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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A fast approximation to supershell partition functions

A formula for supershell partition functions, which play a major role in the Super Transition Array approach to radiative-opacity calculations, is derived as a functional of the distribution of energies within the supershell. It consists in an alternative expansion for an arbitrary number of electrons or holes which also allows for quick approximate evaluations with truncated number of terms in the expansion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2017

Methods of Constructing a Blended Performance Function Suitable for Formation Flight

This paper presents two methods for constructing an approximate performance function of a desired parameter using correlated parameters. The methods are useful when real-time measurements of a desired performance function are not available to applications such as extremum-seeking control systems. The first method approximates an a priori measured or estimated desired performance function by combining real-time measurements of readily available correlated parameters. The parameters are combined using a weighting vector determined from a minimum-squares optimization to form a blended performance function. The blended performance function better matches the desired performance function mini- mum than single-measurement performance functions. The second method expands upon the first by replacing the a priori data with near-real-time measurements of the desired performance function. The resulting blended performance function weighting vector is up- dated when measurements of the desired performance function are available. Both methods are applied to data collected during formation- flight-for-drag-reduction flight experiments.

control systems↗
DOE OSTI2015

Statistics of time delay and scattering correlation functions in chaotic systems. II. Semiclassical approximation

We consider S-matrix correlation functions for a chaotic cavity having M open channels, in the absence of time-reversal invariance. Relying on a semiclassical approximation, we compute the average over E of the quantities Tr[S{sup †}(E − ϵ) S(E + ϵ)]{sup n}, for general positive integer n. Our result is an infinite series in ϵ, whose coefficients are rational functions of M. From this, we extract moments of the time delay matrix Q = − iħS{sup †}dS/dE and check that the first 8 of them agree with the random matrix theory prediction from our previous paper [M. Novaes, J. Math. Phys. 56, 062110 (2015)].

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2003

Approximating the Helium Wavefunction in Positronium-Helium Scattering

In the Kohn variational treatment of the positronium- hydrogen scattering problem the scattering wave function is approximated by an expansion in some appropriate basis set, but the target and projectile wave functions are known exactly. In the positronium-helium case, however, a difficulty immediately arises in that the wave function of the helium target atom is not known exactly, and there are several ways to deal with the associated eigenvalue in formulating the variational scattering equations to be solved. In this work we will use the Kohn variational principle in the static exchange approximation to d e t e e the zero-energy scattering length for the Ps-He system, using a suite of approximate target functions. The results we obtain will be compared with each other and with corresponding values found by other approximation techniques.

DiRienzi, Joseph↗
DOE OSTI2020

Simple hydrogenic estimates for the exchange and correlation energies of atoms and atomic ions, with implications for density functional theory

Exact density functionals for the exchange and correlation energies are approximated in practical calculations for the ground-state electronic structure of a many-electron system. An important exact constraint for the construction of approximations is to recover the correct non-relativistic large-Z expansions for the corresponding energies of neutral atoms with atomic number Z and electron number N = Z, which are correct to leading order (–0.221 Z 5/3 and –0.021 Z ln Z respectively) even in the lowest-rung or local density approximation. We find that hydrogenic densities lead to E x (N,Z) ≈ –0.354 N 2/3 Z (as known before only for Z >> N >> 1) and E c ≈ –0.02 N ln N . These asymptotic estimates are most correct for atomic ions with large N and Z >> N, but we find that they are qualitatively and semi- quantitatively correct even for small N and for N ≈ Z. The large-N asymptotic behavior of the energy is pre-figured in small-N atoms and atomic ions, supporting the argument that widely-predictive approximate density functionals should be designed to recover the correct asymptotics. Here, it is shown that the exact Kohn-Sham correlation energy, when calculated from the pure ground-state wavefunction, should have no contribution proportional to Z in the Z → ∞ limit for any fixed N.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation

Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1982

Heats of formation and thermodynamic functions for C2H, C3H, and C4H from 300 K to 6000 K

A review of the energy level and heat of formation data for the species C2H, C3H, and C4H is given. The procedure for computing thermochemical data from partition function is also reviewed. Working expressions for approximate partition functions, free-energy function, enthalpy function, and heat capacity for a linear polyatomic species are presented.

Saturno, A. F.↗
DOE OSTI2023

Assessing the Role of Interfacial and Metal Sites in Pt/TiO2-Catalyzed Acetic Acid Hydrodeoxygenation

Thermochemical conversion of biomass to produce drop-in quality biofuels typically involves hydrodeoxygenation (HDO) steps following catalytic fast pyrolysis (CFP) to remove excess oxygen and create a more-stable bio-oil product. HDO reactions are performed by co-feeding the CFP vapor-phase product and H2 gas over a bi-functional catalyst. Noble-metal catalysts supported on reducible metal oxides (e.g., Pt/TiO2) are active and selective toward these HDO reactions. Griffin and co-workers showed that Pt/TiO2 catalysts promote the desired deoxygenation steps for m-cresol HDO while mitigating undesired C-C bond-breaking steps that reduce the overall value/energy density of the biofuel. Such model-compound studies to inform the design of improved catalysts for HDO chemistry are necessary to improve the overall process economics/efficiencies for biofuels production. One important class of bio-derived compounds that has not been studied extensively with respect to HDO chemistry, particularly at the atomic level, is carboxylic acids. Past experimental work indicates that Pt/C and Pt/TiO2 catalysts are selective toward C-C and C-O bond-dissociation products for acetic acid HDO, respectively. To understand the role of Pt/TiO2 active sites in this observed change in selectivity and guide catalyst development, the work in this presentation focuses on modeling the role of Pt-metal and Pt-TiO2-interfacial sites in promoting key C-C bond-breaking, C-O bond-breaking, and (de)hydrogenation steps in acetic acid HDO. Density functional theory (DFT) calculations were performed using the Vienna Ab initio Simulation Package (VASP). The exchange-correlation functional was approximated by the Perdew-Burke-Ernzerhof functional. Dispersion interactions were captured using the D3 method. Projector augmented-wave potentials described electron-ion interactions, and electron wavefunctions were expanded via a planewave basis with an energy cutoff of 500 eV. Activation barriers were calculated using the climbing image nudged elastic band method. Results and Discussion: To discern the role of Pt-metal and Pt-TiO2 interface sites in promoting acetic acid HDO chemistry, Pt(111) slab and anatase TiO2(101)-supported Pt-nanowire (PtNW/OH-TiO2) surface models were constructed, respectively. Because H2 is co-fed in HDO reactions, the anatase support was terminated with OH groups. Interfacial vacancies have been shown to facilitate Ru/TiO2-catalyzed phenol HDO; thus, an interfacial model with an OH vacancy was also considered (PtNW/OHv-TiO2). Pt-TiO2-interface sites stabilize adsorption of all studied acetic acid HDO surface intermediates relative to terrace Pt-metal sites, particularly when an interfacial-OH vacancy is present. Oxygenated species prefer to bind at the OH vacancy through the O atom, suggesting a preference for C-O over C-C bond cleavage at these sites. This hypothesis is supported by net-negative and net-positive average shifts in the reaction energy and activation energy barriers for C-O and C-C bond-breaking steps, respectively, at Pt-TiO2-interface sites relative to Pt-metal sites. Using the calculated energetics, the predicted minimum-energy pathway was determined for each surface. Pt(111) is predicted to follow decarboxylation, producing undesired methane and carbon dioxide. Conversely, PtNW/OH-TiO2 and PtNW/OHv-TiO2 are both predicted to produce desired acetaldehyde and ethane. The interfacial vacancy may also play a key role in facilitating the first C-O bond-breaking step in acetic acid HDO, lowering the barrier by 0.6 eV relative to the defect-free interface model. These results demonstrate the critical role of the Pt-TiO2 interface in the shift in acetic acid HDO selectivity experimentally observed on Pt/C and Pt/TiO2 catalysts. The results herein demonstrate the important role of the Pt-TiO2 interface and interfacial oxygen vacancies in improving the carbon efficiency for HDO reactions in CFP upgrading.

BIOMASS FUELS,INORGANIC, ORGANIC, PHYSICAL, AND AN↗
DOE OSTI2019

An analytic expression approximating the Debye heat capacity function

It is important to have analytic expressions for critical functions in the equations of state of materials. The Debye model has been very successful in approximating the thermal energy properties of a variety of solids, but is nonanalytic. Existing approximations suffer from various shortcomings, the most common being lack of applicability over some temperature range. A new analytic and integrable functional form that closely approximates the Debye model for the heat capacity is presented. This form, based on the mean of two Einstein heat capacity functions with a low temperature correction, exhibits deviations from the Debye model smaller than typical experimental scatter in heat capacity data.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Generalized Optimized Effective Potential for Orbital Functionals and Self-Consistent Calculation of Random Phase Approximations

A new self-consistent procedure for calculating the total energy with an orbital-dependent density functional approximation (DFA), the generalized optimized effective potential (GOEP), is developed in the present work. The GOEP is a nonlocal Hermitian potential that delivers the sets of occupied and virtual orbitals and minimizes the total energy. The GOEP optimization leads to the same minimum as does the orbital optimization. The GOEP method is promising as an effective optimization approach for orbital-dependent functionals, as demonstrated for the self-consistent calculations of the random phase approximation (RPA) to the correlation functionals in the particle–hole (ph) and particle–particle (pp) channels. The results show that the accuracy in describing the weakly interacting van der Waals systems is significantly improved in the self-consistent calculations. In particular, the important single excitations contribution in non-self-consistent RPA calculations can be captured self-consistently through the GOEP optimization, leading to orbital renormalization, without using the single excitations in the energy functional.

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

Excitation Energies from the Single-Particle Green’s Function with the GW Approximation

Quasi-particle energies are vital to predicting molecular ionization energies and bulk band structures. The state-of-the-art method for quasi-particle energy calculations, particularly for bulk systems, is the GW approximation. For excited state calculations, one needs to go beyond the GW approximation. The Bethe–Salpeter equation (BSE) is the commonly used approach for bulk-system excited state calculations beyond the GW approximation, which is accurate but computationally cumbersome. In this Article, we create a new method to extract excitation energies directly from the quasi-particle energies based on the GW approximation. Starting from the (N – 1)-electron system, we are able to calculate molecular excitation energies with orbital energies at the GW level for HOMO excitations. Our calculations demonstrate that this method can accurately capture low-lying local excitations as well as charge transfer excitations in many molecular systems. This approach is shown to outperform the time-dependent density functional theory (TDDFT) and are comparable with higher level excited state calculations, including the equation-of-motion couple cluster (EOM-CC) theory and the BSE, but with less computational effort. This new approach provides an efficient alternative to the BSE method for accurate excited state calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Universal approximation of symmetric and anti-symmetric functions

In this work, we consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations. We give constructive approximations with explicit bounds on the number of parameters with respect to the dimension and the target accuracy ϵ. While the approximation still suffers from the curse of dimensionality, to the best of our knowledge, these are the first results in the literature with explicit error bounds for functions with symmetry or anti-symmetry constraints

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Locality of correlation in density functional theory

The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that E{sub C} → −A{sub C} ZlnZ + B{sub C}Z as Z → ∞, where Z is the atomic number, A{sub C} is known, and we estimate B{sub C} to be about 37 mhartree. The local density approximation yields A{sub C} exactly, but a very incorrect value for B{sub C}, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with B{sub C} a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed.

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

Computing partition functions in the one-clean-qubit model

We present a method to approximate partition functions of quantum systems using mixed-state quantum computation. For positive-semidefinite Hamiltonians, our method has an expected running-time that is almost linear in [M/( ε rel Z )] 2 , where M is the dimension of the quantum system, Z is the partition function, and ε rel is the relative precision. It is based on approximations of the exponential operator as linear combinations of certain operators related to block-encoding of Hamiltonians or Hamiltonian evolutions. The trace of each operator is estimated using a standard algorithm in the one-clean-qubit model. For large values of Z , our method may run faster than exact classical methods, whose complexities are polynomial in M . We also prove that a version of the partition function estimation problem within additive error is complete for the so-called DQC1 complexity class, suggesting that our method provides a superpolynomial speedup for certain parameter values. Overall, to attain a desired relative precision, we develop a classical procedure based on a sequence of approximations within predetermined additive errors that may be of independent interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Approximating Density Probability Distribution Functions Across Cosmologies

Using a suite of self-similar cosmological simulations, we measure the probability distribution functions (PDFs) of real-space density, redshift-space density, and their geometric mean. We find that the real-space density PDF is well-described by a function of two parameters: ns, the spectral slope, and σL, the linear rms density fluctuation. For redshift-space density and the geometric mean of real- and redshift-space densities, we introduce a third parameter, ${s}_{L}=\sqrt{\langle {\left({{dv}}_{\mathrm{pec}}^{L}/{dr}\right)}^{2}\rangle }/H$. We find that density PDFs for the LCDM cosmology is also well-parameterized by these three parameters. As a result, we are able to use a suite of self-similar cosmological simulations to approximate density PDFs for a range of cosmologies. We make the density PDFs publicly available and provide an analytical fitting formula for them.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Non-adiabatic approximations in time-dependent density functional theory: progress and prospects

Time-dependent density functional theory continues to draw a large number of users in a wide range of fields exploring myriad applications involving electronic spectra and dynamics. Although in principle exact, the predictivity of the calculations is limited by the available approximations for the exchange-correlation functional. In particular, it is known that the exact exchange-correlation functional has memory-dependence, but in practise adiabatic approximations are used which ignore this. Here we review the development of non-adiabatic functional approximations, their impact on calculations, and challenges in developing practical and accurate memory-dependent functionals for general purposes.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Calculation and interpretation of classical turning surfaces in solids

Abstract Classical turning surfaces of Kohn–Sham potentials separate classically allowed regions (CARs) from classically forbidden regions (CFRs). They are useful for understanding many chemical properties of molecules but need not exist in solids, where the density never decays to zero. At equilibrium geometries, we find that CFRs are absent in perfect metals, rare in covalent semiconductors at equilibrium, but common in ionic and molecular crystals. In all materials, CFRs appear or grow as the internuclear distances are uniformly expanded. They can also appear at a monovacancy in a metal. Calculations with several approximate density functionals and codes confirm these behaviors. A classical picture of conduction suggests that CARs should be connected in metals, and disconnected in wide-gap insulators, and is confirmed in the limits of extreme compression and expansion. Surprisingly, many semiconductors have no CFR at equilibrium, a key finding for density functional construction. Nonetheless, a strong correlation with insulating behavior can still be inferred. Moreover, equilibrium bond lengths for all cases can be estimated from the bond type and the sum of the classical turning radii of the free atoms or ions.

Chemistry↗
DOE OSTI2017

Identifying attributes of CO 2 leakage zones in shallow aquifers using a parametric level set method: Original Research Article: Identifying attributes of CO 2 leakage zones in shallow aquifers using a parametric level set method

Leakage through abandoned wells and geologic faults poses the greatest risk to CO 2 storage permanence. For shallow aquifers, secondary CO 2 plumes emanating from the leak zones may go undetected for a sustained period of time and has the greatest potential to cause large-scale and long-term environmental impacts. Identification of the attributes of leak zones, including their shape, location, and strength, is required for environmental risk assessment. This study applies a parametric level set (PaLS) method to characterize leak zones. Level set methods are appealing for tracking topological changes and recovering unknown shapes of objects. However, level set evolution using the conventional level set methods is computationally challenging. In PaLS, the level set function is approximated by using a weighted sum of basis functions and the level set evolution problem is replaced by an optimization problem. The efficacy of PaLS is demonstrated by reconstructing attributes of a CO 2 leak zone in a carbonate aquifer. Our results show that PaLS is a robust source identification method that can recover the approximate leak zone locations in the presence of measurement errors, model parameter uncertainty, and inaccurate guesses of source flux strengths. Accurate delineation of source geometry is achievable when a relatively dense observation network is used. The PaLS-based, source recovery framework introduced in this work is generic and can be adapted for any reactive transport model by simply switching the pre- and post-processing routines.

54 ENVIRONMENTAL SCIENCES↗