Search NASA⌕ Search

SEARCH · Search NASA

Results for “functions”

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 127 records · Page 7

Function space requirements for the single-electron functions within the multiparticle Schroedinger equation

Our previously described method to approximate the many-electron wavefunction in the multiparticle Schroedinger equation reduces this problem to operations on many single-electron functions. In this work, we analyze these operations to determine which function spaces are appropriate for various intermediate functions in order to bound the output. This knowledge then allows us to choose the function spaces in which to control the error of a numerical method for single-electron functions. We find that an efficient choice is to maintain the single-electron functions in L{sup 2} Intersection L{sup 4}, the product of these functions in L{sup 1} Intersection L{sup 2}, the Poisson kernel applied to the product in L{sup 4}, a function times the Poisson kernel applied to the product in L{sup 2}, and the nuclear potential times a function in L{sup 4/3}. Due to the integral operator formulation, we do not require differentiability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Hexagon functions and the three-loop remainder function

We present the three-loop remainder function, which describes the scattering of six gluons in the maximally-helicity-violating configuration in planar NN = 4 super-Yang-Mills theory, as a function of the three dual conformal cross ratios. The result can be expressed in terms of multiple Goncharov polylogarithms. We also employ a more restricted class of hexagon functions which have the correct branch cuts and certain other restrictions on their symbols. We classify all the hexagon functions through transcendental weight five, using the coproduct for their Hopf algebra iteratively, which amounts to a set of first-order differential equations. The three-loop remainder function is a particular weight-six hexagon function, whose symbol was determined previously. The differential equations can be integrated numerically for generic values of the cross ratios, or analytically in certain kinematic limits, including the near-collinear and multi-Regge limits. These limits allow us to impose constraints from the operator product expansion and multi-Regge factorization directly at the function level, and thereby to fix uniquely a set of Riemann ζ valued constants that could not be fixed at the level of the symbol. The near-collinear limits agree precisely with recent predictions by Basso, Sever and Vieira based on integrability. The multi-Regge limits agree with the factorization formula of Fadin and Lipatov, and determine three constants entering the impact factor at this order. We plot the three-loop remainder function for various slices of the Euclidean region of positive cross ratios, and compare it to the two-loop one. For large ranges of the cross ratios, the ratio of the three-loop to the two-loop remainder function is relatively constant, and close to -7.

extended supersymmetry↗

Examination of How Well Long-Range-Corrected Density Functionals Satisfy the Ionization Energy Theorem

For this work, we calculated the vertical ionization energies (VIE) of 99 species in two ways to examine the accuracy of several long-range-corrected (LC) hybrid meta functionals in comparison with a gradient approximation (GA), global hybrids, and doubly hybrids. In the category of LC functionals, we examined both those with meta ingredients (i.e., that depend on the kinetic energy density) and those without them. The LC-hybrid meta functionals examined are M11, revM11, M11plus, and ωB97M-V. The reference data used to assess accuracy consist of 95 molecules and 4 atoms in the GW100 set. The two methods studied are the ΔSCF method (involving the difference of neutral and cation self-consistent field (SCF) energies) and the ionization energy theorem (involving the orbital energy of the highest occupied molecular orbital, HOMO). We calculated linear correlation coefficients (r 2 ) and mean absolute deviations (MADs) between each approach and the reference VIE value from the CCSD(T)/def2-TZVPP level of theory. We compared the new LC-hybrid meta calculations to calculations with the 10 functionals in a previous VIE study by Brémond et al. and to the calculations with LC-BLYP (LC-Becke, Lee–Yang–Parr), CAM-B3LYP (Coulomb-attenuating-method Becke-3-parameter Lee–Yang–Parr), LC-ωHPBE, and ωB97X-D. The results show that Minnesota LC-hybrid meta functionals have the smallest mean absolute deviation of ionization energy theorem VIEs with the reference data; the LC-ωHPBE functional also does quite well in this test. This is very encouraging and indicates that LC-hybrid meta functionals would be the best starting points for the tuning strategy that has been shown to be a very good procedure for improving time-dependent density functional calculations, and it also helps explain the good success of LC-hybrid meta functionals for molecular excitation energies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Water on BN doped benzene: A hard test for exchange-correlation functionals and the impact of exact exchange on weak binding

Density functional theory (DFT) studies of weakly interacting complexes have recently focused on the importance of van der Waals dispersion forces, whereas the role of exchange has received far less attention. Here, by exploiting the subtle binding between water and a boron and nitrogen doped benzene derivative (1,2-azaborine) we show how exact exchange can alter the binding conformation within a complex. Benchmark values have been calculated for three orientations of the water monomer on 1,2-azaborine from explicitly correlated quantum chemical methods, and we have also used diffusion quantum Monte Carlo. For a host of popular DFT exchange-correlation functionals we show that the lack of exact exchange leads to the wrong lowest energy orientation of water on 1,2-azaborine. As such, we suggest that a high proportion of exact exchange and the associated improvement in the electronic structure could be needed for the accurate prediction of physisorption sites on doped surfaces and in complex organic molecules. Meanwhile to predict correct absolute interaction energies an accurate description of exchange needs to be augmented by dispersion inclusive functionals, and certain non-local van der Waals functionals (optB88- and optB86b-vdW) perform very well for absolute interaction energies. Through a comparison with water on benzene and borazine (B{sub 3}N{sub 3}H{sub 6}) we show that these results could have implications for the interaction of water with doped graphene surfaces, and suggest a possible way of tuning the interaction energy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential

A new non-empirical exchange energy functional of the generalized gradient approximation (GGA) type, which gives an exchange potential with the correct asymptotic behavior, is developed and explored. In combination with the Perdew-Burke-Ernzerhof (PBE) correlation energy functional, the new CAP-PBE (CAP stands for correct asymptotic potential) exchange-correlation functional gives heats of formation, ionization potentials, electron affinities, proton affinities, binding energies of weakly interacting systems, barrier heights for hydrogen and non-hydrogen transfer reactions, bond distances, and harmonic frequencies on standard test sets that are fully competitive with those obtained from other GGA-type functionals that do not have the correct asymptotic exchange potential behavior. Distinct from them, the new functional provides important improvements in quantities dependent upon response functions, e.g., static and dynamic polarizabilities and hyperpolarizabilities. CAP combined with the Lee-Yang-Parr correlation functional gives roughly equivalent results. Consideration of the computed dynamical polarizabilities in the context of the broad spectrum of other properties considered tips the balance to the non-empirical CAP-PBE combination. Intriguingly, these improvements arise primarily from improvements in the highest occupied and lowest unoccupied molecular orbitals, and not from shifts in the associated eigenvalues. Those eigenvalues do not change dramatically with respect to eigenvalues from other GGA-type functionals that do not provide the correct asymptotic behavior of the potential. Unexpected behavior of the potential at intermediate distances from the nucleus explains this unexpected result and indicates a clear route for improvement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Size-dependent error of the density functional theory ionization potential in vacuum and solution

Density functional theory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate density functional theory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate density functionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potential for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. In vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Local and linear chemical reactivity response functions at finite temperature in density functional theory

We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Shrinking Self-Interaction Errors with the Fermi–Löwdin Orbital Self-Interaction-Corrected Density Functional Approximation

The self-interaction error (SIE) is one of the major drawbacks of practical exchange-correlation functionals for Kohn-Sham density functional theory. Despite this, the use of methods that explicitly remove SIE from approximate density functionals is scarce in the literature due to their relatively high computational cost and lack of consistent improvement over standard modern functionals. Here, we assess the performance of a novel approach recently proposed by Pederson, Ruzsinszky, and Perdew for performing self-interaction free calculations in density functional theory based on Fermi-orbitals. To this end, we employ test sets consisting of reaction energies that are considered particularly sensitive to SIE. We found that the parameter-free Fermi-Löwdin orbital self-interaction correction method combined with standard local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof (PBE) functionals gives a much better estimate of reaction energies compared to their parent LSDA and PBE functionals for most of the reactions in these two sets. They also perform on par with the global PBE0 and range-separated LC-ωPBE hybrids, which partially eliminate the SIE by including Hartree-Fock exchange. This shows the potential of the Fermi-Löwdin orbital self-interaction corrected (FLOSIC) method for practical density functional calculations without SIE.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Tuning the reactivity of carbon surfaces with oxygen-containing functional groups

Oxygen-containing carbons are promising supports and metal-free catalysts for many reactions. However, distinguishing the role of various oxygen functional groups and quantifying and tuning each functionality is still difficult. Here we investigate the role of Brønsted acidic oxygen-containing functional groups by synthesizing a diverse library of materials. By combining acid-catalyzed elimination probe chemistry, comprehensive surface characterizations, 15N isotopically labeled acetonitrile adsorption coupled with magic-angle spinning nuclear magnetic resonance, machine learning, and density-functional theory calculations, we demonstrate that phenolic is the main acid site in gas-phase chemistries and unexpectedly carboxylic groups are much less acidic than phenolic groups in the graphitized mesoporous carbon due to electron density delocalization induced by the aromatic rings of graphitic carbon. The methodology can identify acidic sites in oxygenated carbon materials in solid acid catalyst-driven chemistry.

Zhou, Jiahua↗

Fragment approach to constrained density functional theory calculations using Daubechies wavelets

In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Density functional theory of water with the machine-learned DM21 functional

The delicate interplay between functional-driven and density-driven errors in density functional theory (DFT) has hindered traditional density functional approximations (DFAs) from providing an accurate description of water for over 30 years. Recently, the deep-learned DeepMind 21 (DM21) functional has been shown to overcome the limitations of traditional DFAs as it is free of delocalization error. To determine if DM21 can enable a molecular-level description of the physical properties of aqueous systems within Kohn–Sham DFT, we assess the accuracy of the DM21 functional for neutral, protonated, and deprotonated water clusters. Furthermore, we find that the ability of DM21 to accurately predict the energetics of aqueous clusters varies significantly with cluster size. Additionally, we introduce the many-body MB-DM21 potential derived from DM21 data within the many-body expansion of the energy and use it in simulations of liquid water as a function of temperature at ambient pressure. We find that size-dependent functional-driven errors identified in the analysis of the energetics of small clusters calculated with the DM21 functional result in the MB-DM21 potential systematically overestimating the hydrogen-bond strength and, consequently, predicting a more ice-like local structure of water at room temperature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Deconstructing the Soil Microbiome into Reduced-Complexity Functional Modules

The soil microbiome is an invaluable component of the biosphere and critical for ecosystem functions, including biogeochemical cycling, soil-atmosphere gas exchange, degradation of toxic compounds, and promotion of plant growth and stress resistance/resilience. An improved understanding of the soil microbiome will help with predicting how these processes respond to external perturbations, and with harnessing beneficial aspects of the soil microbiome for agronomic applications such as crop amendments. However, the extensive taxonomic and functional diversity inherent within the soil microbiome hinders efficient analysis of this system. Microbial biodiversity in soils is orders of magnitude greater than other commonly studied systems such as the human gut microbiome (Blum, Zechmeister-Boltenstern, and Keiblinger 2019; Berendsen, Pieterse, and Bakker 2012). Thousands of microbial taxa may be found in a single gram of soil (Roesch et al. 2007), and high rates of gene flow and mutation further promote microbial diversification (Sergaki et al. 2018). Concomitantly, functional diversity in soil is similarly extensive. Soil is a heterogeneous mixture of microenvironments with defined physical and chemical attributes (Bach et al. 2018), within which numerous microbial guilds of distinct life-strategies and metabolic capacities can be found (Perez-Garcia, Lear, and Singhal 2016; H.-S. Song et al. 2014). Furthermore, the soil microbiome harbors a significant fraction of rare and/or quiescent members (Blagodatskaya and Kuzyakov 2013) that exist below the threshold of detection of current technologies. Such rare taxa may make significant contributions to process rates (Shade and Gilbert 2015; Dawson et al. 2017), but their scarcity complicates their identification and analysis. Finally, the vast amounts of information generated through holistic analyses of soil communities represent an intense computational burden (Scholz, Lo, and Chain 2012; Prosser 2015) that precludes assessment of the complete functional and taxonomic diversity contained in this ecosystem.

Naylor, Dan T.↗

Functionalized Embedded Monometallic Nickel Catalysts for Enhanced Hydrogen Evolution: Performance and Stability

Viable anionic exchange membrane (AEM) electrolysis for H 2 production requires highly active hydrogen evolution reaction (HER) catalysts that are also robust and cost-effective. Traditionally juxtaposition of two transition metals with one being more oxophilic is necessary for easier access to water in the inner Helmholtz plane as a source of protons in the crucial Volmer step for enhanced HER activity. However, they are prone to passivation at anodic potentials or deactivation via the formation of sub-surface metal hydrides at high cathodic overpotentials. Here we report a method of enabling close juxtaposition of Ni-Ni-oxide surfaces by functionalizing Ni-based catalysts via the careful thermal treatment of carbon-supported Ni nano-particles chelated with a select organic chelating compound referred to as cupferron. This functionalization results in an embedded Ni surface with a clear graphitic coating engendering long-term stability for passivation and subsurface hydride formation. The stability and activity of the functionalized Ni catalyst are demonstrated in half-cell RDE and full-cell AEM membrane-based hydrogen pump experiments. In the case of the latter, the functionalized Ni outperforms carbon-supported Pt.

25 ENERGY STORAGE↗

Statistical measurement of the gamma-ray source-count distribution as a function of energy

Statistical properties of photon count maps have recently been proven as a new tool to study the composition of the gamma-ray sky with high precision. We employ the 1-point probability distribution function of six years of Fermi-LAT data to measure the source-count distribution dN/dS and the diffuse components of the high-latitude gamma-ray sky as a function of energy. To that aim, we analyze the gamma-ray emission in five adjacent energy bands between 1 and 171 GeV. It is demonstrated that the source-count distribution as a function of flux is compatible with a broken power law up to energies of ∼50 GeV. The index below the break is between 1.95 and 2.0. For higher energies, a simple power-law fits the data, with an index of 2.2{sub −0.3}{sup +0.7} in the energy band between 50 and 171 GeV. Upper limits on further possible breaks as well as the angular power of unresolved sources are derived. We find that point-source populations probed by this method can explain 83{sub −13}{sup +7}% (81{sub −19}{sup +52}%) of the extragalactic gamma-ray background between 1.04 and 1.99 GeV (50 and 171 GeV). The method has excellent capabilities for constraining the gamma-ray luminosity function and the spectra of unresolved blazars.

79 ASTRONOMY AND ASTROPHYSICS↗

Environmental remediation with functional aerogels and xerogels

Several different types of aerogel and/or xerogel scaffolds have been demonstrated as effective sorbents for the capture and immobilization of radionuclides in gaseous form [e.g., iodine gas or I2(g), Xe] as well as ionic form (e.g., Ce4+, Cs+, I–, IO3-, Rb+, Sr2+, 99Tc7+, and U6+). These scaffolds have unique properties, which include high specific surface areas, high pore volumes, varieties of pore sizes, and functionalities that provide methods for binding radionuclides through physisorption, chemisorption, or a combination thereof. This combination of properties and functionalities make these types of materials ideal scaffolds for use as sorbents for capturing radionuclides. The primary base materials that will be discussed in this chapter include Ag0-functionalized silica aerogels, Ag+-impregnated aluminosilicate aerogels, Ag0-functionalized aluminosilicate aerogels, metal-impregnated (non-Ag) aluminosilicate aerogels and xerogels, sulfide-based aerogels, and carbon-based aerogel composites. For the capture of I2(g), the materials reported herein show some of the highest iodine loadings ever reported for inorganic sorbents. For the capture of ionic species, these materials also show promise to be some of the next generations of materials for active radionuclide remediation. This progress report will describe how these materials are fabricated, the general properties of these materials, as well as an overview of how they have been used for different applications in environmental remediation of radionuclides.

aerogel, xerogel, iodine, radionuclide remediation↗

Electrochemical Oxidation of Organic Molecules at Lower Overpotential: Accessing Broader Functional Group Compatibility with Electron-Proton Transfer Mediators

CONSPECTUS: Electrochemical organic oxidation reactions are highly appealing because protons are often effective terminal electron acceptors, thereby avoiding undesirable stoichiometric oxidants. These reactions are often plagued by high overpotentials, however, that greatly limit their utility. Single-electron transfer (SET) from organic molecules generates high energy radical-cations. Formation of such intermediates often requires electrode potentials far above the thermodynamic potentials of the reaction and frequently causes decomposition and/or side reactions of ancillary functional groups. In this Account, we show how electrocatalytic electron-proton transfer mediators (EPTMs) address this challenge. EPTMs bypass the formation of radical-cation intermediates by supporting mechanisms that operate at electrode potentials much lower (=1 V) than analogous direct electrolysis reactions. The stable aminoxyl radical TEMPO (2,2,6,6-tetramethylpiperidine N-oxyl) is an effective mediator for electrochemical alcohol oxidation, and we have employed such processes for applications ranging from pharmaceutical synthesis to biomass conversion. A complementary electrochemical alcohol oxidation method employs a cooperative Cu/TEMPO mediator system that operates at 0.5 V lower electrode potential than the TEMPO-only mediated process. This difference, which arises from a different catalytic mechanism, rationalizes the broad functional group tolerance of Cu/TEMPO-based aerobic alcohol oxidation catalysts. Aminoxyl mediators address long-standing challenges in the "Shono oxidation", an important method for a-C–H oxidation of tertiary amides and carbamates. Shono oxidations are initiated by a high-potential SET step that limits their utility. Aminoxyl-mediated Shono-type oxidations have been developed that operate at much lower potentials and tolerate diverse functional groups. Analogous reactivity underlies a-C–H cyanation of secondary cyclic amines, a new method that enables efficient diversification of piperidine-based pharmaceutical building blocks and preparation of non-natural amino acids. Electrochemical oxidations of benzylic C–H bonds are commonly initiated by SET to generate radical cations, but such methods are again plagued by large overpotentials. Mediated electrolysis methods that promote hydrogen-atom-transfer (HAT) from benzylic C–H bonds to Fe-oxo species and phthalimide N-oxyl (PINO) support C–H oxygenation, iodination, and oxidative-coupling reactions. A complementary method merges photochemistry with electrochemistry to achieve amidation of C(sp3)–H bonds. This unique process operates at much lower overpotentials compatible with diverse functional groups. These results have broad implications for organic electrochemistry, highlighting the importance of "overpotential" considerations and the prospects for expanding synthetic utility by using mediators to bypass high-energy outer-sphere electron-transfer mechanisms. Principles demonstrated here for oxidation are equally relevant to electrochemical reductions.

Wang, Fei↗

Screening Hofmann Compounds as CO 2 Sorbents: Nontraditional Synthetic Route to Over 40 Different Pore-Functionalized and Flexible Pillared Cyanonickelates

A simple reaction scheme based on the heterogeneous intercalation of pillaring ligands (HIPLs) provides a convenient method for systematically tuning pore size, pore functionality, and network flexibility in an extended series of pillared cyanonickelates (PICNICs), commonly referred to as Hofmann compounds. The versatility of the approach is demonstrated through the preparation of over 40 different PICNICs containing pillar ligands ranging from ~4 to ~15 Å in length and modified with a wide range of functional groups, including fluoro, aldehyde, alkylamine, alkyl, aryl, trifluoromethyl, ester, nitro, ether, and nonmetalated 4,4'-bipyrimidine. The HIPL method involves reaction of a suspension of preformed polymeric sheets of powdered anhydrous nickel cyanide with an appropriate pillar ligand in refluxing organic solvent, resulting in the conversion of the planar [Ni{sub 2}(CN){sub 4}]{sub n} networks into polycrystalline three-dimensional porous frameworks containing the organic pillar ligand. Preliminary investigations indicate that the HIPL reaction is also amenable to forming Co(L)Ni(CN){sub 4}, Fe(L)Ni(CN){sub 4}, and Fe(L)Pd(CN){sub 4} networks. The materials show variable adsorption behavior for CO{sub 2} depending on the pillar length and pillar functionalization. Several compounds show structurally flexible behavior during the adsorption and desorption of CO{sub 2}. Interestingly, the newly discovered flexible compounds include two flexible Fe(L)Ni(CN){sub 4} derivatives that are structurally related to previously reported porous spin-crossover compounds. The preparations of 20 pillar ligands based on ring-functionalized 4,4'-dipyridyls, 1,4-bis(4- pyridyl)benzenes, and N-(4-pyridyl)isonicotinamides are also described.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗