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At least 1,693 records · Page 94
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Three-body hyperspherical method with infinite angular expansions

The hyperspherical method based on infinite angular expansions is introduced. We approximate the cusp behavior of a wave function using B-spline techniques. Calculations for the ground-state energies of the atomic helium and the e{sup +}Li system are presented as two examples for testing this method. The computed ground-state energy of He is -2.903 724 a.u. with single particle orbitals l{sub max}=8. For the e{sup +}Li system, with l{sub max}=9, the ground-state energy is -0.250 83 a.u., which is better than the configuration interaction result of -0.250 107 82 a.u. with l{sub max}=30.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2013

Multireference symmetry-projected variational approaches for ground and excited states of the one-dimensional Hubbard model

We present a multireference configuration mixing scheme for describing ground and excited states, with well-defined spin and space-group symmetry quantum numbers, of the one-dimensional Hubbard model with nearest-neighbor hopping and periodic boundary conditions. Within this scheme, each state is expanded in terms of nonorthogonal and variationally determined symmetry-projected configurations. The results for lattices up to 30 and 50 sites compare well with the exact Lieb-Wu solutions as well as with results from other state-of-the-art approximations. In addition to spin-spin correlation functions in real space and magnetic structure factors, we present results for spectral functions and density of states computed with an Ansatz whose quality can be well controlled by the number of symmetry-projected configurations used to approximate the systems with $N_e$ and $N_e±1$ electrons. The intrinsic symmetry-broken determinants resulting from the variational calculations have rich structures in terms of defects that can be regarded as basic units of quantum fluctuations. Given the quality of the results here reported, as well as the parallelization properties of the considered scheme, we believe that symmetry-projection techniques, which have found ample applications in nuclear structure physics, deserve further attention in the study of low-dimensional correlated many-electron systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

On the accuracy of density functional theory and wave function methods for calculating vertical ionization energies

The best practice in computational methods for determining vertical ionization energies (VIEs) is assessed, via reference to experimentally determined VIEs that are corroborated by highly accurate coupled-cluster calculations. These reference values are used to benchmark the performance of density functional theory (DFT) and wave function methods: Hartree-Fock theory, second-order Møller-Plesset perturbation theory, and Electron Propagator Theory (EPT). The core test set consists of 147 small molecules. An extended set of six larger molecules, from benzene to hexacene, is also considered to investigate the dependence of the results on molecule size. The closest agreement with experiment is found for ionization energies obtained from total energy difference calculations. In particular, DFT calculations using exchange-correlation functionals with either a large amount of exact exchange or long-range correction perform best. The results from these functionals are also the least sensitive to an increase in molecule size. In general, ionization energies calculated directly from the orbital energies of the neutral species are less accurate and more sensitive to an increase in molecule size. For the single-calculation approach, the EPT calculations are in closest agreement for both sets of molecules. For the orbital energies from DFT functionals, only those with long-range correction give quantitative agreement with dramatic failing for all other functionals considered. The results offer a practical hierarchy of approximations for the calculation of vertical ionization energies. In addition, the experimental and computational reference values can be used as a standardized set of benchmarks, against which other approximate methods can be compared.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Kinetic theory for strongly coupled Coulomb systems

The calculation of dynamical properties for matter under extreme conditions is a challenging task. The popular Kubo-Greenwood model exploits elements from equilibrium density-functional theory (DFT) that allow a detailed treatment of electron correlations, but its origin is largely phenomenological; traditional kinetic theories have a more secure foundation but are limited to weak ion-electron interactions. The objective here is to show how a combination of the two evolves naturally from the short-time limit for the generator of the effective single-electron dynamics governing time correlation functions without such limitations. This provides a theoretical context for the current DFT-related approach, the Kubo-Greenwood model, while showing the nature of its corrections. The method is to calculate the short-time dynamics in the single-electron subspace for a given configuration of the ions. This differs from the usual kinetic theory approach in which an average over the ions is performed as well. In this way the effective ion-electron interaction includes strong Coulomb coupling and is shown to be determined from DFT. The correlation functions have the form of the random-phase approximation for an inhomogeneous system but with renormalized ion-electron and electron-electron potentials. The dynamic structure function, density response function, and electrical conductivity are calculated as examples. The static local field corrections in the dielectric function are identified in this way. The current analysis is limited to semiclassical electrons (quantum statistical potentials), so important quantum conditions are excluded. However, a quantization of the kinetic theory is identified for broader application while awaiting its detailed derivation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Chlorination of Hydrogenated Silicon Nanosheets Revealed by Solid-State Nuclear Magnetic Resonance Spectroscopy

We report two-dimensional silicon nanosheets (Si-NS) synthesized by topotactic deintercalation of CaSi 2 are hypothesized to consist of buckled layers of sp 3 -hybridized silicon atoms that are bonded to three other framework Si atoms and a terminal atom or functional group such as H, Cl, or OH. Here, we apply 1 H{ 35 Cl} and 29 Si{ 35 Cl} Resonance-Echo Saturation-Pulse DOuble-Resonance (RESPDOR) solid-state NMR experiments to directly confirm the presence of chlorinated Si atoms within Si-NS. Plotting the 1 H{ 35 Cl} RESPDOR dephasing as a function of the 35 Cl saturation pulse offset reveals that the 35 Cl quadrupolar coupling constant (C Q ) is 38 MHz, consistent with Cl atoms that are covalently bonded to silicon. Modeling the 1 H{ 35 Cl} RESPDOR dephasing curve shows that the Si–Si interlayer spacing is approximately 6 Å. Plane-wave density functional theory (DFT) calculations show that the direct band gap transition of the Si-NS decreases with increasing chlorination and hydroxylation, suggesting that the band gap of Si-NS can be tuned by modifying the terminal atoms or functional groups.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Toward Fast and Reliable Potential Energy Surfaces for Metallic Pt Clusters by Hierarchical Delta Neural Networks

Data-driven machine learning force fields (MLF) are more and more popular in atomistic simulations, and exploit machine learning methods to predict energies and forces for unknown structures based on the knowledge learned from an existing reference database. The latter usually comes from density functional theory calculations. One main drawback of MLFs is that physical laws are not incorporated in the machine learning models and instead, MLFs are designed to be very flexible to simulate complex quantum chemistry potential energy surface (PES). In general, MLFs have poor transferability, and hence a very large trainset is required to span all the target feature space to get a reliable MLF. This procedure becomes more troublesome when the PES is complicated, with a large number of degrees of freedom, in which building a large database is inevitable and very expensive, especially when accurate but costly exchange-correlation functionals have to be used. In this manuscript, we exploit a high dimensional neural network potential (HDNNP) on Pt clusters of size 6 to 20 as one example. Furthermore, our standard level of energy calculation is DFT GGA (PBE) using a plane wave basis set. We introduce an approximate but fast level with the PBE functional and a minimal atomic orbital basis set, then a more accurate but expensive level, using a hybrid functional or non-local vdw functional and a plane wave basis set, is reliably predicted by learning the difference with HDNNP. Findings show that such a differential approach (named ΔHDNNP) can deliver very accurate predictions (error < 10 meV/atom) in reference to converged basis set energies as well as more accurate but expensive xc functional. The overall speedup can be as large as 900 for 20 atom Pt cluster. More importantly, ΔHDNNP shows much better transferability due to the intrinsic smoothness of delta potential energy surface, and accordingly one can use much smaller trainset data to obtain better accuracy than the conventional HDNNP. A multi-layer ΔHDNNP is thus proposed to obtain very accurate predictions versus expensive non-local vdW functional calculations in which the required trainset is further reduced. The approach can be easily generalized to any other machine learning methods and opens a path to study the structure and dynamics of Pt clusters and nanoparticles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Evaluating Gaussian process metamodels and sequential designs for noisy level set estimation

Abstract We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic simulators, in particular with heavy-tailed simulation noise and low signal-to-noise ratio. To guard against noise misspecification, we assess the performance of three variants: (i) GPs with Student- t observations; (ii) Student- t processes (TPs); and (iii) classification GPs modeling the sign of the response. In conjunction with these metamodels, we analyze several acquisition functions for guiding the sequential experimental designs, extending existing stepwise uncertainty reduction criteria to the stochastic contour-finding context. This also motivates our development of (approximate) updating formulas to efficiently compute such acquisition functions. Our schemes are benchmarked by using a variety of synthetic experiments in 1–6 dimensions. We also consider an application of level set estimation for determining the optimal exercise policy of Bermudan options in finance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networks

There has been much recent interest in designing symmetry-aware neural networks (NNs) exhibiting relaxed equivariance. Such NNs aim to interpolate between being exactly equivariant and being fully flexible, affording consistent performance benefits. In a separate line of work, certain structured parameter matrices -- those with displacement structure, characterized by low displacement rank (LDR) -- have been used to design small-footprint NNs. Displacement structure enables fast function and gradient evaluation, but permits accurate approximations via compression primarily to classical convolutional neural networks (CNNs). In this work, we propose a general framework -- based on a novel construction of symmetry-based structured matrices -- to build approximately equivariant NNs with significantly reduced parameter counts. Our framework integrates the two aforementioned lines of work via the use of so-called Group Matrices (GMs), a forgotten precursor to the modern notion of regular representations of finite groups. GMs allow the design of structured matrices -- resembling LDR matrices -- which generalize the linear operations of a classical CNN from cyclic groups to general finite groups and their homogeneous spaces. We show that GMs can be employed to extend all the elementary operations of CNNs to general discrete groups. Further, the theory of structured matrices based on GMs provides a generalization of LDR theory focussed on matrices with cyclic structure, providing a tool for implementing approximate equivariance for discrete groups. We test GM-based architectures on a variety of tasks in the presence of relaxed symmetry. We report that our framework consistently performs competitively compared to approximately equivariant NNs, and other structured matrix-based compression frameworks, sometimes with a one or two orders of magnitude lower parameter count.

Samudre, Ashwin↗
DOE OSTI2015

Communication: Relation of centroid molecular dynamics and ring-polymer molecular dynamics to exact quantum dynamics

We recently obtained a quantum-Boltzmann-conserving classical dynamics by making a single change to the derivation of the “Classical Wigner” approximation. Here, we show that the further approximation of this “Matsubara dynamics” gives rise to two popular heuristic methods for treating quantum Boltzmann time-correlation functions: centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD). We show that CMD is a mean-field approximation to Matsubara dynamics, obtained by discarding (classical) fluctuations around the centroid, and that RPMD is the result of discarding a term in the Matsubara Liouvillian which shifts the frequencies of these fluctuations. These findings are consistent with previous numerical results and give explicit formulae for the terms that CMD and RPMD leave out.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Derivative-free robust optimization by outer approximations

We develop an algorithm for minimax problems that arise in robust optimization in the absence of objective function derivatives. The algorithm utilizes an extension of methods for inexact outer approximation in sampling a potentially infinite-cardinality uncertainty set. Clarke stationarity of the algorithm output is established alongside desirable features of the model-based trust-region subproblems encountered. We demonstrate the practical benefits of the algorithm on a new class of test problems.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

Density functional study on redox energetics of LaMO{sub 3−δ} (M=Sc–Cu) perovskite-type oxides

This study evaluates the redox energetics of LaMO{sub 3−δ} (M=Sc–Cu) perovskite-type oxides via generalized gradient approximation (GGA) to DFT. Two different approaches to redox energetics of oxygen deficient perovskites of strongly non-stoichiometric (δ=0.5) and dilute defect limits (δ→0) are studied. In the first approach the enthalpies of oxidation are calculated using the stoichiometric end-compounds of LaMO{sub 3} and LaMO{sub 2.5}. The most common structures for the reduced lanthanides and strontides similar to the ones experimentally reported for SrMnO{sub 2.5}, SrFeO{sub 2.5}, and LaNiO{sub 2.5} are considered. The second approach to the oxidation enthalpies termed (δ→0) follow the trend observed experimentally. This approach represents the experimental conditions of the measured oxygen enthalpies, and is hampered less by the artificial features due to spurious self-interaction errors in GGA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Transition metal dimer on Au(111) surface: A first principle study

The adsorption behaviour of transition metal dimers M{sub 2} (M= Cu, Ag, Au) on the Au(111) surface have been studied using the density functional theory formalism. The projector augmented wave method under the spin polarized version of generalized gradient approximation scheme was employed to calculate the total energy. The results suggest that all dimers prefer to orient in parallel to the surface plane, where two M atoms are adsorbed on two nearby threefold fcc sites. We have investigated the chemical interaction between M atoms and Au surface through electronic density of state analysis. It is found that on deposition, the electronic density of states (EDOS) of M{sub 2} dimer becomes broader in comparison to their gas phase spectrum.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Electrical and Optical Characteristics of Si-Nanoparticle Films Deposited onto Substrates by High-Voltage Electrospraying from Ethanol Sols

The optical and electrical characteristics of films consisting of nanocrystalline silicon (nc-Si) deposited onto substrates by the high-voltage electrospraying of nc-Si sols in ethanol are investigated. It is found that the interaction of ethanol droplets carrying Si nanoparticles with a corona-discharge electric field leads to the polymerization of ethanol and the formation of a polymer layer on the Si-nanoparticle surface. A high-voltage facility for depositing the films using an additional focusing electrode allows one to change the geometry of the electric field and intensity in the region of the ethanol droplet flow. As a result, nc-Si films with qualitatively different properties of the polymer on the nanoparticle surface are formed, specifically, nc-Si-A and nc-Si-B, obtained without a focusing electrode and with it, respectively. Upon annealing at temperatures of up to 400°С, the optical band gap E{sub g} of the nc-Si-A films increases from ~1.9 to ~2.2 eV, while the E{sub g} value of the nc-Si-B films remains constant and amounts to 1.85 eV. The constant E{sub g} value of the nc-Si-B films is explained by the properties of the polymer on the Si-nanoparticle surface and the more effective blocking of oxygen penetration from the surrounding environment upon annealing at temperatures of up to 400°C than in the case of a polymer in nc-Si-A films. The temperature dependences of the dark and photoinduced conductivity of nc-Si-A films are approximated with good accuracy by two activation-type exponential functions and the dark activation energies are ~0.75 and 0.1 eV, respectively. The conductivity of the nc-Si-A films noticeably decreases under irradiation of the samples at wavelengths of 460–470 nm. The temperature dependences of the conductivity of the nc-Si-B films are approximated with good accuracy by exponential functions with activation energies of 0.73 (in the dark) and 0.59 eV (under photoexcitation). In contrast to the case of nc-Si-A films, the photoconductivity of nc-Si-B films grows more than fourfold relative to the dark conductivity under analogous illumination. The nc-Si-B films are photoactive and sandwich-like Al/nc-Si-B/Al structures can generate a voltage. The dark conductivity and photoconductivity of the nc-Si-A films in the voltage range of V > 2 V are determined by the two-center Poole–Frenkel effect; the concentration of the centers affecting the Poole–Frenkel conductivity is ~3 × 10{sup 17} cm{sup –3}. In nc-Si-B films in the voltage range of 2–5 V, electron transport is determined by space-charge-limited currents and, at high voltages, by the two-center Poole–Frenkel effect. The concentration of traps contributing to the space-charge-limited currents is ~4 × 10{sup 16} cm{sup –3}. The concentration of Poole–Frenkel centers affecting the conductivity decreases according to the activation law with an activation energy of 0.7 eV from 3 × 10{sup 16} to 2 × 10{sup 14} cm{sup –3} with a decrease in temperature from 120°C to 40°C.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Does the 4f-shell contribute to bonding in tetravalent lanthanide halides?

Lanthanide tetrahalide molecules LnX{sub 4} (Ln = Ce, Pr, Tb; X = F, Cl, Br, I) have been investigated by density functional theory at the levels of the relativistic Zero Order Regular Approximation and the relativistic energy-consistent pseudopotentials, using frozen small- and medium-cores. The calculated bond lengths and vibrational frequencies are close to the experimental data. Our calculations indicate 4f shell contributions to bonding in LnX{sub 4}, in particular for the early lanthanides, which show significant overlap between the Ln 4f-shell and the halogen np-shells. The 4f shells contribute to Ln-X bonding in LnX{sub 4} about one third more than in LnX{sub 3}.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2015

WE-G-207-04: Non-Local Total-Variation (NLTV) Combined with Reweighted L1-Norm for Compressed Sensing Based CT Reconstruction

Purpose: Compressed sensing (CS) has been used for CT (4DCT/CBCT) reconstruction with few projections to reduce dose of radiation. Total-variation (TV) in L1-minimization (min.) with local information is the prevalent technique in CS, while it can be prone to noise. To address the problem, this work proposes to apply a new image processing technique, called non-local TV (NLTV), to CS based CT reconstruction, and incorporate reweighted L1-norm into it for more precise reconstruction. Methods: TV minimizes intensity variations by considering two local neighboring voxels, which can be prone to noise, possibly damaging the reconstructed CT image. NLTV, contrarily, utilizes more global information by computing a weight function of current voxel relative to surrounding search area. In fact, it might be challenging to obtain an optimal solution due to difficulty in defining the weight function with appropriate parameters. Introducing reweighted L1-min., designed for approximation to ideal L0-min., can reduce the dependence on defining the weight function, therefore improving accuracy of the solution. This work implemented the NLTV combined with reweighted L1-min. by Split Bregman Iterative method. For evaluation, a noisy digital phantom and a pelvic CT images are employed to compare the quality of images reconstructed by TV, NLTV and reweighted NLTV. Results: In both cases, conventional and reweighted NLTV outperform TV min. in signal-to-noise ratio (SNR) and root-mean squared errors of the reconstructed images. Relative to conventional NLTV, NLTV with reweighted L1-norm was able to slightly improve SNR, while greatly increasing the contrast between tissues due to additional iterative reweighting process. Conclusion: NLTV min. can provide more precise compressed sensing based CT image reconstruction by incorporating the reweighted L1-norm, while maintaining greater robustness to the noise effect than TV min.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Exploring the exact limits of the real-time equation-of-motion coupled cluster cumulant Green’s functions

In this paper, we analyze the properties of the recently proposed real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green’s function approach [Rehr et al., J. Chem. Phys. 152, 174113 (2020)]. We specifically focus on identifying the limitations of the original time-dependent coupled cluster (TDCC) ansatz and propose an enhanced double TDCC ansatz, ensuring the exactness in the expansion limit. In addition, we introduce a practical cluster-analysis-based approach for characterizing the peaks in the computed spectral function from the RT-EOM-CC cumulant Green’s function approach, which is particularly useful for the assignments of satellite peaks when many-body effects dominate the spectra. Our preliminary numerical tests focus on reproducing, approximating, and characterizing the exact impurity Green’s function of the three-site and four-site single impurity Anderson models using the RT-EOM-CC cumulant Green’s function approach. The numerical tests allow us to have a direct comparison between the RT-EOM-CC cumulant Green’s function approach and other Green’s function approaches in the numerical exact limit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Convergence of ray sequences of Frobenius-Padé approximants

Let σ-hat be a Cauchy transform of a possibly complex-valued Borel measure σ and {p_n} a system of orthonormal polynomials with respect to a measure μ, where supp(μ)∩supp(σ)=∅. An (m,n)th Frobenius-Padé approximant to σ-hat is a rational function P/Q, deg (P)≤m, deg (Q)≤n, such that the first m+n+1 Fourier coefficients of the remainder function Q σ-hat −P vanish when the form is developed into a series with respect to the polynomials p{sub n}. We investigate the convergence of the Frobenius-Padé approximants to σ-hat along ray sequences n/(n+m+1)→c>0, n−1≤m, when μ and σ are supported on intervals of the real line and their Radon-Nikodym derivatives with respect to the arcsine distribution of the corresponding interval are holomorphic functions. Bibliography: 30 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Characterizing large river sounds: Providing context for understanding the environmental effects of noise produced by hydrokinetic turbines

Underwaternoise associated with the installation and operation of hydrokinetic turbines in rivers and tidal zones presents a potential environmental concern for fish and marine mammals. Comparing the spectral quality of sounds emitted by hydrokinetic turbines to natural and other anthropogenic sound sources is an initial step at understanding potential environmental impacts. Underwater recordings were obtained from passing vessels and natural underwater sound sources in static and flowing waters. Static water measurements were taken in a lake with minimal background noise. Flowing water measurements were taken at a previously proposed deployment site for hydrokinetic turbines on the Mississippi River, where sounds created by flowing water are part of all measurements, both natural ambient and anthropogenic sources. Vessel sizes ranged from a small fishing boat with 60 hp outboard motor to an 18-unit barge train being pushed upstream by tugboat. As expected, large vessels with large engines created the highest sound levels, which were, on average, 40 dB greater than the sound created by an operating hydrokinetic turbine. As a result, a comparison of sound levels from the same sources at different distances using both spherical and cylindrical sound attenuation functions suggests that spherical model results more closely approximate observed sound attenuation.

54 ENVIRONMENTAL SCIENCES↗