster (EOM-CC) methods and continue developing libtensor (our open-source general tensor contraction library for many-body methods). We carried out extensive benchmarks and also carried out several applications.

36 MATERIALS SCIENCE↗

Q4Q: Quantum Computation for Quantum Prediction of Materials and Molecular Properties

We aim at exploring the potential of quantum computation to solve practical problems that are currently targeted by “traditional” high performance computing (HPC). Along the way, we will develop theoretical frameworks and algorithmic strategies. We propose computational research activities that will advance the application of quantum computers to selected materials/molecular properties: (1) Band structure of solids; (2) Molecular electronic/vibronic properties; (3) Free energies and phase transitions.

36 MATERIALS SCIENCE↗