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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.

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At least 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Multimodal Bayesian registration of noisy functions using Hamiltonian Monte Carlo

Functional data registration is a necessary processing step for many applications. The observed data can be inherently noisy, often due to measurement error or natural process uncertainty; which most functional alignment methods cannot handle. A pair of functions can also have multiple optimal alignment solutions, which is not addressed in current literature. In this paper, a flexible Bayesian approach to functional alignment is presented, which appropriately accounts for noise in the data without any pre-smoothing required. Additionally, by running parallel MCMC chains, the method can account for multiple optimal alignments via the multi-modal posterior distribution of the warping functions. To most efficiently sample the warping functions, the approach relies on a modification of the standard Hamiltonian Monte Carlo to be well-defined on the infinite-dimensional Hilbert space. In this work, this flexible Bayesian alignment method is applied to both simulated data and real data sets to show its efficiency in handling noisy functions and successfully accounting for multiple optimal alignments in the posterior; characterizing the uncertainty surrounding the warping functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Towards an Optimal Gradient-dependent Energy Functional of the PZ-SIC Form

Results of Perdew–Zunger self-interaction corrected (PZ-SIC) density functional theory calculations of the atomization energy of 35 molecules are compared to those of high-level quantum chemistry calculations. While the PBE functional, which is commonly used in calculations of condensed matter, is known to predict on average too high atomization energy (overbinding of the molecules), the application of PZ-SIC gives a large overcorrection and leads to significant underestimation of the atomization energy. The exchange enhancement factor that is optimal for the generalized gradient approximation within the Kohn-Sham (KS) approach may not be optimal for the self-interaction corrected functional. The PBEsol functional, where the exchange enhancement factor was optimized for solids, gives poor results for molecules in KS but turns out to work better than PBE in PZ-SIC calculations. The exchange enhancement is weaker in PBEsol and the functional is closer to the local density approximation. Furthermore, the drop in the exchange enhancement factor for increasing reduced gradient in the PW91 functional gives more accurate results than the plateaued enhancement in the PBE functional. A step towards an optimal exchange enhancement factor for a gradient dependent functional of the PZ-SIC form is taken by constructing an exchange enhancement factor that mimics PBEsol for small values of the reduced gradient, and PW91 for large values. The average atomization energy is then in closer agreement with the high-level quantum chemistry calculations, but the variance is still large, the F 2 molecule being a notable outlier.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Multicomponent density functional theory embedding formulation

Multicomponent density functional theory (DFT) methods have been developed to treat two types of particles, such as electrons and nuclei, quantum mechanically at the same level. In the nuclear-electronic orbital (NEO) approach, all electrons and select nuclei, typically key protons, are treated quantum mechanically. For multicomponent DFT methods developed within the NEO framework, electron-proton correlation functionals based on explicitly correlated wavefunctions have been designed and used in conjunction with well-established electronic exchange-correlation functionals. Herein a general theory for multicomponent embedded DFT is developed to enable the accurate treatment of larger systems. In the general theory, the total electronic density is separated into two subsystem densities, denoted as regular and special, and different electron-proton correlation functionals are used for these two electronic densities. In the specific implementation, the special electron density is defined in terms of spatially localized Kohn-Sham electronic orbitals, and electron-proton correlation is included only for the special electron density. The electron-proton correlation functional depends on only the special electron density and the proton density, whereas the electronic exchange-correlation functional depends on the total electronic density. This scheme includes the essential electron-proton correlation, which is a relatively local effect, as well as the electronic exchange-correlation for the entire system. This multicomponent DFT-in-DFT embedding theory is applied to the HCN and FHF{sup −} molecules in conjunction with two different electron-proton correlation functionals and three different electronic exchange-correlation functionals. The results illustrate that this approach provides qualitatively accurate nuclear densities in a computationally tractable manner. The general theory is also easily extended to other types of partitioning schemes for multicomponent systems.

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

Exchange-correlation energies of atoms from efficient density functionals: influence of the electron density

The primary goal of Kohn–Sham density functional theory is to evaluate the exchange-correlation contribution to electronic properties. However, the accuracy of a density functional can be affected by the electron density. Here we apply the nonempirical Tao–Mo (TM) semilocal functional to study the influence of the electron density on the exchange and correlation energies of atoms and ions, and compare the results with the commonly used nonempirical semilocal functionals local spin-density approximation (LSDA), Perdew–Burke–Ernzerhof (PBE), Tao–Perdew–Staroverov–Scuseria (TPSS), and hybrid functional PBE0. We find that the spin-restricted Hartree–Fock density yields the exchange and correlation energies in good agreement with the Optimized Effective Potential method, particularly for spherical atoms and ions. However, the errors of these semilocal and hybrid functionals become larger for self-consistent densities. We further find that the quality of the electron density have greater effect on the exchange-correlation energies of kinetic energy density-dependent meta-GGA functionals TPSS and TM than on those of the LSDA and GGA, and therefore, should have greater influence on the performance of meta-GGA functionals. Lastly, we show that the influence of the density quality on PBE0 is slightly reduced, compared to that of PBE, due to the exact mixing.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Comparative study of Minnesota functionals performance on ferroelectric BaTiO 3 and PbTiO 3

Density functional theory based simulations are the leading tool for the computational investigation of ferroelectrics and the parametrization of their classical potentials. However, the predictions often depend strongly on the exchange correlation functional. The most popular choices, LDA and GGA, tend to underestimate or overestimate some structural, electric, and energy properties. These impede development of highly accurate classical potentials that extend the reach of first-principles simulations to finite temperatures and realistic sizes. In this work, we investigate the performance of recently developed Minnesota exchange correlation functionals on prototypical ferroelectrics BaTiO 3 , and PbTiO 3 , in comparison with some popular ones. We find that there exists strong correlation between predictions for some properties (tetragonality, phase energy difference, and polarization) by different functionals. Along the correlation line, we find a range of functionals (including some from the Minnesota suite) whose predictions fall in between those of LDA and GGA and, therefore, offer an improvement. A way to relatively rank functional performance with respect to chosen benchmarks is proposed and applied to identify the top performers for BaTiO 3 and PbTiO 3 . Here, the performance is found to be material dependent. Therefore, we propose that the performance assessment carried out in this work is employed to "screen" functionals prior to their use on ferroelectrics. Quick and computationally inexpensive, it is likely to lead to improved descriptions, especially for classical potential parametrization. The Minnesota functional suite is found to be suitable for this task.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Leaf traits and canopy structure together explain canopy functional diversity: an airborne remote sensing approach

Plant functional diversity is strongly connected to photosynthetic carbon assimilation in terrestrial ecosystems. However, many of the plant functional traits that regulate photosynthetic capacity, including foliar nitrogen concentration and leaf mass per area, vary significantly between and within plant functional types and vertically through forest canopies, resulting in considerable landscape-scale heterogeneity in three dimensions. Hyperspectral imagery has been used extensively to quantify functional traits across a range of ecosystems but is generally limited to providing information for top-of-canopy leaves only. On the other hand, lidar data can be used to retrieve the vertical structure of forest canopies. Because these data are rarely collected at the same time, there are unanswered questions about the effect of forest structure on the 3-D spatial patterns of functional traits across ecosystems. In the United States, the National Ecological Observatory Network's Airborne Observation Platform (NEON AOP) provides an opportunity to address this structure-function relationship by collecting lidar and hyperspectral data together across a variety of ecoregions. With a fusion of hyperspectral and lidar data from the NEON AOP and field-collected foliar trait data, we assessed the impacts of forest structure on spatial patterns of N. In addition, we examine the influence of abiotic gradients and management regimes on top of canopy %N and total canopy N (i.e. the total amount of N (g/m 2 ) within a forest canopy) at a NEON site consisting of a mosaic of open longleaf pine and dense broadleaf deciduous forests. Here, our resulting maps suggest that in contrast with top-of-canopy values, total canopy N variation is dampened across this landscape resulting in relatively homogeneous spatial patterns. At the same time, we found that leaf functional diversity and canopy structural diversity showed distinct dendritic patterns related to the spatial distribution of plant functional types.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Performance of density functionals for modeling vapor liquid equilibria of CO 2 and SO 2

Vapor liquid equilibria (VLE) and condensed phase properties of carbon dioxide and sulfur dioxide are calculated using first principles Monte Carlo (FPMC) simulations to assess the performance of several density functionals, notably PBE-D3, BLYP-D3,PBE0-D3, M062X-D3, and rVV10. GGA functionals were used to compute complete vapor liquid coexistence curves (VLCCs) to estimate critical properties, while the hybrid and nonlocal vander Waals functionals were used only for computing density at a single state point due to the high computational cost. Our results show that the BLYP-D3 functional performs well in predicting VLE properties for both molecules when compared with other functionals. In the liquid phase, pair correlation functions reveal that there is not a significant difference in the location of the peak for the first solvation shell while the peak heights are different for different functionals. Altogether, theBLYP-D3 functional is a good choice for modeling VLE of acidic gases with significant environmental implications such as CO 2 and SO 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Density functional theory for d- and f-electron materials and compounds

Here, the fundamental requirements for a computationally tractable Density Functional Theory-based method for relativistic f- and (nonrelativistic) d-electron materials and compounds are presented. The need for basing the Kohn–Sham equations on the Dirac equation is discussed. The full Dirac scheme needs exchange-correlation functionals in terms of four-currents, but ordinary functionals, using charge density and spin-magnetization, can be used in an approximate Dirac treatment. The construction of a functional that includes the additional confinement physics needed for these materials is illustrated using the subsystem-functional scheme. If future studies show that a full Dirac, four-current based, exchange-correlation functional is needed, the subsystem functional scheme is one of the few schemes that can still be used for constructing functional approximations.

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

Functional integrals and inequivalent representations in Quantum Field Theory

We discuss canonical transformations in Quantum Field Theory in the framework of the functional-integral approach. In contrast with ordinary Quantum Mechanics, canonical transformations in Quantum Field Theory are mathematically more subtle due to the existence of unitarily inequivalent representations of canonical commutation relations. When one works with functional integrals, it is not immediately clear how this algebraic feature manifests itself in the formalism. Here we attack this issue by considering the canonical transformations in the context of coherent-state functional integrals. Specifically, in the case of linear canonical transformations, we derive the general functional-integral representations for both transition amplitude and partition function phrased in terms of new canonical variables. By means of this, we show how in the infinite-volume limit the canonical transformations induce a transition from one representation of canonical commutation relations to another one and under what conditions the representations are unitarily inequivalent. We also consider the partition function and derive the energy gap between statistical systems described in two different representations which, among others, allows to establish a connection with continuous phase transitions. We illustrate the inner workings of the outlined mechanism by discussing two prototypical systems: the van Hove model and the Bogoliubov model of weakly interacting Bose gas. - Highlights: • Functional integrals are sensitive to representations of the Heisenberg–Weyl algebra. • Inequivalent representations can be exhibited in the functional integral formalism. • Passage among inequivalent representations is seen as second-order phase transition. • The inequivalence of representations is physically marked by an infinite energy gap.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Schrödinger potentials solvable in terms of the general Heun functions

Highlights: •There are 35 Schrödinger potentials solvable in terms of the Heun functions. •Only 11 of the potentials are independent. •9 potentials have sub-potentials with solution via a single hypergeometric function. •Many subpotentials are solved through a combination of two hypergeometric functions. •A generalization of the third exactly solvable hypergeometric potential is presented. -- Abstract: We show that there exist 35 choices for the coordinate transformation each leading to a potential for which the stationary Schrödinger equation is exactly solvable in terms of the general Heun functions. Because of the symmetry of the Heun equation with respect to the transposition of its singularities only eleven of these potentials are independent. Four of these independent potentials are always explicitly written in terms of elementary functions, one potential is given through the Jacobi elliptic sn-function, and the others are in general defined parametrically. Nine of the independent potentials possess exactly or conditionally integrable hypergeometric sub-potentials for which each of the fundamental solutions of the Schrödinger equation is written through a single hypergeometric function. Many of the potentials possess sub-potentials for which the general solution is written through fundamental solutions each of which is a linear combination of two or more Gauss hypergeometric functions. We present an example of such a potential which is a conditionally integrable generalization of the third exactly solvable Gauss hypergeometric potential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A flexible class of priors for orthonormal matrices with basis function-specific structure

Statistical modeling of high-dimensional matrix-valued data motivates the use of a low-rank representation that simultaneously summarizes key characteristics of the data and enables dimension reduction. Low-rank representations commonly factor the original data into the product of orthonormal basis functions and weights, where each basis function represents an independent feature of the data. However, the basis functions in these factorizations are typically computed using algorithmic methods that cannot quantify uncertainty or account for basis function correlation structure a priori. While there exist Bayesian methods that allow for a common correlation structure across basis functions, empirical examples motivate the need for basis function-specific dependence structure. We propose a prior distribution for orthonormal matrices that can explicitly model basis function-specific structure. The prior is used within a general probabilistic model for singular value decomposition to conduct posterior inference on the basis functions while accounting for measurement error and fixed effects. We discuss how the prior specification can be used for various scenarios and demonstrate favorable model properties through synthetic data examples. Finally, we apply our method to two-meter air temperature data from the Pacific Northwest, enhancing our understanding of the Earth system’s internal variability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Chemical Functional Groups Regulate Ion Concentrations and pHs in Nanopores

Understanding ion behaviors in functionalized nanopores is essential to deciphering reactions in both natural and engineered systems, such as sediments, biological ion channels, and membranes. While many efforts have shown the modified ion behaviors in the functionalized nanopores, a direct measurement and analysis to show how chemical functional groups affect ion concentrations in nanopores are critically needed. In this work, we present a plasmonic nanosensor that can measure the local concentrations of protons, anions (phosphate, nitrate, sulfate, and arsenate), and cations (mercury, lead, and copper) in functionalized nanopores, and we compare their concentrations in nanopores with the corresponding bulk concentrations. Notably, chemical functional groups induced ion concentrations differently in nanopores. In pristine nanopores and methyl- and phenyl-functionalized nanopores, we discovered an unexpected concurrence of an enhanced anion concentration and a suppressed cation concentration. In addition, the nanopore pH is dependent on bulk solution compositions and can be lower by 2.5 units, even when the bulk solution is well-buffered. In contrast, for hydrophilic (amine, thiol, and carboxyl) nanopores, pH depended on the p K a of the functional groups, and the heavy metal concentrations depended on chemical interactions with the functional groups. Our findings provide a better understanding of water chemistry in nanopores and can help precisely control ions in nanopores to benefit the design of membrane-based desalination techniques, CO 2 storage, and porous catalysts.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Balancing the Hydrogen Evolution Reaction, Surface Energetics, and Stability of Metallic MoS 2 Nanosheets via Covalent Functionalization

We modify the fundamental electronic properties of metallic (1T phase) nanosheets of molybdenum disulfide (MoS 2 ) through covalent chemical functionalization, and thereby directly influence the kinetics of the hydrogen evolution reaction (HER), surface energetics, and stability. Chemically exfoliated, metallic MoS 2 nanosheets are functionalized with organic phenyl rings containing electron donating or withdrawing groups. We find that MoS 2 functionalized with the most electron donating functional group (p-(CH 3 CH 2 ) 2 NPh-MoS 2 ) is the most efficient catalyst for HER in this series, with initial activity that is slightly worse compared to the pristine metallic phase of MoS 2 . The p-(CH 3 CH 2 ) 2 NPh-MoS 2 is more stable than unfunctionalized metallic MoS 2 and outperforms unfunctionalized metallic MoS 2 for continuous H 2 evolution within 10 min under the same conditions. With regards to the entire studied series, the overpotential and Tafel slope for catalytic HER are both directly correlated with the electron donating strength of the functional group. The results are consistent with a mechanism involving ground-state electron donation or withdrawal to/from the MoS 2 nanosheets, which modifies the electron transfer kinetics and catalytic activity of the MoS 2 nanosheet. The functional groups preserve the metallic nature of the MoS 2 nanosheets, inhibiting conversion to the thermodynamically stable semiconducting state (2H) when mildly annealed in a nitrogen atmosphere. We propose that the electron density and, therefore, reactivity of the MoS 2 nanosheets are controlled by the attached functional groups. Functionalizing nanosheets of MoS 2 and other transition metal dichalcogenides provides a synthetic chemical route for controlling the electronic properties and stability within the traditionally thermally unstable metallic state.

08 HYDROGEN↗
DOE OSTI2015

Thermal weights for semiclassical vibrational response functions

Semiclassical approximations to response functions can allow the calculation of linear and nonlinear spectroscopic observables from classical dynamics. Evaluating a canonical response function requires the related tasks of determining thermal weights for initial states and computing the dynamics of these states. A class of approximations for vibrational response functions employs classical trajectories at quantized values of action variables and represents the effects of the radiation-matter interaction by discontinuous transitions. Here, we evaluate choices for a thermal weight function which are consistent with this dynamical approximation. Weight functions associated with different semiclassical approximations are compared, and two forms are constructed which yield the correct linear response function for a harmonic potential at any temperature and are also correct for anharmonic potentials in the classical mechanical limit of high temperature. Approximations to the vibrational linear response function with quantized classical trajectories and proposed thermal weight functions are assessed for ensembles of one-dimensional anharmonic oscillators. This approach is shown to perform well for an anharmonic potential that is not locally harmonic over a temperature range encompassing the quantum limit of a two-level system and the limit of classical dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Methane dissociation on Pt(111): Searching for a specific reaction parameter density functional

The theoretical description of methane dissociating on metal surfaces is a current frontier in the field of gas-surface dynamics. Dynamical models that aim at achieving a highly accurate description of this reaction rely on potential energy surfaces based on density functional theory calculations at the generalized gradient approximation. We focus here on the effect that the exchange-correlation functional has on the reactivity of methane on a metal surface, using CHD{sub 3} + Pt(111) as a test case. We present new ab initio molecular dynamics calculations performed with various density functionals, looking also at functionals that account for the van der Waals (vdW) interaction. While searching for a semi-empirical specific reaction parameter density functional for this system, we find that the use of a weighted average of the PBE and the RPBE exchange functionals together with a vdW-corrected correlation functional leads to an improved agreement with quantum state-resolved experimental data for the sticking probability, compared to previous PBE calculations. With this semi-empirical density functional, we have also investigated the surface temperature dependence of the methane dissociation reaction and the influence of the rotational alignment on the reactivity, and compared our results with experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

TRISO Fuel’s Safety Functions, Contributions to Reactor Safety, and Necessary Safety Limits

Safety functions are the actions, passive or active, that structures, systems, and components of nuclear facility that contribute to the safety of the workers, the public, or the environment. Well-defined safety functions are the foundation of a solid safety case for a reactor. For reactors that use TRISO-coated particles, the TRISO fuel plays an important part of the safety case because of its ability to contain radionuclides in the fuel itself. This ability enables the use of a functional containment strategy for the reactor where radionuclide retention is the primary safety function supported by the safety functions of controlling reactivity control and controlling heat rejection. This paper establishes at a deeper level the role that TRISO fuel plays in each of these safety functions and associated quality assurance and testing requirements for TRISO particle manufacturing to ensure these safety functions. Safety limits necessary to protect these safety functions include: operational limits, time at temperature limits, and fission gas release activity limits. In conclusion, this approach demonstrates the role that specific aspects of TRISO fuel play in protecting the safety of workers, the public, and the environment.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2015

The Hubbard dimer: a density functional case study of a many-body problem

This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy–Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the 'failure' of the Kohn–Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree–Fock and Bethe ansatz local density approximation) to show their successes and limitations. Here, we also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Density functional theory of material design: fundamentals and applications—II

Abstract This is the second and the final part of the review on density functional theory (DFT), referred to as DFT-II. In the first review, DFT-I, we have discussed wavefunction-based methods, their complexity, and basics of density functional theory. In DFT-II, we focus on fundamentals of DFT and their implications for the betterment of the theory. We start our presentation with the exact DFT results followed by the concept of exchange-correlation (xc) or Fermi-Coulomb hole and its relationship with xc energy functional. We also provide the exact conditions for the xc-hole, xc-energy and xc-potential along with their physical interpretation. Next, we describe the extension of DFT for non-integer number of electrons, the piecewise linearity of total energy and discontinuity of chemical potential at integer particle numbers, and derivative discontinuity of the xc potential, which has consequences on fundamental gap of solids. After that, we present how one obtains more accurate xc energy functionals by going beyond the LDA. We discuss the gradient expansion approximation (GEA), generalized gradient approximation (GGA), and hybrid functional approaches to designing better xc energy functionals that give accurate total energies. However, these functionals fail to predict properties like the ionization potential and the band gap. Thus, we next describe different methods of modelling these potentials and results of their application for calculation of the band gaps of different solids to highlight accuracy of different xc potentials. Finally, we conclude with a glimpse on orbital-free density functional theory and the machine learning approach.

36 MATERIALS SCIENCE↗