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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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DOE OSTI2014

Perspective: Fifty years of density-functional theory in chemical physics

Since its formal inception in 1964–1965, Kohn-Sham density-functional theory (KS-DFT) has become the most popular electronic structure method in computational physics and chemistry. Its popularity stems from its beautifully simple conceptual framework and computational elegance. The rise of KS-DFT in chemical physics began in earnest in the mid 1980s, when crucial developments in its exchange-correlation term gave the theory predictive power competitive with well-developed wave-function methods. Today KS-DFT finds itself under increasing pressure to deliver higher and higher accuracy and to adapt to ever more challenging problems. If we are not mindful, however, these pressures may submerge the theory in the wave-function sea. KS-DFT might be lost. I am hopeful the Kohn-Sham philosophical, theoretical, and computational framework can be preserved. This Perspective outlines the history, basic concepts, and present status of KS-DFT in chemical physics, and offers suggestions for its future development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Vibrationally specific photoionization cross sections of acrolein leading to the Χ{sup ~}A{sup '} ionic state

The vibrational branching ratios in the photoionization of acrolein for ionization leading to the Χ{sup ~}A{sup '} ion state were studied. Computed logarithmic derivatives of the cross section and the corresponding experimental data derived from measured vibrational branching ratios for several normal modes (ν{sub 9}, ν{sub 10}, ν{sub 11}, and ν{sub 12}) were found to be in relatively good agreement, particularly for the lower half of the 11–100 eV photon energy range considered. Two shape resonances have been found near photon energies of 15.5 and 23 eV in the photoionization cross section and have been demonstrated to originate from the partial cross section of the A{sup ′} scattering symmetry. The wave functions computed at the resonance complex energies are delocalized over the whole molecule. By looking at the dependence of the cross section on the different normal mode displacements together with the wave function at the resonant energy, a qualitative explanation is given for the change of the cross sections with respect to changing geometry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Systematic structure of the neutron drip-line {sup 22}C nucleus

In the present work we systematically discuss the nuclear structure of the the heaviest particle-bound carbon isotope, {sup 22}C. The ground state wave function of the carbon isotope is calculated using the {sup 20}C core plus two-valence neutron based on a phenomenological mean-field MF potential. We apply the deduced wave function to provide the nuclear matter density which is necessary in the calculations of the total reaction cross section. Calculations show that there is a reasonable good description of the experimental binding energy BE and root-mean square RMS radius. The exotic structure and configuration of the ground state carbon isotope is explained and a consistent explanation on the two-neutron halo (Borromean) nucleus is given.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

On the v-representabilty problem in density functional theory: Application to non-interacting systems

Based on a computational procedure for determining the functional derivative with respect to the density of any antisymmetric N-particle wave function for a non-interacting system that leads to the density, we devise a test as to whether or not a wave function known to lead to a given density corresponds to a solution of a Schrödinger equation for some potential. We examine explicitly the case of non-interacting systems described by Slater determinants. Here, numerical examples for the cases of a one-dimensional square-well potential with infinite walls and the harmonic oscillator potential illustrate the formalism.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Anharmonic Bloch oscillations of electrons in electrically biased superlattices

The phenomenon of anharmonic Bloch oscillations (i.e., oscillations with a frequency which is a multiple of the Bloch frequency) is considered. The energy-band structure of silicon-carbide polytypes where these oscillations are observed is calculated ab initio. A one-dimensional model potential making it possible to calculate the Stark wave functions in a biased superlattice is constructed for these polytypes. The transfer matrix method is used to find the set of energy levels (the so-called Stark ladder) and calculate the electron wave functions. It is shown that both radiative transitions between neighboring Stark levels (at the Bloch frequency) and transitions in the form of jumps via several levels, accompanied by emission at frequencies that are multiples of the Bloch frequency, may occur. The calculated probabilities of transitions between Stark-ladder levels increase with increasing applied field strength.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Beyond Single-Reference Fixed-Node Approximation in Ab Initio Diffusion Monte Carlo Using Antisymmetrized Geminal Power Applied to Systems with Hundreds of Electrons

Diffusion Monte Carlo (DMC) is an exact technique to project out the ground state (GS) of a Hamiltonian. Since the GS is always bosonic, in Fermionic systems, the projection needs to be carried out while imposing antisymmetric constraints, which is a nondeterministic polynomial hard problem. In practice, therefore, the application of DMC on electronic structure problems is made by employing the fixed-node (FN) approximation, consisting of performing DMC with the constraint of having a fixed, predefined nodal surface. How do we get the nodal surface? The typical approach, applied in systems having up to hundreds or even thousands of electrons, is to obtain the nodal surface from a preliminary mean-field approach (typically, a density functional theory calculation) used to obtain a single Slater determinant. This is known as single reference. In this paper, we propose a new approach, applicable to systems as large as the C 60 fullerene, which improves the nodes by going beyond the single reference. In practice, we employ an implicitly multireference ansatz (antisymmetrized geminal power wave function constraint with molecular orbitals), initialized on the preliminary mean-field approach, which is relaxed by optimizing a few parameters of the wave function determining the nodal surface by minimizing the FN-DMC energy. We highlight the improvements of the proposed approach over the standard single-reference method on several examples and, where feasible, the computational gain over the standard multireference ansatz, which makes the methods applicable to large systems. We also show that physical properties relying on relative energies, such as binding energies, are affordable and reliable within the proposed scheme.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Communication: Three-electron coalescence points in two and three dimensions

The form of the wave function at three-electron coalescence points is examined for several spin states using an alternative method to the usual Fock expansion. We find that, in two- and three-dimensional systems, the non-analytical nature of the wave function is characterized by the appearance of logarithmic terms, reminiscent of those that appear as both electrons approach the nucleus of the helium atom. The explicit form of these singularities is given in terms of the interelectronic distances for a doublet and two quartet states of three electrons in a harmonic well.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2019

[Am(C 5 Me 4 H) 3 ], an organometallic americium complex

Organometallic synthetic chemistry of transplutonium elements is an area that has been stagnant for decades. Here, we observe the small-scale synthesis, isolated yield, single-crystal X-ray structure, 1H NMR, solution/solid-state UV-vis-nIR spectroscopy, and Density Functional Theory/ab initio Wave Functional Theory calculations on an Am3+ organometallic complex,[Am(C 5 Me 4 H) 3 ]. This constitutes the first quantitative data on Am–C bonding in a molecular species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Efficient Calculation of NMR Shielding Constants Using Composite Method Approximations and Locally Dense Basis Sets

This paper presents a systematic study of applying composite method approximations with locally dense basis sets (LDBS) to efficiently calculate NMR shielding constants in small and medium-sized molecules. The pcSseg-n series of basis sets are shown to have similar accuracy to the pcS-n series when n ≥ 1 and can slightly reduce computational costs. We identify two different LDBS partition schemes that perform very effectively for density functional calculations. Here, we select a large subset of the recent NS372 database containing 290 H, C, N, and O shielding values evaluated by reference methods on 106 molecules to carefully assess methods of the high, medium, and low computational costs to make practical recommendations. Our assessment covers conventional electronic structure methods (density functional theory and wave function) with global basis calculations, as well as their use in one of the satisfactory LDBS approaches, and a range of composite approaches, also with and without LDBS. Altogether 99 methods are evaluated. On this basis, we recommend different methods to reach three different levels of accuracy and time requirements across the four nuclei considered.

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

Examining the Effect of Exchange-Correlation Approximations in First-Principles Dynamics Simulation of Interfacial Charge Transfer

We examine the extent to which the exchange-correlation (XC) approximation influences modeling interfacial charge transfer using fewest-switches surface hopping (FSSH) simulations within the single-particle description. A heterogeneous interface between a lithium ion and an extended boron-nitride sheet was considered here, being an extreme case in which wave function localization and energy level alignments are highly sensitive to the XC approximation. The PBE0 hybrid XC approximation yields nonadiabatic couplings (NACs) that are significantly smaller than the values obtained from the PBE-GGA approximation by an order of magnitude for localized electronic states. This difference between the two XC functionals for the calculated NACs was found to derive mainly from the wave function characteristics rather than from the lattice movement although first-principles molecular dynamics trajectories, along which NACs are obtained, differ noticeably between the two XC functionals. Using the NACs and single-particle energy level alignments at different levels of theory, FSSH simulations were performed to model the electron transfer dynamics at the interface. Here, the electron transfer time scale was found to vary as much as, but not more than, 1 order of magnitude. The time scale was found to be quite sensitive to both NACs and energy level alignments. While the order of magnitude consistency for the charge transfer rate is encouraging even for this rather extreme model of heterojunction interface, continued advancement in electronic structure methods is required for quantitatively accurate determination of the transfer rate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Mechanism of Oxidation of Ethane to Ethanol at Iron(IV)–Oxo Sites in Magnesium-Diluted Fe 2 (dobdc)

The catalytic properties of the metal–organic framework Fe 2 (dobdc), containing open Fe(II) sites, include hydroxylation of phenol by pure Fe 2 (dobdc) and hydroxylation of ethane by its magnesium-diluted analogue, Fe 0.1 Mg 1.9 (dobdc). In earlier work, the latter reaction was proposed to occur through a redox mechanism involving the generation of an iron(IV)–oxo species, which is an intermediate that is also observed or postulated (depending on the case) in some heme and non-heme enzymes and their model complexes. In the present work, we present a detailed mechanism by which the catalytic material, Fe 0.1 Mg 1.9 (dobdc), activates the strong C–H bonds of ethane. Kohn–Sham density functional and multireference wave function calculations have been performed to characterize the electronic structure of key species. We show that the catalytic non-heme-Fe hydroxylation of the strong C–H bond of ethane proceeds by a quintet single-state s-attack pathway after the formation of highly reactive iron–oxo intermediate. The mechanistic pathway involves three key transition states, with the highest activation barrier for the transfer of oxygen from N 2 O to the Fe(II) center. The uncatalyzed reaction, where nitrous oxide directly oxidizes ethane to ethanol is found to have an activation energy of 280 kJ/mol, in contrast to 82 kJ/mol for the slowest step in the iron(IV)–oxo catalytic mechanism. Futhermore, the energetics of the C–H bond activation steps of ethane and methane are also compared. Dehydrogenation and dissociation pathways that can compete with the formation of ethanol were shown to involve higher barriers than the hydroxylation pathway.

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

Diuranium(IV) Carbide Cluster U 2 C 2 Stabilized Inside Fullerene Cages

>Novel actinide cluster fullerenes, U 2 C 2 @ I h (7)-C 80 and U 2 C 2 @ D 3 h (5)-C 78 , were synthesized and fully characterized by mass spectrometry, single-crystal X-ray crystallography, UV–vis–NIR, nuclear magnetic resonance spectroscopy (NMR), X-ray absorption spectroscopy (XAS), Raman spectroscopy, IR spectroscopy, as well as density functional and multireference wave function calculations. The encapsulated U 2 C 2 is a novel example of a uranium carbide cluster featuring two U centers bridged by a C≡C unit. The U–C bond distances in these U 2 C 2 clusters are in the range between 2.130 and 2.421 Å. While the U 2 C 2 cluster in U 2 C 2 @C 80 adopts a butterfly-shaped geometry with a U–C 2 –U dihedral angle of 112.7° and a U–U distance of 3.855 Å, the U–U distance in U 2 C 2 @C 78 is 4.164 Å and the resulting U–C 2 –U dihedral angle is increased to 149.1°. The combined experimental and quantum-chemical results suggest that the formal U oxidation state is +4 in the U 2 C 2 cluster, and each U center transfers three electrons to the C 2 n cage and one electron to C 2 . Different from the strong U ＝ C covalent bonding reported for U 2 C 2 @ C 80 , the U–C bonds in U 2 C 2 are less covalent and predominantly ionic. The C–C triple bond is somewhat weaker than in HCCH, and the C–C π bonds undergo donation bonding with the U centers. This work shows that the combination of the unique encapsulation effect of fullerene cages and the variable oxidation states of actinide elements can lead to the stabilization of novel actinide clusters, which are not accessible by conventional synthetic methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Estimation of beryllium ground state energy by Monte Carlo simulation

Quantum Monte Carlo method represent a powerful and broadly applicable computational tool for finding very accurate solution of the stationary Schrödinger equation for atoms, molecules, solids and a variety of model systems. Using variational Monte Carlo method we have calculated the ground state energy of the Beryllium atom. Our calculation are based on using a modified four parameters trial wave function which leads to good result comparing with the few parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Beryllium. Our calculation gives good estimation for the ground state energy of the Beryllium atom comparing with the corresponding exact data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Detecting coherent core-hole wave-packet dynamics in N 2 by time- and angle-resolved inner-shell photoelectron spectroscopy

Here, we introduce an imaging technique to follow core-hole wave-packet oscillations in the nitrogen molecule. In this scheme, an attosecond x-ray pulse core-ionizes the nitrogen molecule and a subsequent attosecond x-ray pulse probes the evolution of the electron dynamics. We can image the oscillation of the core-hole between the two atomic sites by measuring the angular correlation between photoelectrons. Analytical relations for the angular correlation are derived based on the plane-wave approximation for the photoelectron wave function. We confirm these results with a scattering calculation for the photoelectron wave function. The feasibility of the experimental realization of this scheme is discussed in light of current and future capabilities of x-ray free-electron lasers.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Twisted bilayer graphene. I. Matrix elements, approximations, perturbation theory, and a k · p two-band model

We investigate the twisted bilayer graphene (TBG) model of Bistritzer and MacDonald (BM) [Bistritzer and MacDonald, Proc. Natl. Acad. Sci. 108, 12233 (2011)] to obtain an analytic understanding of its energetics and wave functions needed for many-body calculations. We provide an approximation scheme for the wave functions of the BM model, which first elucidates why the BM K M -point centered original calculation containing only four plane waves provides a good analytical value for the first magic angle (θ M ≈ 1°). The approximation scheme also elucidates why most of the many-body matrix elements in the Coulomb Hamiltonian projected to the active bands can be neglected. By applying our approximation scheme at the first magic angle to a Γ M -point centered model of six plane waves, we analytically understand the reason for the small Γ M -point gap between the active and passive bands in the isotropic limit w 0 = w 1 . Furthermore, we analytically calculate the group velocities of the passive bands in the isotropic limit, and show that they are almost doubly degenerate, even away from the Γ M point, where no symmetry forces them to be. Furthermore, moving away from the Γ M and K M points, we provide an explicit analytical perturbative understanding as to why the TBG bands are flat at the first magic angle, despite the first magic angle is defined by only requiring a vanishing K M -point Dirac velocity. We derive analytically a connected “magic manifold” w 1 = $2\sqrt{1 + w^{2}_{0}}$ $-\sqrt{2 + 3w^2_0}$, on which the bands remain extremely flat as w 0 is tuned between the isotropic (w 0 = w 1 ) and chiral (w 0 = 0) limits. We analytically show why going away from the isotropic limit by making w 0 less (but not larger) than w 1 increases the Γ M -point gap between the active and the passive bands. Finally, by perturbation theory, we provide an analytic Γ M point k ∙ p two-band model that reproduces the TBG band structure and eigenstates within a certain w 0 , w 1 parameter range. Further refinement of this model are discussed, which suggest a possible faithful representation of the TBG bands by a two-band Γ M point k ∙ p model in the full w 0 , w 1 parameter range.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Spurious long-range entanglement and replica correlation length

Topological entanglement entropy has been regarded as a smoking-gun signature of topological order in two dimensions, capturing the total quantum dimension of the topological particle content. An extrapolation method on cylinders has been used frequently to measure the topological entanglement entropy. Here in this paper, we show that a class of short-range entangled 2D states, when put on an infinite cylinder of circumference L , exhibits the entanglement Rényi entropy of any integer index α ≥ 2 that obeys S α = a L-γ , where α, γ > 0 . Under the extrapolation method, the subleading term γ would be identified as the topological entanglement entropy, which is spurious. A nonzero γ is always present if the 2D state reduces to a certain symmetry-protected topological 1D state, upon disentangling spins that are far from the entanglement cut. The internal symmetry that stabilizes γ > 0 is not necessarily a symmetry of the 2D state, but should be present after the disentangling reduction. If the symmetry is absent, γ decays exponentially in L with a characteristic length, termed as a replica correlation length, which can be arbitrarily large compared to the two-point correlation length of the 2D state. We propose a simple numerical procedure to measure the replica correlation length through replica correlation functions. We also calculate the replica correlation functions for representative wave functions of Abelian discrete gauge theories and the double semion theory in 2D, to show that they decay abruptly to zero. This supports a conjecture that the replica correlation length being small implies that the subleading term from the extrapolation method determines the total quantum dimension.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1987

Uncertainty relations for light waves and the concept of photons

A Lorentz-covariant localization for light waves is presented. The unitary representation for the electromagnetic four-potential is constructed for a monochromatic light wave. A model for covariant superposition is constructed for light waves with different frequencies. It is therefore possible to construct a wave function for light waves carrying a covariant probability interpretation. It is shown that the time-energy uncertainty relation (Delta-t)(Delta-omega) = about 1 for light waves is a Lorentz-invariant relation. The connection between photons and localized light waves is examined critically.

Han, D.↗